hi! I have the answers to A. AND B. which are k=1.243% for a and k= 0.20% for bWhere y is the population after t time, A is the initial population and k is the growth constant.Therefore, for each case, we calculate the value of k:(a)t = 4y = 1375000A = 1309000Solving for k:1375000=1309000⋅ek⋅4e4k=137500013090004k=ln(13750001309000)k=ln(13750001309000)4k=0.01229≅0.0123→1.23%(b)t = 4y = 1386000A = 1375000Solving for k:1386000=1375000⋅ek⋅4e4k=138600013750004k=ln(13860001375000)k=ln(13860001375000)4k=0.00199≅0.002→0.20%(c)To compare we calculate the quotient between both periods:

LK = 2.91m

JK = 7.99m

hypotenuse = 8.5m

angle = 20°

LK = side opposite the angle 20°

Since we know the hypotenuse and we need to find the opposite, we would apply sine ratio

sine ratio = opposite/hypotenuse

sin 20° = LK/8.5

LK = 8.5(sin 20°)

LK = 8.5(0.3420)

LK = 2.907

To the nearest hundredth, LK = 2.91m

JK = base = adjacent

We would apply cosine ratio

cos 20° = adjacent/hypotenuse

cos 20° = JK/8.5

JK = 8.5(cos20°)

JK = 8.5(0.9397)

JK = 7.98745

To the nearest hundredth, JK = 7.99m

EXPLANATION

The coordinate son the plane when x=-3 are y=9 ---> A= (-3,9)

The points on the parabola when y= 16 are x=4 ---> (x_1,y_1) = (4,16) and (x_2,y_2) = (-4,16)

Before we calculate the perpendicular line, let's rewrite our line equation in slope-intercept form. The slope-intercept form is

Where m represents the slope and b the y-intercept.

Rewritting our equation, we have

This means the slope of our line is equal to - 3.

Two perpendicular lines are related by their slope. Let's say two lines are perpendicular, this means the slope of one of the lines is equal to minus the inverse the slope of the other. If we call the slope of one of those lines as m_1, the slope of the perpendicular line m_2 is given by

Using this relation, we can find the slope of a perpendicular line. Since the slope of our line is equal to - 3, then, the slope of the perpendicular line is

In slope-intercept form, our perpendicular line has the following form

To find our y-intercept, we can use our given point that belongs to this line.

The point is (-3, 1), evaluating this point in our equation, we have

Then, our line is

The are of the octsagon is given by:

where a is the lenght of its side.

Since the second octagon has sile lengths equal to 18.03, its area is:

Therefore the area is 1563.6 squared centimeters

Given that the birth alternates between a boy and a girl, there are 2 options which are as follows.

Let

G = Girls

B = boys

Therefore,

The probability that the youngest will be a boy in this scenario will be

The inverse of cubing a number is applying cubic root

Now, let's go through the examples:

When you want to find the square root of a number x you have to ask yourself:

Which number, when multiplied by itself, will give me x ?

For example,

Because

This way,

Now for the cubic root:

When you want to find the cubic root of a number y you have to ask yourself:

Which number, when multiplied by itself two times, will give me y ?

For instance,

Because

Therefore,

The initial equation is:

so we can move all term with x to the left and the constants to the right so:

Now we divide by 8 bout side of the equation so:

Given: 0.6 divided by 30

We will find the result as follows:

So, the answer will be 0.02

To start, we need write the polynomials:

Now we gonna find the difference between first polynomial and second, like this:

tip: Special care with operate signs.

That is the final solution, you can solve that polynomial if you need.

Answer:

Explanation:

Using the graph of both equations, we want to get the correct option

We start by making a plot of the two on same axes

We have the plot of the functions as follows:

Now, let us take a look at the options:

a) This is wrong. The functions have two intersection points

b) This is incorrect. They have equal y-intercepts at y = 2

c) This is correct. The quadratic function have a greater maximum

To answer this question, we need to find, first of all, the corresponding probability for the events. Then, we have:

1. The probability of an even number is:

We have that in a single 6-sided die, we have that the only even numbers are 2, 4, and 6. If we roll the die one time, then the probability of this event is:

2. The probability of resulting 1 or 3 is - if the die is rolled one time:

3. The probability of resulting in a 5 is - if the die is rolled one time:

Then, if we add all the corresponding probabilities we have:

To find the expected value of the game, we have to find the product of the probability by the corresponding amount of money of the event as follows:

Or

If we round the answer in terms of dollars rounded to the nearest cent (hundredth), we have that the expected value is:

In other words, if we play the game, we will expect to lose 83 cents of a dollar (per game) or 0.83 dollars.

In summary, we have that the expected value of the game is -$0.83.

Solution:

Given:

From the table, the probability that Michiko will hava a quiz on Wednesday is 0.070.

This is the probability of success.

Hence, the probability that Michiko will not have a quiz on Wednesday is the probability of failure.

Thus,

Hence, the probability of failure (the probability that Michiko will not have a quiz on Wednesday is 0.93.

As a percent,

Therefore, the probability that Michiko will not have a quiz on Wednesday is 93%

ANSWER:

911.6 ft

EXPLANATION:

Given:

To find:

The distance between the two ships

Let's go ahead and draw a sketch as seen below;

Let's go ahead and solve for the value of AC by taking the tangent of angle 12.5 degrees as seen below;

Let's now solve for the value of AD by taking the tangent of angle 8 degrees as seen below;

Therefore the distance between the two ships will be;

So the two ships are 911.6 ft

the initial function is:

now we replace the values in x that gives the table so:

for -2:

for 0:

for 2:

for 4:

ANSWER is hands lens.

This is the best tool to see the animal up close.

We have the following inequality:

x > - 0.75

This is the same as state "x is greater than -0.75". Therefore, any value greater than -0.75 is a solution to this inequality

Considering this rule, we can answer each item:

a) The statement "-0.75 is a solution to the inequality" is FALSE, because, or rule states that x must be greater than -0.75.

b) The statement "There are many solutions to this inequality" is TRUE. Actually, there is an infinite number of solutions to this inequality (some of them can be expressed by -0.74, -0.73, -0.72...)

c) The statement "All the solutions to the inequality are negative" is FALSE, since any positive (or null) number is also greater than -0.75.

d) The statement "The inequality -0.75 < x is equivalent to the given inequality" is TRUE, since this inequality is tha same as the statement "-0.75 is less than x", which is a different form of express the original statement "x is greater than -0.75".

e) The statement "-4.5 is a solution to the inequality" is FALSE, because -4.5 is less than -0.75, which contradicts or rule.

Using the function  f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg

The salinity s calculated using the logarithmic function model

f(x) = 28.7 + 1.2log (x + 1)

given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters

for x = 797 meters

f(x) = 28.7 + 1.2log (x + 1)

f(x) = 28.7 + 1.2log (797 + 1)

f(x) = 28.7 + 1.2log (798)

f(x) = 28.7 + 1.2 * 2.902

f(x) = 28.7 + 3.4824

f(x) = 32.1824

f(x) = 32.18  (to the nearest hundredth)

Learn more about logarithm here:

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The required value of the x is given as 8.66 for the given triangle.

Given that,
A figure of the triangle is shown, with the help of trigonometric operators we have to determine x.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

Here,
Tan60 = x/ 5
x = tan60 × 5
x = 1.732 × 5
x = 8.66

Thus, the required value of the x is given as 8.66 for the given triangle.

Learn more about trigonometry equations here:

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Answer:

Subtract 4

Explanation:

In the number pattern:

We subtract the next term from the previous term below:

We see that each one gives a subtraction of 4.

Therefore, the rule of the pattern is 'Subtract 4'.

The cost function is,

The cost of 15 ounce container is,

Thus, option (A) is the correct solution.

Part A)

2.7 --- 60%

Therefore in order to know what is the 100% we will do the next operation

2.7 is 60% of 4.5

Part B)

4.2 --- 10%

In order to know the 100% we will do the next operation

4.2 is 10% of 42

Part C)

58 --- 100%

214.6 --- ?

214.6 is 370% of 58

The following information below can be obtained from the image;

Blue Marbles: 6

Red Marbles: 5

Yellow Marbles: 3

Total marbles = 14

The probability of an event, E, is given as:

Hence, the number that belongs in the green box is 3

Given: A high school teacher grades a math test. She wants to see the numerical grade of each student.

Required: To identify which item the teacher should use so she can quickly see

how many students got each score.

Explanation: A line plot is a plot that shows the frequency of data along a number line as shown in the figure below-

ANSWER

0.1069

EXPLANATION

We have two possible outcomes for each experiment: the seed grows or the seed does not grow. So, this follows a binomial distribution, where, in this case, the probability of success is the probability that a seed does not grow - note that we want to find what is the probability that a number of seeds do not grow.

We know that the probability that a seed grows is 85%, so there is a 15% chance the seed does not grow. This experiment is repeated 9 times (9 seeds) and we want to find what is the probability that the number of successes is 3 - remember that "success" is that the seed doesn't grow.

To find this, we have to use the binomial probability formula,

For this problem:

• n = 9

• x = 3

• p = 0.15

• q = 0.85

So we have,

Hence, the probability that exactly 3 seeds don't grow is 0.1069, rounded to four decimal places.

EXPLANATION

Given the system of equations:

(1) 60x + 110y = 265

(2) 120x + 90y = 270

We can apply the substraction method as shown as follows:

Multiply 60x + 110y = 265 by 2:

----> (60x + 110y = 265)*2 -------> 120x + 220y = 530

Subtract the equations:

120x + 220y = 530

- (120x + 90y = 270)

--------------------------------

130y = 260

Divide both sides by 130:

y= 260/130

Simplifying:

y= 2

Replacing on the first equation:

60x + 110(2) = 265

Applying the distributive property:

60x + 220 = 265

Subtracting 220 to both sides:

60x = 265 - 220

Subtracting like terms:

60x = 45

Dividing both sides by 60:

x = 45/60

Simplifying:

x= 3/4

The solutions to the system of equations are:

x=3/4 y=2

Answer:15,970

Step-by-step explanation:

6The mean number of children each team member will bring

Here, we want to get the mean number of students that each team member willl bring

From the histogram, we can deduce the following;

a) 4 team members will bring no (0) children

b) 3 team members will bring 1 children each

c) 5 team members will bring 2 children each

d) 2 team members will bring 3 children each

e) 1 team member will bring 5 children

So the totla number of children at the party will be;

4(0) + 3(1) + 5(2) + 2(3) + 1(5)

= 0 + 3 + 10 + 6 + 5 = 24 children

The number of team members is 4 + 3 + 5+2 + 1 = 15

So, the mean number each will bring is; the number of children attending the party divided by the number of team members

Solution:

Given:

A regular pentagon rotated counterclockwise about its center.

To get the angle by which it rotated, we draw lines from each of the vertexes to the center to divide the pentagon into 5 equal triangles as shown;

The angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;

To get angle EOC, we use the property of the sum of angles at a point.

The sum of angles at a point is 360 degrees.

Since it is a regular polygon, each of these angles is equal.

Hence,

Thus, the measure of angle EOC is;

Therefore, the angle by which the pentagon is rotated through its center so that the vertex at E is moved to C is;

The slope is define as the rate of y coordinate with respect to the x coordinate.

In the line D which is parallel to x axis has the constant y coordinate i.e

y = -3

So, for the numerator of the slop for line D is ( -3) - ( -3) = 0

Thus the slope will be express as :

Thus the slope of line is 0

Now, for the line A :

The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.

i.e. x = -5

So, substitute the value in the expression for the slope :

Slope of line A is not define

In the line B and C, the coordinates of x and y aixs are changes countinously

thus thier slopes will be well define.

Answer : Slope of line A is not define.