HELP PLEASE! 66pts!
Solve for x. SHOW WORK!
2^(3x+1)=1/4

Answer: Par affluence

Step-by-step explanation: Car chaque 3 min le nombre de client augmentera

The derivative of tan(cos(t) with respect to t at t= (π/2) is 1.

The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given expression is tan(cos(t)). The derivation will be done as below,

[tex]\dfrac{d}{dx}tan(cos(t))=sec^2(cos(t)\dfrac{d}{dx}(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(t)sec^2(cos(t)\\\dfrac{d}{dx}tan(cos(t))=-sin(\dfrac{\pi}{2} )sec^2(cos\dfrac{\pi}{2})\\\\\dfrac{d}{dx}tan(cos(t))=sec^2(0)\\\dfrac{d}{dx}tan(cos(t))=1[/tex]

Therefore, the derivative of tan(cos(t) with respect to t at t= (π/2) is 1.

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a) At t = 0days : 300insects

b) The growth rate is 5.12% each day.

c) Population after 10days: P(10) =494.61

d) The population to reach 420 is equals roughly 70.129 hours

e) The insect population double in  t=6.020 days , which is 144.48 hours.

What is Population?

Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.

Given: t in days, P(t)=300e(0.05t).

(a) The total number of insects at time t=0 days is equal to

P(0)=300(1)

P(0) =300.

(b) The growth rate is calculated as the percentage increase over time, which is equal to-

P(t+1)/P(t)=300e(0.05(t+1))/300e(0.05t)

P(t+1)/P(t) =e^(0.05(1))

P(t+1)/P(t) =1.0512

Therefore, the growth rate is 5.12% each day.

(c) Population after 10 days.

P(10)=300e^(0.05*10)

P(10) =300(1.6487)

P(10) =494.61

(d) When P(t)=420, the population will reach 420,

or 300e0.05t=420,

take log

0.05t=log(1.4), or

t = 2.922 days,

for the population to reach 420.

equals roughly 70.129 hours

(e) When P(t)=2*300=600 the population will double.

300e^(0.05t)=600

=> e^(0.05t)=600/300=2

Take log

(log 0.05t=log(2)),

t=6.020 days , which is 144.48 hours.

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The simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

Let us solve the given algebraic expression by the long division method:

We are given the expression:

(2x^3 + 3x + 7) / (x^2 + x + 10)

We need to perform the division of the given algebraic expression:

x^2 + x + 10  ) 2x^3 + 3x + 7 ( 2x - 2

                       2x^3 + 2x^2 + 20x

                     -         -            -        

                         -2x^2 - 17x + 7

                         -2x^2 - 2x  - 20

                         +        +       +          

                                  -15x + 27

So,

quotient = 2x - 2

remainder =  -15x + 27

Thus, the simplified value of the given expression (2x^3 + 3x + 7) / (x^2 + x + 10) is: the quotient will be 2x - 2 and the remainder will be -15x + 27.

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Answer: The sum is 55/28.

Alternate Answer: 1 27/28

Step-by-step explanation:

In this equation, the common denominator between the three fractions would be twenty eight.

5/7 converts to 20/28

1/2 converts to 14/28

3/4 converts to 21/28

After adding all the new fractions together, you get 55/28.

In this backgammon game, the probability used is Classical one.

Probability:

Probability refer the possible way of happening the particular event.

Given,

Virginia want to know how likely it is for her to win a backgammon game if she only needs to roll a double six to win.

Here we need to identify whether the given probability is empirical or classical.

In order to find the type of probability, first we have to know the definition of each of them.

So, classical probability means the the statistical concept that measures the likelihood (probability) of something happening where as the empirical probability means the  probability that is based on historical data.

Therefore, based on the definition, the given situation is purely based on the classical probability.

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Answer:

heyyy

Step-by-step explanation:

Answer:

It is a binomial, so it is (ax+b)^2. In this case, a=3, b=-8, and there are 2 terms. The constant is 64 and the leading coefficient is 9.

The height of the triangle pictured in the question is 2 units.

According to the question,

We have the following information:

Area of triangle = 8

Base of triangle = 8

We know that the following formula is used to find the area of triangle:

Area of triangle = 1/2*base*height

Area of triangle = 1/2*8*height

8 = 4*height

Dividing by 4 on both the sides:

Height = 8/4

Height of the triangle = 2 units

(Note that every physical quantity has some units of measurements. For example, the unit of measurement of area is square units.)

Hence, the height of the triangle pictured in the question is 2 units.

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Answer: -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4096)ˣ  = 8

log ₂ (4096)ˣ = log ₂ 8

x·log ₂ (4096) = log ₂ 8

x = log ₂ 8 / log ₂ (4096)

x = log ₂ 2³ / log ₂ 2¹²

x = 3 / 12

x = 1 / 4

Answer:

29.16% is spent

you have to divide 350 by 1200 then multiply by 100 then the answer will come

The measures, using the binomial distribution, are given as follows:

a) Probability that exactly six arrive within two days: 0.735 = 73.5%.

b) Probability that exactly five arrive within two days: 0.232 = 23.2%.

c) Mean: 5.7 letters.

d) Variance: 0.285 letters².

e) Standard deviation: 0.534 letters.

The mass function, formula for the probability of x successes, is defined as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters of the mass function are listed as follows:

Hence, in the context of this problem, the values of these parameters are given as follows:

n = 6, p = 0.95.

The probability that all six arrive within two days is of:

P(X = 6) = 0.95^6 = 0.735 = 73.5%.

The probability that five arrive within two days is:

P(X = 5) = 6 x 0.95^5 x 0.05 = 0.232 = 23.2%.

The statistical measures are calculated as follows:

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Answer:

1-3+2-5+-1-11

Step-by-step explanation:

I hope this helps :’)

The amount of money Samantha would have in the account 18 years after her initial investment is $2406.61

The principal amount = $1000

The interest rate = 5%

Time period = 18 years

The interest is compounded annually

The compound interest

A = [tex]P(1+\frac{r}{n})^{nt}[/tex]

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

n is the number of times the interest applied

A = [tex]1000(1+0.05)^{18}[/tex]

A = 1000 × 2.40661

Multiply the terms

A = $2406.61

Hence, the amount of money Samantha would have in the account 18 years after her initial investment is $2406.61

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The expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f, so option A is correct.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

The total no of french fries = 68,

The no of friends = f,

The no of french fries given to each friend = 13

The equation according to the question is given as,

The french fries left = The total no of french fries - The no of french fries given to each friend × The no of friends

Substitute the values,

The french fries left = 68 - 13 × f

Therefore, the expression shows how many french fries he had left after giving some to his friends is 68 - 13 × f.

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To answer this question we will use The Linear Programming concept

The formula for the moose population is

The moose population in 2006 would be

We use the year 1990 as the base year for creating the equation of the moose population. We could assume that:

The moose population of the year: P(x)

The moose population in year 1990: a

The year difference to 1990: x

The linear change of the moose population: b

Hence, we could make some assumption about the relationship between each elements mentioned above, where the moose population of the year would be depends on the linear change of the population added into the original moose population in year 1990. We could write this relationship into the equation (i):

P(x) = a + bx ... (i)

Using data provided from the question, we could make some other equations and find the value of b:

P(x) = a + bx

P(4) = a + 4b = 3280 ---> year 1994 ... (ii)

P(7) = a + 7b = 4120 ---> year 1997 ... (iii)

We could do some eliminations between equations (ii) and (iii)

3280 = a + 4b

4120 = a + 7b -

840 = 3b

b = 280 ... (iv)

After finding the value of b, we could subtitute its value into equation (ii) to find the value of a:

3280 = a + 4b

3280 = a + 4(280)

3280 = a + 1120

a = 2160 ... (v)

After finding the value of a and b, we could rewrite the equation (i) by inserting the and b values.

P(x) = a + bx

P(x) = 2160 + 280x ... (vi)

Next, we will predict the moose population to be in 2006.

First, we should determine the value of x, the difference between the year 2006 to the base year 1990.

x = 2006 - 1990

x = 16 ... (vii)

We would subtitute the equation (vii) into equation (vi) to predict the moose population to be in 2006:

P(16) = 2160 + 280(16)

P(16) = 6640...(viii)

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Answer:

C

Step-by-step explanation:

1000*0.04 = 40

(9/12) * 40 = 30

Answer:

Mai made 7 batches of pink paint.

Mai used 49 cups of white paint.

Step-by-step explanation:

Part 1. Every 2 cups of red paint are 1 batch of pink paint. This means to find the number of batches of pink paint Mai made, we need to divide 14/2. 14/2 = 7. This means she made 7 batches of pink paint.

Part 2. For every 2 cups of red paint, there are 7 cups of white paint.

For every 1 cup of red paint, there are 3.5 cups of white paint.

This means that we need to multiply 14 x 3.5.

14 x 3.5 = 49.

This means she used 49 cups of white paint.

Answer: 59.28

Step-by-step explanation:

your welcome :)

Answer:

x = 130

Step-by-step explanation:

x - 37 = 93 ( add 37 to both sides )

x = 130

Answer:

x=130

Step-by-step explanation:

x-37=93

x=93+37

x=130

x-37=93

-37-93= x (- / - =+ )

130=x

So, your answer is 130

According to the concept of quadratic equation, the minimum cost for the x ray machine is $17, 484

Quadratic equation:

Basically, the polynomial equation with highest degree of two is called a quadratic equation.

The general equation is given by ax² + bx + c = 0, where a ≠ 0.

Given,

A medical equipment industry manufactures X-ray machines. The unit cost C (the cost in dollars to make each X-ray machine) depends on the number of machines made. If .x machines are made, then the unit cost is given by the function C (x)=0.5x²-320x+68,684.

Here we need to find the minimum unit cost.

Here we know that the standard form of a quadratic is given by:

=> ax² + bx + c

From this function, we have to calculate the value of x as,

=> x = -b/ 2a

While we compare the standard form with the given function,

=> C (x)=0.5x²-320x+68,684.

Then we get the value of

=> a = 0.5

=> b = -320

=> c = 68,684

So, the value of x is calculated as,

=> x = -(-320) / 2(0.5)

=> x = 320 / 1

=> x = 1

Now, we have to plug this value into original function would give us the minimum (unit cost):

=> C(320) = 0.5(320)²- 320 (320) + 68,684.

=> C(320) = 0.5(102400) - 102400 + 68, 684

=> C(320) = 51200 - 102400 + 68684

=> C(320) = 17, 484

Therefore, the minimum unit cost is $17, 484

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The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.

To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:

The function for this problem is defined as follows:

y = 1.5x² + 4x - 2.

Hence the numeric values of the coefficients are listed as follows:

a = 1.5, b = 4, c = -2.

Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:

The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).

The x-coordinate of the vertex is given as follows:

x = -b/2a = -4/3 = -1.33.

Hence the y-coordinate of the vertex is of:

y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.

The problem asks for the graph of the following function:

y = 1.5x² + 4x - 2.

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The value of h in the given polygon is 34.8°

A polygon is a two-dimensional geometric figure that has a finite number of sides. The sides or edges of a polygon are made of straight line segments connected end to end to form a closed shape. The point where two line segments meet is called vertex or corners, and subsequently, an angle is formed. If a polygon contains congruent sides, then that is called a regular polygon.

The sum of the interior angles of a regular polygon = (n - 2) x 180

where n = number of sides of the polygon

here n = 20

Sum of the interior angle = (20 - 2) x 180

Sum of the interior angle = 3240°

which also means that 20(5h - 12) = 3240

100h -240 = 3240

100h = 3240+240

100h = 3480

h = 3480/100

h = 34.8°

In conclusion, the value of h = 34.8°

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in this situation Zero represents, The surface of the water

-4 represents the sand that lies under 4 feet of water.

4 represents a branch 4 feet above the water.

Upon analysis, it can be said that as we move downwards, the value increases in negative sign

As we move upwards, the value increases in positive sign

The surface of water becomes the origin, as it is zero.

Therefore, , in this situation Zero represents, The surface of the water

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The equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

According to the question,

We have the following information:

Point through which line is passing = (1/3,4)

Slope of the line = 0

We know that the following formula is used to find the equation of the line passing through a point:

y-y' = m(x-x')

We have x' = 1/3 and y' = 4.

y-4 = 0(x-1/3)

y-4 = 0

Adding 4 on both sides of the equation:

y = 4

Hence, the equation of the line that passes through the point P(1/3,4) and has no slope is y = 4.

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He needs 10 litres of solution of 40% and 20 litres of 70% solution to make 30 litres of 60% acid solution.

According to the question,

We have the following information:

Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution.

Now, let's take x litres of 40% solution and y litres of 70% solution.

So, we have the following expressions:

x+y = 30

x = 30-y ....(1)

40x/100 + 70y/100 = 30*60/100

Dividing 100 on the numerator by 100 on denominator:

40x+70y = 1800

Dividing both sides by 10:

4x+7y = 180

Putting the value of x from equation 1:

4(30-y)+7y = 180

120-4y+7y = 180

120+3y = 180

Subtracting 120 from both the sides:

3y = 180-120

3y = 60

y = 60/3

y = 20

Now, putting this value of y in equation 1:

x = 30-y

x = 30-20

x = 10

Hence, he needs 10 litres of 40% solution and 20 litres of 70% solution to make 30 litres of 60% acid solution.

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Answer:

one ninths

Step-by-step explanation:

1/3-2/9 - fraction calculator. The result is 1/9 ≅ 0.1111111 = one ninth.