The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 400,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 40,000 mosquitoes/day. Determine the population of mosquitoes in the area at any time. (Note that the variable t represents days.) Enter an exact answer.

Replace g(x) with 16:

16 = 3x-2

Add 2 to both sides:

18 = 3x

Divide both sides by 3:

X = 18/3

X = 6

Answer:

Step-by-step explanation:

Given the vectors  u = (1, −1, −2) and v = (1, 1, 2),

projection of u on v is expressed as [tex]proj_v u = \dfrac{u*v}{|v|^2}*v[/tex]

u.v = (1, −1, −2).(1, 1, 2)

u.v = 1(1)+(-1)(1)+(-2)(2)

u.v = 1-1-4

u.v = -4

|v| = √1²+1²+ 2²

|v| = √1+1+4

|v| = √6

|v|² = (√6)²

|v|² = 6

[tex]proj_v u = \dfrac{-4}{6}*(1,1,2)\\proj_v u = (\dfrac{-4}{6}, \dfrac{-4}{6}, \dfrac{-4}{3} )[/tex]

Similarly for projection of v on u;

[tex]proj_u v = \dfrac{u*v}{|u|^2}*u[/tex]

|u| = √1²+(-1)²+ (-2)²

|u| = √1+1+4

|u| = √6

|u|² = (√6)²

|u|² = 6

[tex]proj_u v = \dfrac{-4}{6}*(1,-1,-2)\\proj_u v = (\dfrac{-4}{6}, \dfrac{4}{6}, \dfrac{4}{3} )[/tex]

Answer:

5x + 2y + 5z

Step-by-step explanation:

Step 1: Write out expression

3x + 4y + 5z + 2x - 2y

Step 2: Combine like terms (x)

5x + 4y + 5z - 2y

Step 3: Combine like terms (y)

5x + 2y + 5z

Answer:

874.9022

hope this helps

The given decimal rounded to the nearest ten-thousandth is 874.9022.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

The given decimal number is 874.902237102.

The decimal is rounded to the nearest ten-thousandth is 874.9022.

Therefore, the given decimal rounded to the nearest ten-thousandth is 874.9022.

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Answer:

1/35

Step-by-step explanation:

We can use proportion.

5 dresses --- 1/7

1 dress ----      x

x = 1*1/7: 5= 1/7 *1/5 = 1/35

Answer:

see below

Step-by-step explanation:

5/10 divide ?/?= 1/2

5/10 divide by 5/5 = 1/2

2. 12/15 divide ?/? = 4/5

12/15 divide by 3/3 = 4/5

3. 10/12divide ?/? = 5/6

10/12 divide by 2/2 = 5/6

4. 14/18 divide ?/? = 7/9

14/18 divide by 2/2 = 7/9

Answer:

z = 8.2

Step-by-step explanation:

6.7z = 5.2z + 12.3

combine like terms by subtracting 5.2z from both sides

1.5z = 12.3

divide by 1.5

z = 8.2

Answer:

8.2

Step-by-step explanation:

5.2z+12.3=6.7z

12.3=6.7z-5.2z

12.3=1.5z

z=8.2

Answer: x=6.67

Step-by-step explanation:

Since these parallelograms are similar, we can use proportions to solve for x.

[tex]\frac{15}{9} =\frac{x}{4}[/tex]              [cross multiply]

[tex]60=9x[/tex]            [divide both sides by 9]

[tex]x=6.67[/tex]

Now, we know that x=6.67.

Answer:

20/3

Step-by-step explanation:

9/4=15/x

cross multiply and get:

9x=15x4

9x=60

divide both sides by 9 so

x=60/9 which when simplified is equal to 20/3

Step-by-step explanation:

A factor is an independent variable that is manipulated in an experiment.

Every factor has two or more levels, which are different values of the factor.

A combination of factor levels is called a treatment.

There is one factor: number of jumps.

This factor has two levels: sets of 10 and sets of 20.

For a single factor experiment, the levels are also the treatments: Jump 10 program and Jump 20 program.

Answer: q -> p

Step-by-step explanation:

just took the test

Answer:

x=70

Step-by-step explanation:

180-45=2x-5

135=2x-5

135+5=2x

140=2x

x=70

Answer:

x= 105

Step-by-step explanation:

Let the unknown angle at the base be y.  We know the base angles of an isosceles triangle are the same

The sum of the angles of the triangles are

30 + y +y = 180

30 + 2y = 180

2y = 180-30

2y = 150

y = 75

We know that x+y = 180 since it forms a straight line

x+75 =180

x = 180-75

x = 105

Answer:The abc conjecture It is stated in terms of three positive integers, a, b and c (hence the name) that are relatively prime and satisfy a + b = c. So a conjecture is like an educated guess.

Hey there! I happy to help!

Here's how to find the distance between any two points.

Find the difference between the x values.

-4-3=-7

Square it.

-7²=49

Find the difference of the y values.

6-(-7)=6+7=13

Square that.

13²=169

Add up the two numbers you got.

169+49=218

And square root it.

√218≈14.76.

Have a wonderful day! :D

Answer:

v = 23.370 mph

Step-by-step explanation:

It is given that,

The world record for the 100 meter dash is finished in 9.572 seconds in Berlin. We need to find the Bolt’s average race speed in miles per hour.

We know that,

1 mile = 1.609 km

or

1 mile = 1609.34 m

⇒ 100 m = 0.0621 miles

1 hour = 3600 seconds

⇒ 1 second = (1/3600) hour

Average speed = distance/time

So,

[tex]v=\dfrac{\dfrac{100}{1609.34 }\text{miles}}{\dfrac{9.572}{3600}\ \text{hour}}\\\\v=23.36963\ \text{mph}[/tex]

or

v = 23.370 mph

Hence, Bolt’s average race speed is 23.370 mph.

Answer:

Area of the trapezoid = 18 m²

Step-by-step explanation:

Formula to calculate the area of a trapezoid is,

Area of a trapezoid = [tex]\frac{1}{2}(b_1+b_2)h[/tex]

Where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel sides of the trapezoid

And h = distance between the parallel sides

From the figure attached,

[tex]b_1[/tex] = 5 m

[tex]b_2[/tex] = (6 + 1) = 7 m

h = 3 m

By substituting these values in the formula,

Area of a trapezoid = [tex]\frac{1}{2}(5+7)3[/tex]

                                 = 6 × 3

                                 = 18 m²

Therefore, area of the given trapezoid is 18 m².

Hey there! I'm happy to help!

We have 5 numbers that will give us an average score of 80.

75,82,71,84,x

What we do is add these all up and divide by 5 to get 80. Let's go backwards to find x.

We multiply by 5.

80(5)=400

We subtract all of the numbers except for x.

400-75-82-71-84=88

Therefore, the score on the next test has to be 88 to have the student's average be 80.

Have a wonderful day! :D

Answer:

No, it's not a one-to-one function

Step-by-step explanation:

Given

[tex]f(x) = round(x)[/tex]

Required

Determine if this function is one-to-one

I'll answer this question using the following illustrations;

Assume x = 4.6

[tex]f(x) = round(x)[/tex] would be

[tex]f(4.6) = round(4.6)[/tex]

[tex]f(4.6) = 5[/tex]

Also assume x = 4.8

[tex]f(x) = round(x)[/tex] would be

[tex]f(4.8) = round(4.8)[/tex]

[tex]f(4.8) = 5[/tex]

More generally;

[tex]4.5 \leq\ x\leq\5.4[/tex]

Would result in:

[tex]f(x) = 5[/tex]

Since, there's a always a possibility of f(x) having one value for various values of input x, then we can conclude that the function is not a one-to-one function

The function f(x) = round(x) is not one - to - one since different input values of X could yield the same output.

For instance :

Given that x = 1.4

f(x) = round(x)

f(1.4) = round(1.4)

Output = 1 ( nearest integer)

Since, different input values of X could yield the same the output, then the function is not one - to - one.

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Answer:

x=18

Step-by-step explanation:

am=by which means you can make the equations equal each other

4x-22=2x+14

2x=36

x=18

Answer:

$16.92

Step-by-step explanation:

Just divide 42.30 by 2.5 and it will give you the answer

Answer:

Step-by-step explanation:

25 324 796657

Answer:35.18

Step-by-step explanation:

Did this 7 years ago

The required value of 42.5 – 7.32 is 35.18.

Subtraction of 7.32 from 42.5 to be determined

Subtraction is defined as the value that should be reduced to the subtraction value.

Here, subtraction of 7.32 from 42.5,
⇒ 42.5 - 7.32
= 35.18

Thus, the required value of 42.5 – 7.32 is 35.18.

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Answer:a

Step-by-step explanation:

i think

Steps to solve:

5-3x/5

~Divide the numerator to the denominator

-3/5x + 1

Best of Luck!

Answer:

379/100

Step-by-step explanation:

IS THIS IT???

Answer:

- 1 1/3 which is none of the answers loll

Answer:

-1 and 1/3

Step-by-step explanation: negative one and one third

Answer:

  -1

Step-by-step explanation:

"Evaluate the expression for ..." means "put these numbers where these variables are and do the arithmetic."

  [tex]\sqrt{b}+\dfrac{25}{a}=\sqrt{16}+\dfrac{25}{-5}\\\\=4-5=\boxed{-1}[/tex]

Answer:

Step-by-step explanation:

the zeros of a function f are found by solving the equation f(x) = 0. Example 1. Find the zero of the linear function f is given by. f(x) = -2 x + 4 I hope this helps.