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Question 1, 6.8.1
Part 1 of 5
The size P of a certain insect population at time t (in days). obeys the function P(t) = 300e0.05t
(a) Determine the number of insects at t=0 days.
(b) What is the growth rate of the insect population?
(c) What is the population after 10 days?
(d) When will the insect population reach 420?
(e) When will the insect population double?
(a) What is the number of insects at t=0 days?
0 insects
HW Score: 0%, 0 of 4 points
O Points: 0 of 1
**

Answer:

It looks just fine! Well done!

It looks just fine! Well done!A bit more simply,

It looks just fine! Well done!A bit more simply,(A+C)(AD+AD)+AC+C=(A+C)AD+AC+C=AAD+CAD+AC+C=AD+(AD+A+1)C=AD+C

Step-by-step explanation:

Hope this helped

Answer:

y = 2(x + 4)(x - 3)

Step-by-step explanation:

Knowing the x-intercepts, we can set up the equation:

y = (x + 4)(x - 3)

However, we are unaware of whether there is a dilation applied to it, so we input a point on the parabola. "a = dilation"

-12 = a(2 + 4)(2 - 3)

-12 = a(6)(-1)

-12 = -6a

2 = a

Now, we can write the equation for the parabola:

y = 2(x + 4)(x - 3)

These lines y = 12x + 1 and y = 2x + 4 intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Given are two equations y = 12x + 1 and y = 2x + 4.

Now by graphing we conclude that these lines intersect at only one point, therefore, this system of equations has a unique solution and also one real solution.

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The five consecutive odd integers are 11, 13, 15, 17 and 19.

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Odd numbers are whole numbers that cannot be divided exactly into pairs.

Therefore, odd integers are integers that cannot be divided exactly into pairs.

Hence, let's find five consecutive odd integers if the sum of the first three integer is 3 more than the sum of the last 2.

let

the first odd integer = x

x + x + 2 + x + 4 = x + 6 + x + 8 + 3

3x + 6 = 2x + 17

3x - 2x = 17 - 6

x = 11

Therefore, the consecutive odd integers are 11, 13, 15, 17 and 19.

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The expressions which have only one constant are:

A. 18+5r³

B. 90(h-4)

Given: we have a set of equations.

an equation is  a combination of variables and constants.

In the given set of equations we have a single variable with a single constant.

those are:

→ 18+5r³

→  90(h-4)

In the other equations we don't have constants.

A constant is defined as an object whose value is fixed regardless of changes in its usage.

Even after the expression is changed, these values stay the same.

Natural numbers, whole numbers, real numbers, integers, and decimal numbers are examples of constants in mathematics.

A variable is a thing whose value changes depending on how it's used and isn't fixed.

Hence we get the required answer.

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Answer: 8÷2 or 8/2 and also just in case, the answer is 4

Step-by-step explanation: Ok, 8 markers split equally between 2 students, this means that for each marker that student one takes, student two also takes one. they repeat this until there are no more markers left. This ends up with the two students each having four markers. Now, what is 8 divided by 2? Why yes, the answer is 4, just like the word problems answer. So the word problem "Two students share 8 markers equally" translates to 8÷2.

Hope this helps!

Answer:

25.12

Step-by-step explanation:

C = [tex]\pi[/tex]d  The d is the diameter.  This is the distance across the ha that goes through  the middle of the circle.

C 3.14(8)  The c stands for the circumference or the distance around the circle.  We generally use 3.14 for [tex]\pi[/tex]

C= 25.12

Answer:

(x,y)=(0,4)

Step-by-step explanation:

write as systems as equations, multiply both sides of the equation by -1, sum the equations vertically to eliminate at least one variable, divide both sides of the equation by -19, substitute the given value of x into the equation 5x+y=4, The possible solution of the system is the ordered pairs (x,y) =(0,4), then you're done. whew. ;)

5x - 3x = 2x

2x = 40

x = 20

x * 8 = 160

Answer:

Step-by-step explanation:

a.

f(d)=11(1.01^d

d=6.97 days

b.

t

f(c) represents the size of algae after c days

c.

f(2)=11(1.01)^2

f(7)=11(1.01)^7

[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]

Answer:

1170 teenagers would have corrective devices

Step-by-step explanation:

hope this helps :)

The probability of getting a total that is a factor of 21 is 2/9

Tom rolls 2 fair dice and adds the results from each

Total number of outcomes = 6 × 6

= 36

The probability = Number  of favorable outcomes / Total number of outcomes

The factors of 21 = 1, 3, 7, 21

The possible outcomes = {(1,2), (2,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}

Number of possible outcomes = 8

The probability = Number  of favorable outcomes / Total number of outcomes

Substitute the values in the equation

= 8 / 36

= 2/9

Hence, the probability of getting a total that is a factor of 21 is 2/9

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The general form of a linear equation is slope m and y-intercept c is given as y = mx + c thus the slope of the line y = -2x + 4 is -2 so option (C) is correct.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given line,

y = -2x + 4

The general form of a linear equation is the slope(m) and y-intercept (c) is given as

y = mx + c

Compare,

m = -2 and c = 4

Slope = -2 and y-intercept = 4

Hence "The slope of the line y = -2x + 4 is -2 and y-intercept is 4".

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In the given equation we get the following values:

M = 2

C = 5

Given, we have the equation:

Y = 2x + 5

we are asked to determine the following values of m and c.

The given equation is in the form of slope intercept form.

slope intercept form is given as:

y = mx+c

hence :

M = 2 and

C = 5

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:

hence we get the required values.

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Answer:

you multiply the numbers to find the area so W*H with times hight so the answer would be 6,250

If a 40-foot rope is cut into 2 pieces.  the length of the longer rope piece x  is 23ft.

Seven less than 4 times = 4x-7

4x-7=5(40-x)

4x-7=200-5x

Collect like terms

9x=207

Divide both side by 9x

x = 207 /9

x=23 ft  (longer part of the rope)

Shorter part of the rope

40-x where x is 23

40 -23

= 17ft

Therefore the longer part is 23ft.

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In given order puzzle Aya's bag is the heaviest bag .

What is order puzzle?

 A puzzle is a thing that is difficult to understand or explain. The term also refers to a game, toy, or problem designed to test ingenuity or knowledge. Math puzzles are problems that require mathematical logic and calculation. These types of puzzles carry recreational as well as educational value for the pupils.

Here the given statements ,

=> Alex bag > Hisham bag

And Hisham bag < Aya bag and Irene bag

Now ,

=> Aya bag > Alex bag and Irene bag

Then combine the given ,

=> Aya bag> Alex bag>Irene bag>Hisham bag.

Therefore Aya's bag is the heaviest bag.

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The cost of covering the felt with glitter is $3,317.60.

The cost of the outdoor carpeting to cover the patio is $240.

The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

52 x 58 = 3,016 in²

Cost of covering the felt = cost of the glitter per feet  are of the felt

$1.10 x 3,016 = $3,317.60

A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

Area of a trapezoid =   1/2 x (19 + 13) x 10

Area of a trapezoid =  1/2 x 32 x 10 = 160 ft²

Cost of the outdoor carpeting =cost per square feet x area of the patio

$1.50 x 160 = $240

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Answer:

5.92

Step-by-step explanation:

Line in standard form

-6x + y - 7 = 0

distance = |-6 * 6 + 1 * 7 - 7|/([tex]\sqrt{(-6^2)+ 1^2)}[/tex]

|-36 +7 - 7| = √37

|-36|/√37

36/√37

5.918363 = 5.92

The slope equation form is :

m = - 7/5

Slope Solution

To calculate the slope use the slope formula.

m = (y2- y1)/(x2- x1)

Where (x1,y1) and (x2,y2) are 2 coordinate points.

Here the 2 points are (0,-3) and (-5,4)

let (x1,y1) = (0,-3) and (x2,y2) = (-5,4)

m = (4 - (-3))/((-5) - 0)

m = 7/((-5) )

m = - 7/5

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Answer:

Step-by-step explanation:

Hi,  Danna,  these are tough to figure out...

so,  first check to see if the 3 known angles add up to 180°,  they don't I checked, so, it tells us that the one angle 96° up at the top,  does not include ∠2 , which is good, b/c we now know 2 of the angles in that inner triangle.. and we know that a triangle adds up to 180° , so just find that last angle... the one opposite to ∠1 .... nice, if we get the ∠1' angle we can then also figure out ∠1

180-96-30=54

∠1' =54°

so ∠1= 180-54 =126°

we now know ∠1

use that , and that the next smaller triangle also adds up to 180

to find ∠2

∠2= 180-28-126=26°

∠1=126°

∠2 = 26°

:)  it's tough to think all of that through.  don't worry.  just keep working these , they will get easier.

Answer:

Estimation and Confidence Intervals

Step-by-step explanation:

Just found it on a math website basically.

After 5 years, Offer A will offer a higher total salary.

The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value.

The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values.

Given

a)  that a candidate receives job offers from two different companies, with Offer A offering a starting salary of $ 55,000 and a 5% increase for 5 years and Offer B offering a starting salary of $ 56,000 and an increase of $ 2,000 per year, it is necessary to perform the following calculation to determine which offer will result in a higher total income after 5 years:

b) Offer A -> Arithmetic

=>55000 x 1.05 ^ 5 = X

=>55000 x 1.2762 = X

70,195.48 = X

Offer B -> Geometric

=>56000 + (5 x 2000) = X

=>56000 + 10000 = X

66,000 = X

c) Hence comparing the above 2, Offer A will provide a greater total income after 5 years.

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The correct statement will be  "Neither ordered pair is a solution".

What are ordered pairs?

Given equation is:  6x = 14

For ordered pair (-9, 3) ,  the values of x=-9 and y=3

Plugging these values into the given equation

6(-9) = 14

-54 = 14 (False)

Now for ordered pair (2, -4) ,  the values of x=2 and y=-4

Plugging these values into the given equation

6(2) = 14

12 = 14 (False)

The correct statement will be  "Neither ordered pair is a solution".

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Using the multiplication, 192 unique keys will result from the distribution.

In the given question we have to find the number of unique keys will result from the distribution.

As given that a package contains 12 electrical locks, each with a unique key.  A package is delivered to 16 job site superintendents.

So 1 package have 12 electrical locks with a unique key.

Package delivered to 16 job site.

We can find the total number of unique keys y multiplying the total number of electrical locks with a unique key in a pckage to the total number of site of package delivery.

So total keys=12×16

Total keys=192

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Answer:

  y = -3x +7

Step-by-step explanation:

You want the equation of the median line through point A, given that the vertices of the triangle are A(2, 1), B(-2, 3) and C(4, 5).

The median will go through the midpoint of the segment opposite vertex A. That midpoint is ...

  D = (B +C)/2

  D = ((-2, 3) +(4, 5))/2 = (-2+4, 3+5)/2 = (2, 8)/2 = (1, 4)

The slope of the line is given by the slope formula:

  m = (y2 -y1)/(x2 -x1)

Then the slope of AD is ...

  m = (4 -1)/(1 -2) = 3/-1 = -3

The point-slope equation of the line with slope m through point (h, k) is ...

  y -k = m(x -h)

The equation of the line with slope -3 through point A(2, 1) is ...

  y -1 = -3(x -2) . . . . . equation of the median line

This can be simplified to slope-intercept form:

  y = -3x +6 +1 . . . . . eliminate parentheses, add 1

  y = -3x +7 . . . . . slope-intercept equation of the median line

Answer:

6x + 3y

Step-by-step explanation:

=3x + (3)(x) + (3)(y)

=3x + 3x + 3y

=3x + 3x +3y

=(3x + 3x) + (3y)

=6x + 3y

Answer:

I do not see the choices.  There could be more than one right answer

6x + 3y

Step-by-step explanation:

3x + 3(x+y)

3x + 3x + 3y

6x + 3y

The simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

What is a radical expression?

An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

We have,

k² = 17

The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.

[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]

[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]

[tex]k= 17^{\frac{1}{2} }[/tex]

[tex]k = -17^{\frac{1}{2} }[/tex]

Hence, the simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

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Check the picture below.

[tex]cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{16}}\implies cos(\theta )=\cfrac{1}{4}\implies \theta =cos^{-1}\left( \cfrac{1}{4} \right)\implies \theta \approx 75.5^o[/tex]

Make sure your calculator is in Degree mode.