Finding the time given an exponential function with base e that models a real-world situation

802/198​ is equal to 4.0505

Answer:

-22

Step-by-step explanation:

Hello!

We can convert it into Slope-Intercept form: [tex]y = mx + b[/tex]

The y-intercept is -22.

Given:

Solve the expression,

Answer: n = 180

Answer:

√52

Step-by-step explanation:

[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]

[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]

Given:

a. The amount of flour that the bakery used this month was a 50% increase relative to last month.

So, we will draw a diagram that represents the situation

As shown, for last month, we have drawn a rectangle divided into two equal areas, each one represents 50%

this month was a 50% increase, so, we have drawn 3 areas which represent 50% increase

b. The amount of milk that the bakery used this month was a 75% decrease relative to last month.

As shown, for last month, we have drawn a rectangle with four equal areas

75% decrease, so, we have to remove 3 areas to make the remaining = 25%

So, the difference will give a 75% decrease

 Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.

Polynomial equation illustration

     Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

6h²(5 + 9h)(5 - 9h)

6h²(9h + 5)(5 - 9h)

6h²(9h + 5)(-9h + 5)

6h²(9h + 5)(-9h + 5)

54(-9h +5)h³ + 30(-9h + 5)h²

(-486h)4 + 270h³+30(-9h+5)h²

(-486h)4 + 270h³-270h³+150h²

(-486h)4 + 150h²

(-486h)4 + 150h²

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Given

Series of numbers

first day = 4

second day = 8

Third day = 16

4, 8, 16, ...

From the exponential sequence

First term a = 4

common ratio r = second term/first term

= 8/4 = 2

r = 2

answer: D. x = 4

We need to calculate 1/5 + 1/2:

H = 1/5 + 1/2

Then: H = 7/10

To answer this question, we need to remember the rules of transformations of functions, the rules are shown below:

From the table, we notice that if we subtract a number we are performing a vertical translation down.

Therefore, the correct word to fill the blank is down and the correct option is C.

ANSWER:

5

STEP-BY-STEP EXPLANATION:

We have the following expression:

We substitute the value of w, when it is equal to 3, just like this:

The value of the expression is equal to 5

Using combinations, the number of ways is 36,036.

How many distinct orders of light bulbs are there?

So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.

Therefore, using combinations, the number of ways is 36,036.

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Remember that the control variable does not change in the experiment or in any study.

So the control here will be all the plants because you can not control the type of the plant.

Answer:b

Step-by-step explanation:

Answer:

i also don't know

Step-by-step explanation:

i also don't know..,......

The height of the ball was 182.25 feet and it took 6 seconds for the ball to hot the ground.

Given that:-

Quadratic equation:-

[tex]h(t)=-16t^2+84t+72[/tex]

We have to find the ball's height, in feet and how many seconds it takes to hit the ground.

Differentiating the given equation, we get

dh/dt=-32t + 84

Putting dh/dt = 0, we get,

-32t + 84 = 0

t = 84/32 = 21/8 seconds

Putting t = 21/8, we will get the maximum height that the ball will reach.

Hence,

[tex]h(21/8)=-16(21/8)^2+84(21/8)+72[/tex]

h(21/8) = -16(441/64)+84(21/8)+72 = -110.25 + 220.50 +72 = 182.25 feet

At h = 0, the ball will have hit the ground.

Hence, we can write,

[tex]h(t) = 0 = -16t^2+84t+72[/tex]

Dividing -4 from the equation, we get,

[tex]4t^2-21t-18=0[/tex]

Using middle term split theorem, we can write,

[tex]4t^2-24t+3t-18=0\\[/tex]

4t(t-6)+3(t-6) = 0

(t-6)(4t+3) = 0

Hence, the values of t can be:-

t = 6, -3/4

As the time cannot be negative, hence the ball will hit the ground after 6 seconds.

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we have the system

y < -2x^2+4x-2

The solution for this inequality is the shaded area below the vertical dashed parabola

and

the solution for this inequality is the shaded area above the solid line y=(2/3)x-3

therefore

the solution for this system of inequalities

Is the shaded area below the vertical dashed parabola y=-2x^2+4x-2 and above the solid line y=(2/3)x-3

see the attached figure to better understand the problem

We have that a loaf of sandwich bread contains 24 slices, then we have that the ratio must be constant between the loaves and the slices. If we have 1 loaf: 24 slices, this ratio must be equal in the table.

Therefore, we have that the only table that follows this is the table that has:

If we have:

2/48 = 1/24

3/72 = 1/24

4/96 = 1/24

The ratio of loaves to slices is the same, that is, 1 / 24.

Answer:

2 hours

Explanation:

The first bicyclist rides at a speed of 8 mph. Therefore:

One hour later, the second bicyclist leaves and rides at a speed of 12 mph.

Therefore, the time of the second bicyclist = (t-1) hours.

Therefore:

Since the second bicyclist will catch up to the first bicyclist, the distance traveled will be the same.

So:

Therefore, the second bicyclist will have traveled for:

(t-1) = (3-1) =2 hours.

Answer:

None are solutions.

Step-by-step explanation:

Divide each value of y by 2 and see if it equals 6. If it does, then it is a solution. If it doesn't then it isn't a solution.

6 ÷ 2 = 6

3 ≠ 6

not a solution

16 ÷ 2 = 6

8 ≠ 6

not a solution

10 ÷ 2 = 6

5 ≠ 6

not a solution

14 ÷ 2 = 6

7 ≠ 6

not a solution

In a x-y coordinate plane of you moves to the right it increase the value of x and if you moves vertically it increases the value of y.

The ordered pair is (x,y)

The given system of equations are

y=-3x/2 + 6

y=5x - 7

We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.

For the first equation,

y = - 3x/2 + 6

if x = 0, y = 3 * 0/2 + 6 = 6

If x = 1, y = - 3 * 1/2 + 6 = 4.5

if x = 2, y = - 3 * 2/2 + 6 = 3

We would plot these values on the graph

For the second equation,

y = 5x - 7

if x = 0, y = 5 * 0 - 7 = - 7

If x = 1, y = 5 * 1 - 7 = - 2

if x = 2, y = 5 * 2 - 7 = 3

We would plot these values on the graph

The diagram of the graph is shown below

Looking at the graph, at the point where both lines meet,

x = 2, y = 3

Thus, the solution is (2,3)

Given:

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.

Required:

To write an inequality to find the three numbers and to solve the inequality.

Explanation:

(a)

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.

(b)

Problem

Solution

We have the following sequence of terms 34,25,16,7,....

Part a

The common difference for this case would be:

25-34= -9

16-25=-9

7-16= -9

Then the answer for part a would be -9

Part b

We want to write the following form:

an = a1 + (n-1) d

For this case d=-9, a1= 34

And then we can write the genral expression like this:

an = 34 + (n-1 ) (-9)

With n = 1,2,3,4....

Part c

In order to find the 20 th term we can replace n =20 and we got:

a20= 34 + (20-1) (-9) = 34-171= -137

Answer:47

Step-by-step explanation: First multiply 3x8=24 then subtract 3x4=12 from it. Which will get you 12 then add 35 to 12 which will get you 47.

35 + 3(8-4) = ?

Do the parentheses first : 8 - 4 = 4

= 35 + 3(4)

Then multiply- that's the one that is in parentheses : 3 x 4 = 12

= 35 + 12

Then just straight up add : 35 + 12 = 47

35 + 3(8-4) = 47

So ? = 47

First, remember that:

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this problem, notice that:

2 + 3 is not greater than 5.

3 + 5 is not greater than 2.

2 + 5 is not greater than 3.

So, the statement is false. A triangle can't have sides 2

Answer

Explanation

Given:

You flip a coin 3 times.

To determine the tree diagram to see all of the possible outcomes when you flip a coin 3 times, we first note that we can get either Heads or Tails. So the tree diagrams is shown below:

The possible outcomes would be:

HHH, HHT,HTH,HTT,THH,THT,TTH,TTT

We can notice that there are 8 possible outcomes. But, the number of cases to get exactly 3 heads is just 1.

Hence, the probability of getting 3 heads is:

Probability = 1/8 =0.125

Therefore, the probability that you flip a heads all 3 times is 0.125.

Answer

Check Explanation

Explanation

Before we start answering, we should first explain what these terms stand for

- Domain

The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.

- x-intercept

The x-intercept refers to the value of x when the value of y or f(x) = 0, that is, the value of x at which the graph of the function crosses the x-axis. To obtain this, we just solve for x when y or f(x) = 0

- y-intercept

The y-intercept refers to the value of y or f(x) when the value of x = 0, that is, the value of y when it crosses the y-axis. To obtain this, we just substitute 0 for x and solve for f(x)

We can now solve

- For the domain, we can tell that x can take on any real number value and provide an answer for f(x) except the point where the denominator of this is equal to 0. At the point where the denominator is 0, f(x) will tend to infinity.

2x + 4 = 0

2x = -4

Divide both sides by 2

(2x/2) = (-4/2)

x = -2

So, the domain of this function is all real number values for x except x = -2

- For the x-intercept, we just solve for x when f(x) = 0

The x-intercept = 4.

In coordinate form, the x-intercept is (4, 0)

- For the y-intercept, we just solve for f(x) when x = 0

The y-intercept = -3

In coordinate form, the y-intercept is (0, -3)

For the second question

- The domain will be all real number values of x except when (x - 3) = 0

x - 3 = 0

x = 3

The domain will be all real number values of x except when x = 3.

- For the x-intercept, we just solve for x when f(x) = 0

The x-intercept = -4.5

In coordinate form, the x-intercept = (-4.5, 0)

- For the y-intercept, we solve for f(x) when x = 0

The y-intercept = -3

In coordinate form, the y-intercept is (0, -3)

For the third question

- For the domain, we first solve for when x² - 9 = 0

x² - 9 = 0

x² = 9

x = ±√9

x = ±3

x = +3 or -3

The domain of this function is all real number values of x except when x = +3 and x = -3

- For the x-intercept, we solve for x when f(x) = 0

The x-intercepts are at -4 and +4.

In coordinate form, the x-intercept are (-4, 0) and (4, 0)

- For the y-intercept, we solve for f(x) when x = 0

The y-intercept = (16/9) = 1.7778

In coordinate form, the y-intercept is (0, 1.7778)

Hope this Helps!!!

This is a problem based on permutations. We must select four jobs among ten jobs and see how many arrangments can be made.

The formula for the number of permutations is:

Where:

• n = total number of jobs = 10,

• r = number of jobs to be selected = 4.

Replacing these data in the formula above, we get:

5040

Given

x = 0.5; y = 0.8

The constant of proportionality has to be calculated to estimate the other values.

The constant of proportionality "k" determines the relation of x and y, which can be represented as: y = kx.

So, in this exercise,

y = 1.6y

(1) From this, we can estimate the value of y when x = 3.

(2) If we want how long it will take to fill the tank with 40 gallons:

It will take 25 minutes.

(3) Finally, the constant of proportionality is 1.6 (as calculated above).

It tells us that the ratio between the gallons water of water and time. In other words, it tells us that for each 1 minute, 1.6 gallons are filled.

To solve for x, first, we add 4y to the equation:

Now, we divide by 3:

Answer: