The area of an oil spill is doubling in size every day. At the start of the day on May 1, the oil spill covers 20 square meters. During which day will the area exceed 500 square meters?

Answer: D) y = 2ˣ

Step-by-step explanation:

The graph is the shape of exponential growth.  The only option that satisfies this is D.

A) y = - (1/2)ˣ is a reflection over the x-axis of exponential decay

B) y = (1/2)ˣ is exponential decay because (1/2) < 1

C) y = - 2ˣ is a reflection over the x-axis of exponential growth

D) y = 2ˣ is exponential growth

Answer:

Part a) [tex]y=400(2.5)^{x}[/tex]

Part b) [tex]3,814,697\ rice\ weevil\ population[/tex]

Part c)  [tex]16.1\ weeks[/tex]

Step-by-step explanation:

Part a) Write and simplify a formula that can be used to predict the rice weevil population for any week after the beginning of the study

we know that

100%+150%=250%=250/100=2.5

In this problem we have an exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

a is the initial value

b is the base

y ----> is the rice weevil  population

x ----> the number of weeks

In this problem

a=400 rice weevils

b=2.5

substitute

[tex]y=400(2.5)^{x}[/tex]

Part b) Use the formula to predict the rice weevil population 10 weeks after the beginning of the study. Show your work

we have

[tex]y=400(2.5)^{x}[/tex]

so

For x=10 weeks

substitute

[tex]y=400(2.5)^{10}=3,814,697\ rice\ weevil\ population[/tex]

Part c) Use the formula to predict when the rice weevil population will reach 1,000,000,000.

we have

[tex]y=400(2.5)^{x}[/tex]

so

For y=1,000,000,000 rice weevil  population

substitute in the formula and solve for x

[tex]1,000,000,000=400(2.5)^{x}[/tex]

Simplify

[tex]2,500,000=(2.5)^{x}[/tex]

Apply log both sides

[tex]log(2,500,000)=x*log(2.5)[/tex]

[tex]x=log(2,500,000)/log(2.5)=16.1\ weeks[/tex]

A function assigns the values. The number of weeks it will take for the population of 400 to be 1,000,000,000 is 16.1 weeks.

A function assigns the value of each element of one set to the other specific element of another set.

A.) Given there are 400  rice weevils at the beginning. And the population is expected to grow at a rate of 150% each week. Therefore, the function that can represent the population can be written as,

Population after n weeks = 400×(1+1.5)ⁿ = 400×(2.5)ⁿ

where n is the number of weeks.

B.) The population of the rice weevils after 10 weeks will be,

Population after 10 weeks = 400×(2.5)¹⁰ = 3,814,697.266 ≈  3,814,697

C.) The time needed for the population to reach 1,000,000,000 will be,

1,000,000,000 = 400(2.5)ⁿ

2,500,000 = 2.5ⁿ

n = 16.0776 ≈ 16.1 weeks

Hence, the number of weeks it will take for the population of 400 to be 1,000,000,000 is 16.1 weeks.

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Answer:

x = 11

Step-by-step explanation:

24/(3x-3) = 44/(5x)

120x = 132x - 132

-12x = -132

x = 11

Answer:

A)

Blue: [tex]\frac{6}{10} =\frac{3}{5}[/tex]

Red: [tex]\frac{1}{10}[/tex]

B)

Blue: [tex]\frac{16}{40} =\frac{2}{5}[/tex]

Red: [tex]\frac{8}{40} =\frac{1}{5}[/tex]

C)

No the experimental probabilities found in "A" are not equal to the probabilities found in "B". The sample size of the the experiment was not large enough to reflect the actual probability.

D)

Blue: 80

Yellow: 50

Red: 40

Orange: 30

The answer is:

The total fall in 30 feet will be 7.5 inches.

To calculate the total fall in 30 feet, given the slope (decreasing rate for this case), we need to use the following equation:

[tex]TotalFall=\frac{\frac{1}{4} inch}{foot}*FeetAmount[/tex]

We are asked to calculate the total fall in 30 feet, so, substituting it into the equation, we have:

[tex]TotalFall=\frac{\frac{1}{4} inch}{foot}*30feet[/tex]

[tex]TotalFall=7.5inch[/tex]

Hence, we have that the total fall in 30 feet will be 7.5 inches.

Have a nice day!

Final answer:

To calculate the total fall in elevation for a sewer line with a 1/4" per foot grade over 30 feet, simply multiply 1/4" by 30, resulting in a total fall of 7.5 inches.

Explanation:

The student is asking how to calculate the total fall in elevation for a sewer line that has a consistent slope over a given distance. The slope given is 1/4" per foot of sewer line. To find the total fall over 30 feet, you need to multiply the slope per foot with the total distance.

Calculation:

Determine the slope per foot, which is 1/4".

Multiply this slope by the total distance, which is 30 feet.

1/4" x 30 = 7.5". This is the total fall in elevation over 30 feet.

The total fall in elevation for a sewer line over 30 feet, with a slope of 1/4" per foot, is 7.5 inches.

Answer:

1.48

Step-by-step explanation:

4 times 2 = 8

4 minus 3 = 1

The three-digit no. is 2a a a - 3 whose hundredth digit is twice the size of the tenth digit. The unit's digit is 3 less than the tenth digit.

The standard decimal form of numbers is written in base 10 as there are 10 different numbers from 0 to 9.

Each digit has a face value and a place value.

Let, The tens digit be 'a'.

Given, The hundredth's digit is twice the size of the tenth's digit.

∴ The hundredth digit be '2a' and the unit digit is (a - 3).

So, The 3-digit no. is 2a a a - 3, where a is, {2, 3, 4}.

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Answer:

The points you need to graph are (-4,0) (-1,9) (2,0)

Step-by-step explanation:

Hope this helps!

Answer:

135

Step-by-step explanation:

The little cubes with side length 1/3 unit have volume (1/3 unit)³ or (1/27 unit)³.  Divide the prism volume (5 units³) by (1/27 units³) to determine how many little cubes are required to fill the prism:

5 units³

--------------- = 135 little cubes.

1/27  unit

Note:  This assumes that the dimensions of the prism are such that there is no wasted space when all these little cubes are packed inside.  For example, if the width of the prism were 3, then we assume that 3 little cubes would fit that particular dimension.

There are 135 cubes in the cube with a volume of 5 cubic units and the small cube has a side length of 1/3 unit.

It is defined as three-dimensional geometry that has six square faces and eight vertices.

As we know, the volume of the cube = side³

The volume of the rectangular prism = 5 cubic units

The volume of the small cube with side lengths of 1/3 unit is:

= (1/3)×(1/3)×(1/3)

= 1/27

The number of cubes in the big cube = 5/(1/27)

= 5×27

= 135 cubes

Thus, there are 135 cubes in the cube with a volume of 5 cubic units and the small cube has a side length of 1/3 unit.

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Answer:

  10.8 ft

Step-by-step explanation:

The height from the base can be found from the formula for the volume. Fill in the given information and solve for the height.

  V = (1/3)Bh = (1/3)s²·h

  432 ft³ = (1/3)(12 ft)²·h . . . . . fill in side length and volume

  h = 432 ft³/(48 ft²) = 9 ft . . . divide by the coefficient of h

The slant height is the hypotenuse of a right triangle with this height as one leg and half the side length as the other leg.

  slant height = √((9 ft)² +(12 ft/2)²) = √(117 ft²) = 3√13 ft

  slant height ≈ 18.817 ft ≈ 18.8 ft

Answer:

the answer is 10. you go left to right since the equation falls under the peMdas part

Answer:

d. 20+10+5+2.5+...

Step-by-step explanation:

No geometric series with a common ratio of magnitude greater than 1 will have a finite sum. Nor will any arithmetic series.

Those descriptions exclude answer choices a, b, c. Choice d is a geometric series with a common ratio of 1/2, so will have a finite sum. (It is 40.)

Given : A  = 24 sq feet

A = 0.5 base x height

base = x , height = x+2

A = 0.5 x(x+2)  = 24 sq feet

1) 0.5 x(x+2) = 24 (A) 

2) x^2 + 2x - 48 = 0 (D)

To check the rest un-wrap the bracket:

x^2 + (x+2)^2 = 24

x^2 + x^2 + 4 + 4x = 24

2x^2 + 4x - 20 = 0

x^2 + 2x - 10= 0 (NO)

Likewise:

x^2 + (x+2)^2 = 100

x^2 + x^2  +4 + 4x = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

3) x^2 + 2x - 48 = 0 (F)

To sum up: that's what apply:

1) 0.5 x(x+2) = 24 (A) 

2) x^2 + 2x - 48 = 0 (D)

3) x^2 + 2x - 48 = 0 (F)

Answer:

s ^3sqrt27 or A

Step-by-step explanation:

The answer is B

3x4=12

3x5=15

9x3= 27

B) 3x9= (3x5) + (3x4)

The inequality that can be used to find the interval of time in which the stick reaches a height of more than 8 feet is  -[tex]16t^2 + 48t > 8[/tex]

To solve this inequality, let's rearrange it:

-[tex]16t^2 + 48t - 8 > 0[/tex]

Now, we have a quadratic inequality. To solve it, we'll first find the critical points by setting the expression equal to zero:

[tex]-16t^2 + 48t - 8 = 0[/tex]

Now, we'll use the quadratic formula to find the roots:

[tex]t = [ -b ± √(b^2 - 4ac) ] / (2a)[/tex]

Where a = -16, b = 48, and c = -8.

Plugging in these values, we get:

[tex]t = [ -48 ± √(48^2 - 4(-16)(-8)) ] / (2(-16))[/tex]

[tex]t = [ -48 ± √(2304 - 512) ] / (-32)[/tex]

[tex]t = [ -48 ± √(1792) ] / (-32)[/tex]

[tex]t ≈ [ -48 ± 42.35 ] / (-32)[/tex]

Now, we have two critical points:

t1 ≈ (-48 + 42.35) / (-32) ≈ 0.186

t2 ≈ (-48 - 42.35) / (-32) ≈ 2.814

Now, we'll test intervals between and outside these critical points to determine when the inequality is satisfied:

For t < 0.186: The quadratic term dominates, leading to a negative value.

For 0.186 < t < 2.814: The quadratic term dominates, leading to a positive value.

For t > 2.814: The linear term dominates, leading to a negative value.

So, the solution to the inequality is 0.186 < t < 2.814.

Thus, the stick reaches a height of more than 8 feet between approximately 0.186 seconds and 2.814 seconds.

Complete question:

Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

Answer:

Down below

Step-by-step explanation:

Well, the company can predict that most of the 8 dentists recommend the ProTooth toothbrush about 88 percent of the dentists recommend it 88 percent =0.88 as a decimal.  

They can also predict that the one person that didn't recommend it beacause maybe there was a downside to the Protooth brush that the person didn't like

In a survey of 64 dentists, 56 of them will recommend a ProTooth toothbrush is the predicted option.

This involves gathering of information through relevant questions from a sample of people to better understand them.

7/8 was the initial recommendation

We can get the final one by multiplying both sides by same value.

7 × 8  = 56

8 × 8      64

Therefore, in a survey of 64 dentists, 56 of them will recommend a ProTooth toothbrush.

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Answer:

P(Male or Type B) > P(Male | Type B)

Step-by-step explanation:

Total Female = 85 type A, 12 type B  ⇒ 97 Female.

Total Male = 65 type A, 38 type B   ⇒ 103 Male

Total type A = 65 + 85 = 150

Total type B = 12 + 38 = 50

total number of people = 97 + 103 = 200

Then the probability would be:

P(Male | Type B) = [tex]\frac{number of male in B}{total number of male}[/tex]

                           = [tex]\frac{38}{103}[/tex]

                           = 0.368

P(Male or Type B) = [tex]\frac{total number of male + (total number of people in B - total number of male in B)}{total number of male}[/tex]

                              =  [tex]\frac{103 + (50 - 38)}{200}[/tex]

                              = [tex]\frac{103 + 12}{200}[/tex]

                              = [tex]\frac{115}{200}[/tex]

                              = 0.575

 Hence, P(Male or Type B) > P(Male | Type B)

Answer:

118.3 m²

Step-by-step explanation:

The area (A) of a triangle is

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Note the legs 13 and 18.2 are at right angles to each other, hence

A = 0.5 × 13 × 18.2 = 118.3

Answer:

D

Step-by-step explanation:

well you see I just guessed :D

Answer: 1/3 or 1 out of 3 times

Step-by-step explanation: It seems as though there are only three options for it to land on, Upper case, g, and f-therefore you have a 1 in 3 chance for each

Answer:

18  and 6

Step-by-step explanation:

Answer:

select -3 and 2

Step-by-step explanation:

f(x)=g(x) means set them equal and solve for x

x^2+2x-8=-x^2+4

Add x^2 on both sides and subtract 4 on both sides.

2x^2+2x-12=0

Divide both sides by 2

x^2+x-6=0

Think of two numbers that multiply to be -6 and add up to be 1

that is 3 and -2

so The factored form is (x+3)(x-2)=0

So x=-3 or x=2

Answer:

neither

Step-by-step explanation:

First differences are 3, 5, 7, 9, and the differences of these (2nd differences) are constant at 2. The degree of the polynomial function describing the sequence is equal to the number of the differences that are constant. Here, that is 2nd differences, so the sequences is described by a 2nd-degree (quadratic) polynomial.

It is not linear (arithmetic) or exponential (first differences have a common ratio).

Answer:

It is a Geometric series.

Step-by-step explanation:

It has a common ratio equal to a:

3a^2 / 3a = a, 3a^3 / 3a^2 = a  and so on..

It is a Geometric series.

Answer with explanation:

 The given series is:

      [tex]3 a + 3 a^2 + 3 a^3 + . . . + 3 a^n[/tex]

If you will try out to find out the ratio of

    [tex]\rightarrow\frac{\text{Second term}}{\text{First term}} {\text{or}}\frac{\text{Third term}}{\text{Second term}}  {\text{or}} \frac{\text{Fourth term}}{\text{Third term}} ........\\\\ \rightarrow\frac{3a^2}{3a}=\frac{3a^3}{3a^2}=\frac{3a^4}{3a^3}=......=a[/tex]

The Ratio of Succeeding term to it's preceding term in the given sequence is constant equal to a.

So, if any Sequence follows this kind of rule or pattern we call it Geometric Progression.

Option B:→ Geometric

Answer:

[tex] \tan(35) = \frac{x}{40} \\ 40 \tan(35 ) = x \\ 28 = x \\ now \: to \: find \: h \\ h = x + 5 \\ h = 28 + 5 \\ h = 33 \: ft. [/tex]

Choice B

Step-by-step explanation:

Tangent is opposite divided by adjacent. You use tangent because they told you the student stands 40 ft. away from the base of the flag pole (adjacent side) and you need to find the opposite side which I called x. When I'm talking about sides it's in reference to the 35 degree angle that is given.

Google soh cah toa for an explanation if you need more help.

I hope this helps. This is what you do when you are bored on a Friday night lol.

Answer:

4/5 hour (48 minutes)

Step-by-step explanation:

Janet works at the rate of ...

(1 job)/(3 hours) = (1/3) job/hour

So, in 1 hour, she has worked 1/3 of the job, leaving 2/3 of the job remaining when Garry shows up.

Garry works at the rate of ...

(1 job)/(2 hours) = 1/2 job/hour

So, together they work at the rate of ...

(1/3 job/hour) + (1/2 job/hour) = (2/6 +3/6) job/hour = 5/6 job/hour

Then the time it takes to do the remaining 2/3 job is ...

(2/3 job)/(5/6 job/hour) = (2/3·6/5) hour = 4/5 hour

It will take 4/5 hour for them to finish the job together.

Answer: 4/5 of an hour or 48 minutes

Step-by-step explanation:

Janet's Rate : 1 job / 3 hours = 1/3 job/hour

In 1 hour, 1/3 of the job is already finished by her, so there is 2/3 of the job left.

Garry's Rate:

1 job / 2 hours = 1/2 job/hour

Janet an Garry's Rate:

1/3 job/hour + 1/2 job/hour = 2/6 +3/6 job/hour = 5/6 job/hour

Time to do remaining 2/3 of job:

2/3 job / 5/6 job/hour = 2/3 * 6/5 hour = 4/5 hour

Answer:

It will take 4/5 of an hour for them to finish the job together.

                                 I Hope This Helps!

Answer:

Can I have the options? Then I would be glad to answer

Step-by-step explanation:

Answer:

The awnser for plato users is 45 degrees. which is (A)

Step-by-step explanation:

Answer:

The sum of all exterior angles of BEGC is equal to 360° ⇒ answer F only

Step-by-step explanation:

* Lets revise some facts about the quadrilateral

- Quadrilateral is a polygon of 4 sides

- The sum of measures of the interior angles of any quadrilateral is 360°

- The sum of measures of the exterior angles of any quadrilateral is 360°

* Lets solve the problem

- DEGC is a quadrilateral

∵ m∠BEG = (19x + 3)°

∵ m∠EGC = (m∠GCB + 4x)°

∵ The sum of the measures of its interior angles is 360°

∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360

∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ add the like terms

∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ -3 from both sides

∴ 23x + 2m∠GCB + m∠CBE = 375

∵ The sum of measures of the exterior angles of any quadrilateral is 360°

∴ The statement in answer F is only true

Answer:

F

Step-by-step explanation:

Answer:

a. 1.75

Step-by-step explanation:

r values, or the correlation coefficient  must be between -1 and 1, inclusive

-1 is a perfect negative correlation

0 is no correlation

+1 is a perfect positive correlation

1.75 is not between -1 and 1