A scientist studies the population of an insect colony. She begins her study with 10,000 insects in the colony and measures the population of the colony
each year. She uses the given formula to model the insect population, P, é years since the beginning of the study.
P= 10,000(1.08)
By what percent does the Insect population grow each year?
%

Answer:

it is 8^2.

Step-by-step explanation:

8 ^ 3 = 8 x 8 x 8

8^3/8 = 8 x 8 x 8 / 8

you cross one 8 on the bottom and the top which leaves you with 8 x 8 or 8^2

Answer:

Solution given:

single positive exponent

[tex]\frac{8^{3} }{8}=8^{3-1}=8² [/tex]

single positive exponent is 8².

Note:

we have

[tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]

Answer: We know that the trainer earns $2,456.75 every month, and she earns an extra $4.75 every time she sells a gym membership.

And last month she sold 32 gym memberships

We can calculate the total amount of money the trainer earned from selling gym memberships by multiplying the number of memberships sold by the amount earned per membership:

32 memberships * $4.75 per membership = $152.00

To find the total amount of money the trainer earned last month, we can add the amount earned from selling gym memberships to the amount earned from her salary:

$2,456.75 + $152.00 = $2,608.75

So, the total amount of money the trainer earned last month is $2,608.75

Step-by-step explanation:

The exponential function that represents the population is y = a*3^x.

What is exponential function?

The formula for exponential functions is y = ab^x, where b is the constant ratio and a  is the starting point. Observe that as the value of x increases by a constant amount, the value of y increases by a common ratio by looking at a table of ordered pairs. All exponential functions share this trait.

We have to find the exponential function for the given table.

Since,

Exponential function = ab^x

where,

a is the starting point

b is the common ratio.

Here,

Common ratio = 24/8 = 72/24 = 216/72 = 648/216 = 3

So, the function becomes,

Exponential function = y = a*3^x

Hence, the exponential function that represents the population is

y = a*3^x.

To know more about exponential function, click on the link

https://brainly.com/question/2456547

#SPJ4

The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).

Parallel lines are coplanar, infinite straight lines in geometry that don't cross at any point. Planes in the same three-dimensional space that never cross each other are said to be parallel.

Curves that are parallel to one another and maintain a set minimum distance do not touch or intersect. A line and a plane that do not share a point are also referred to as being parallel in three-dimensional Euclidean space. But skew lines are used to describe two noncoplanar lines.

We know that slope of parallel line are same. Thus, slope is 5 in y = 5x + 9

Now we need to put the values in y intercept form to find out the equation

y - y1 = m(x - x1)

y - (-3) = m(x - (-2))

y + 3 = 5(x + 2)

y = 5x + 10 - 3

y = 5x + 7

Thus, The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).

Learn more about Parallel lines

https://brainly.com/question/16701300

#SPJ1

Answer:

2 hours + 14

Step-by-step explanation:

Since 1 hour = 60 min

Divide by 60 maximum it goes in 134, 2 times the excess is your minutes.

Answer:

$150

Step-by-step explanation:

100/8=12.5

12.5*12=150

Answer:

7^12

Step-by-step explanation:

When dividing two exponents by the same base, it is the same as subtracting the power (14-2).

Answer:

-

Step-by-step explanation:

There needs to be more information. Where is the point at?

If Alice tests positive and the experts are right on the population prevalence, the probability that Alice has the disease is 0.489.

In the given question, a new disease has been observed, and experts believe that 1% of the population have it.

A test is developed that has 95% true positive rate and 1% false positive rate.

From the given data,

Let E be the event that a patient has a disease and F be the event that a patient has tested positive.

Then according to Bayes' theorem we have,

P(E/F) = P(E)P(E/F)}/(P(E)P(E/F)+P(E')P(F/E')

P(E/F) = (1*95)/(1*95)*(99*1)

P(E/F) = 95/194

P(E/F) = 0.489 (approx.)

Hence, the probability that Alice has the disease 0.489.

To learn more about Bayes' theorem link is here

brainly.com/question/28096770

#SPJ4

Answer:

8 1/8

Step-by-step explanation:

1st I'm going to turn these into improper fractions with a golf swing (multiply the bottom, add the top, keep denominator the same)

3 times 4 + 3 = 15, so we get 15 over 4

4 times 8 + 3 = 35, so we get 35 over 8

Next I am going to give them a common denominator. (Their least common multiple is 8)

one denominator is already 8, so we need to fix the other one by multiplying it by two (multiply both sides)

15/4 times 2/2 = 30/8

Now we add the two fractions (DO NOT ADD DENOMINATORS)

30/8 + 35/8 = 65/8

Finally to make it a mixed number, ask self, how many times does 8 go into 65? 8 times. That's the whole number. what's left over? 1. That is the numerator. The denominator stays the same.

Answer:

43.98

Step-by-step explanation:

have a nice day :)

Answer: 1000

Step-by-step explanation:

i took this quiz before ! !

Answer:

Angle ADC = 7x - 6°

Step-by-step explanation:

4x - 12 + 3x + 6 = 7x - 6

Answer:

Step-by-step explanation:

Diagonal BD of a given rhombus is angle bisector of ∠ADC, so:

Substitute the values and solve for x:

Find the value of ∠ADC:

Answer:

69.4

Step-by-step explanation:

34 + 34 = 68

.7+.7=1.4

68+1.4= 69.4

The correct answer is   A.  {(-8,-14), (-7,-12), (-6,-10), (-5,-8)} which  sets of ordered pairs represents a function.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, we have,

sets of ordered pairs represents a function are,

{(-8,-14), (-7,-12), (-6,-10), (-5,-8)}

{(-4,-14), (-9,-12), (-6,-10), (-9,-8)}

{(8,-2), (9,-1), (10,2), (8,-10)}

{(-8,-6), (-5,-3), (-2,0), (-2,3)}

Now, we know that,

A function has no repeated values of the independent variable.

So, we have now,

Only choice A meets that requirement.

And,

B: (-9, 12) and (-9, 8) both have -9 as a first value; not a function.

C: (8, -2) and (8, -10) both have 8 as a first value; not a function.

D: (-2, 0) and (-2, 3) both have -2 as a first value; not a function.

To learn more on function click:

brainly.com/question/21145944

#SJP1

The Lorenz curve is used to show: B The degree of inequality in the distribution of income within a country.

Lorenze curve can be defined as the curve that help to show how income is share or distributed within a country.

Lorenz curve is important as it play a major role when it comes to how wealth or income should be share in a country by using a pictorial representation to show inequality in income.

Inconclusion the Lorenz curve is used to show: B The degree of inequality in the distribution of income within a country.

Learn more about lorenz curve here:https://brainly.com/question/25751847

Answer:

Yes, they are equivalent

Step-by-step explanation:

Tell whether the rates are equivalent.

Rate formula = Speed(miles)/Time(hour)

1)7 1/2 miles for every 3/4 hour

Hence

Rate = 7 1/2 miles ÷ 3/4 hour

= 15/2 ÷ 3/4

= 15/2 × 4/3

= 5 × 2

= 10 miles per hour

2) 1/2 mile for every 3 minutes

Time = 60 minutes = 1 hour

3 minutes = x

x = 3/60

x = 0.05 hour

Hence

Rate = 1/2 mile ÷ 0.05 hour

= 0.5 mile ÷ 0.05 hour

= 10 mile per hour

Therefore, both rates are equivalent

Answer:

triangle B

Step-by-step explanation:

...............

Answer:

5. It has no solution because this symbol > is greater than and it says that -1 > n>5.

-1 is not greater than 5.

Step-by-step explanation:

Have a nice day! :-)

In order to determine which inequality represents a graph, you need to look at the inequality and identify if the equation is an open or closed interval. If it is an open interval, it will be represented by a dashed line on the graph. If it is a closed interval, it will be represented by a solid line on the graph.

1. Look at the inequality and identify if the equation is an open or closed interval.

2. If it is an open interval, it will be represented by a dashed line on the graph.

3. If it is a closed interval, it will be represented by a solid line on the graph.

4. Determine the starting and ending points of the inequality, and plot them on the graph.

5. Draw the line that connects the two points, either dashed or solid, depending on whether the interval is open or closed.

6. Shade the area of the graph that is represented by the inequality.

7. Label the graph with the inequality, the points, and the shading.

Learn more about inequality here

https://brainly.com/question/28823603

#SPJ4

Answer:

C

Step-by-step explanation:

Any parallel line to the Y axis is infinite/undefined. Which means no function at all.

Answer:

the axis of symmetry is 0 which is x=0

Step-by-step explanation:

Answer:

Law of cosines:

[tex] {x}^{2} = {a}^{2} + {b}^{2} - 2ab \cos( \gamma ) \\ = {12}^{2} + {15}^{2} - 2(12)(15) \cos(144) \\ = 144 + 225 - 360( - 0.809) \\ = 660.246 \\ x = 25.7[/tex]

the given triangle A 45-45-90 triangle is a right triangle having interior angles measuring 45°, 45°, and 90° in degrees.

A 45-45-90 triangle is also an isosceles triangle, which means that its two legs are equal in length.

All 45-45-90 triangles are similar to each other.

Line segments DE and FG are perpendicular to side AB of the 45-45-90 triangle, ABC. Triangles ADE and AFG are also 45-45-90 triangles now, △ABC~△ADE~△AFG.

The ratio of the side lengths of a 45-45-90 triangle is:

                                          ratio= 1:1: √2

The legs of opposite the 45° angles (the shorter sides) are √2÷2of the length of the hypotenuse (the side opposite the 90° angle)

The hypotenuse is √2 times the length of either leg.

Since a 45-45-90 triangle is also an isosceles triangle, then, the two legs are equal on measuring. Assuming x is the length of the leg and b is the length of the hypotenuse and using the Pythagorean Theorem:

x^2 + x^2= b^2

Thus, the ratio of the side lengths of a 45-45-90 triangle are x:x:√2 or 1:1: √2 respectively.

To know more about Triangle:

brainly.com/question/2773823

#SPJ4

The inequality which shows that Shelby should work for h hours is given by 15.5 h - 300 ≥ 280.

Given that,

Rent = 300 dollars

Shelby wants to have at least $280 left over after paying rent.

The total earnings of Shelby calculated in a week are given as, 15.5 h

where,

h is the number of hours

To that we have to substract the rent amount, and we'll get how much does she have left after paying rent,

15.5 h - 300

And she wants this amount to be at least 280 dollars. The inequality can therefore be expressed as follows,

15.5 h - 300 ≥ 280

To know more about inequalities:

https://brainly.com/question/29101873

#SPJ4

Answer:

if the question is how much did you spend in total then your answer would be $9.77, let me know if this is not the question

Step-by-step explanation:

3.99 + 3.99 + 1.79

Answer:

$9.77

Step-by-step explanation:

hope the picture explains it :)