X/7=4 What number must be multiplied on both sides in order to isolate x on the left side of the equation

Answer:

Part 1) The exponential function is equal to [tex]y=1,350(0.95)^{x}[/tex]

Part 2) The population in 2010 was  [tex]992\ fish[/tex]

Step-by-step explanation:

Part 1) Write an exponential decay function that models this situation

we know that

In this problem we have a exponential function of the form

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

where

y ----> the fish population of Lake Collins since 2004

x ----> the time in years

a is the initial value

b is the base

we have

[tex]a=1,350\ fish[/tex]

[tex]b=(100\%-5\%)=95\%=0.95[/tex]

substitute

[tex]y=1,350(0.95)^{x}[/tex] ----> exponential function that represent this scenario

Part 2) Find the population in 2010

we have

[tex]y=1,350(0.95)^{x}[/tex]

so

For [tex]x=(2010-2004)=6\ years[/tex]

substitute

[tex]y=1,350(0.95)^{6}=992\ fish[/tex]

Final answer:

The exponential decay function for the fish population in Lake Collins is P(t) = 1350 * e^(-0.05t). Using this, the estimated fish population in 2010 is about 1,000.

Explanation:

We need to write an exponential decay function to model the decreasing fish population in Lake Collins and then use it to find the population in 2010.

To create an exponential decay function, we can use the formula P(t) = P0 * e^(rt), where:

P(t) is the population at time t,

P0 is the initial population,

r is the rate of decay (as a negative value), and

t is the time in years since the initial count.

Given the initial population of 1,350 fish in 2004 and a decay rate of 5% per year, we can write the function as:

P(t) = 1350 * e^(-0.05t)

To find the population in 2010, we first calculate the time passed since 2004, which is 6 years. Thus, t = 6:

P(6) = 1350 * e^(-0.05*6)

Calculating this gives us:

P(6) ≈ 1350 * e^(-0.3) ≈ 1350 * 0.740818 ≈ 1000 (rounded to the nearest whole number)

Therefore, the fish population in 2010 was approximately 1,000 individuals.

Answer:

  (x, y) = (7/12, 11 1/6)

Step-by-step explanation:

A graph will show you the solution is near (x, y) ≈ (0.6, 11.2). For an exact answer, an algebraic solution is indicated.

Subtracting the second equation from the first gives ...

  0 = 12x -7

  7/12 = x

Substituting for x in the second equation gives ...

  y = 2(7/12) +10 = 7/6 +10

  y = 11 1/6

Answer:

  see below

Step-by-step explanation:

If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...

  arccos((√3)/2) = β = 30°

This fact matches only one answer choice.

Step-by-step answer:

Given:

Geometric sequence with

second term, T2 = 6

third term, T3 = 12

Wants to have the explicit and recursive rules.

Solution:

common ratio, r = 12/6 = 2

Therefore the first term, T1

= second term /r

= 6/2

=3

Thus the absolute rule is

Tn = T1 *r^(n-1)      where T1 = 3, r=2.  Check: T3 = T1*2^(3-1) = 3*2^2=12 ...good

The recursive rule (depending on the previous term)

Tn = Tn-1*r = 2*Tn-1

The explicit rule for the sequence is a_n = 3 * 2^(n-1), and the recursive rule is a_n = a_(n-1) * 2. These were determined by identifying the common ratio of the sequence as 2.

In a geometric sequence, each term is generated by multiplying the previous term by a common ratio. Given the second term (6) and third term (12) in the sequence, we can identify the common ratio by dividing the third term by the second term. So, 12 divided by 6 equals 2. Therefore, the common ratio is 2.

So, the explicit rule (the nth term) of this sequence would be: a_n = a_1 * r^(n-1) = 6 / 2 * 2^(n-1) = 3 * 2^(n-1).

The recursive rule for the sequence would be: a_n = a_(n-1) * r = a_(n-1) * 2.

To summarize, we determined the common ratio to be 2 by dividing the third term by the second term. We then used this ratio to create the explicit and recursive rules for the geometric sequence.

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Answer:

yellow b/c there are the most

Step-by-step explanation:

Answer:

90.51 (rounded to the nearest hundredth)

Step-by-step explanation:

We can use trigonometry to figure this out

sin = opposite side / hypothenuse

The 45° angle's opposite side is a leg of the triangle

sin 45 = leg / 128

sin 45 * 128 = (leg / 128 ) * 128

0.7071 * 128 =  leg

90.51 = leg

Answer:

b

Step-by-step explanation:

Answer:

It depends on how you define an outcome.

Usually, the outcomes are considered to be the number showing on the top face of the die (number cube) when it comes to rest on a horizontal surface. If that is how you define outcomes, then the sample space is the set of numbers 1–6: {1, 2, 3, 4, 5, 6}.

Step-by-step explanation:

"This experiment" covers a lot of territory. The student could be checking to see if the die stays on the table or falls to the floor. The student could be experimenting to see if the die changes color or makes a certain kind of noise. The experiment could involve the number of times the die rolls over to a new face before it comes to rest. Until the experiment is properly defined, the sample space is unknown.

If the experiment is to see what number shows on the top face of the die at rest on a horizontal surface, then the sample space is presumably the set of numbers 1 through 6.

Answer:   [tex]32\pi[/tex] cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

[tex]r=\frac{8units}{2}\\\\r=4units[/tex]

Since you already know that height and  the radius, you can substitute them into the formula. Then, the volume of this cone is:

[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]

[tex]V_{cone}=32\pi \ units^3[/tex]

Answer: 48

Step-by-step explanation:

Answer:

  B. 40/61

Step-by-step explanation:

There are 40 spots out of the 61 in the lot with numbers greater than or equal to 22. The probability of choosing one of them at random is 40/61.

_____

About the answer choices

61/21 and 61/40 are both numbers that are greater than 1. A probability is always a number between 0 and 1 (inclusive), so these answers can be rejected immediately.

There are 21 spots with numbers less than 22, so 21/61 is the probability of choosing one of those. That is not what the question is asking for.

Answer:

Step-by-step explanation:

I'll show you with an example.  I'll make a table and then show you how to find the exponential equation, ok?

 x                 y

 0                 3

 1                  12

 2                 48

 3                192

The standard form of an exponential equation is

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

We will take 2 (x,y) coordinates from our table and fit them into the equations to solve for a and b.  Using the point (0, 3):

[tex]3=a(b)^0[/tex]

b to the 0 power is equal to 1, so the equation then becomes a(1) = 3 so a = 3.  We will use the other x, y coordinate along with that a value to now solve for b:

[tex]12=3(b)^1[/tex]

b to the first is b, so now that equation becomes 3b = 12 and b = 4.  Filling that info back into the standard form:

[tex]y=3(4)^x[/tex]

There you go!

Answer:

b = 17

Step-by-step explanation:

Since PQ = RQ then ΔPQR is isosceles and QS is a perpendicular bisector

Hence PS = RS = 17 ⇒ b = 17

m<6 = 180° - m<3

m<6 = 180° - 130°

m<6 = 50°

Answer: m6 equals 50 degrees

Step-by-step explanation: Since AB and CD are parallel u just solve for m2 which is the same as m6 which would be 180-130=50

Answer:

25% = 1/4

Step-by-step explanation:

It is 25% because there are 4 outcomes that you can get which are

HT, TH, HH, TT

H = Head

T = Tail

and out of the four outcomes, there is one that will be Head first and Tails on the second flip. So 1 out of 4 = 25%

 The answer is C. I have the work for it in the image bellow

Hope this helped!

~Just a girl in love with Shawn Mendes

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-9)^2+y^2=4\implies (x-\stackrel{h}{9})^2+(y-\stackrel{k}{0})^2=2^2~\hfill \stackrel{center}{(9,0)} \\\\\\ (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=4\implies (x-\stackrel{h}{3})^2+(y-\stackrel{k}{2})^2=2^2~\hfill \stackrel{center}{(3,2)}[/tex]

Check the picture below.

well, its radius didn't change, anyhow, you know what to check out.

Answer:

The circle moves left and up

Step-by-step explanation:

The circle's center changes from (9, 0) to (3,2) and the radius stayed the same.

Answer:

Jackie's total contribution the school would be $18.00

Step-by-step explanation:

Jackie's contribution to the school bazaar = a batch of baklava

No. of pieces in a batch = 12 pieces

Price of one piece = $1.50

CASE: All baklava is sold

No. of pieces of Baklava sold = 12 pieces

Price of 12 pieces of Baklava = no. of pieces * Price of one piece

= 12 * $1.50

= $18.00

Step-by-step explanation:

After taking the square root:

x + 2 = ±2

Notice that x + 2 can also equal -2, because (-2)² = 4.

Answer:

option C

Step-by-step explanation:

Area of the triangle=4x²+4x+1

it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.

From the given information:

[tex]\( \angle BAD + \angle ABD = 90^\circ \)[/tex]

[tex]\( \angle CBD + \angle BCD = 90^\circ \)[/tex]

[tex]\( \angle ABD + \angle DBC = 90^\circ \)[/tex]

[tex]\( \angle BAD + \angle BCD = 90^\circ \)[/tex]

We can see that:

[tex]\( \angle BAD + \angle ABD = \angle CBD + \angle BCD \)[/tex]

[tex]\( \angle BAD + \angle BCD = \angle ABD + \angle DBC \)[/tex]

[tex]\( \angle BAD + \angle BCD = \angle BAD + \angle BCD \)[/tex]

From equations (1) and (2), we can conclude that:

[tex]\[ \angle BAD + \angle ABD = \angle CBD + \angle BCD = \angle ABD + \angle DBC \][/tex]

This implies that [tex]\( \angle ABD = \angle CBD \) and \( \angle BCD = \angle DBC \).[/tex]

Therefore, it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.

The complete question is:

According to the diagram below, which similarity statements are true? Check all that apply.

A. △ ABDsim △ BCD

B. △ ABCsim △ BDC

C. △ ABCsim △ ADB

D. △ ABDsim △ ADC

The similarity statements that are true are:

[tex]\(\triangle ABD \sim \triangle BCD\):[/tex]

  - Since D lies on AC and [tex]\( \angle ADB = \angle BDC = 90^\circ \),[/tex] both [tex]\(\triangle ABD\)[/tex]and \[tex](\triangle BCD\)[/tex]share [tex]\( \angle ADB = \angle BDC \).[/tex]

  - They both share the common angle [tex]\( \angle B \).[/tex]

  - Therefore, [tex]\(\triangle ABD \sim \triangle BCD\).[/tex]

[tex]\(\triangle ABC \sim \triangle ADB\):[/tex]

  - Both triangles share the angle [tex]\( \angle A \).[/tex]

  - They both have right angles at [tex]\( \angle ABC = \angle ADB = 90^\circ \).[/tex]

  - Therefore, [tex]\(\triangle ABC \sim \triangle ADB\).[/tex]

[tex]\(\triangle ABC \sim \triangle BDC\):[/tex]

  - Both triangles share the angle [tex]\( \angle C \).[/tex]

  - They both have right angles at [tex]\( \angle ABC = \angle BDC = 90^\circ \).[/tex]

  - Therefore, [tex]\(\triangle ABC \sim \triangle BDC\).[/tex]

There are 6 letters: (4 consonants, 2 vowels)

The probability that Allen will not select a consonant is: (2/6 which simplifies to 1/3) because there are only 2 letters out of the 6 that are not consonants

Fraction: 1/3

Decimal: 0.3333

Percentage: 33.33%

The probability that Allen does not select a consonant is 1/3 as a fraction, 0.3333 as a decimal, and 33.33% as a percentage.

You've asked what the probability is that Allen will not select a consonant when drawing one letter from the mix of letters 's, c, h, o, o, l'. First, let's determine how many vowels and consonants there are in the selection. We have two vowels ('o', 'o') and four consonants ('s', 'c', 'h', 'l'). This gives us a total of six letters.

To find the probability of not selecting a consonant, we look at the likelihood of selecting a vowel instead, since those are the only two types of letters available. There are 2 vowels out of a total of 6 letters. The probability as a fraction is thus 2/6, which simplifies to 1/3.

To express this probability as a decimal, divide the numerator by the denominator: 1 divided by 3 equals approximately 0.3333. Finally, to express this as a percentage, multiply the decimal by 100 to get 33.33%.

In summary:

Answer:

6√2.

Step-by-step explanation:

The two radii are equal length and form a right angle, so the resulting triangle is 45-45-90.  Therefore, the length of the chord (the hypotenuse of the triangle) is 6√2.

Answer:

54 ft^2

Step-by-step explanation:

Bathroom area is 15 ft^2

The kitchen is twice the bathroom

2*15 = 30 ft^2

Kitchen: 30 ft^2

Front door: 9ft^2

The total is all the areas added together

Total = bathroom + kitchen + front door

         = 15 ft^2     + 30 ft^2  + 9 ft^2

         = 54  ft^2

Answer:

33.75

Step-by-step explanation:

Step 1- Find the decimal form of 35%

Step 2- When you find that multiply that by 25

Step 3- When you find the answer to step 2 add that to 25

That is your answer

Final answer:

The price that Fred will pay the groomer the next time when his dog has a haircut is  $33.75.

Explanation:

The question asks us to calculate the new price Fred will pay for his dog's haircut after the groomer increases the price by 35%. To find the new price, we'll use the formula for calculating percentage increase, which is: New Price = Original Price + (Original Price * Percentage Increase).

First, convert the percentage increase to a decimal by dividing it by 100, so 35% becomes 0.35. Then, multiply the original price of $25 by 0.35 to find the amount of the increase, which is $8.75.Finally, add the increase to the original price to find the new price, which is $25 + $8.75 = $33.75. So, Fred will pay $33.75 the next time his dog has a haircut.

Answer:

Step-by-step explanation:

<EAF is a central angle. Its measure is 12o

Arc EF has angular measure of 12 degrees as well.

The formula for the arc length in cm is

Arc length = (given arc angle/360) * 2 * pi * r

r = 30 cm which is given

Given arc angle = 12 degrees.

Arc length = (12/360) * 2* pi * r

Arc length = 1/30 * 2*pi * 30

Arc length = 6.28

Answer:

26

Step-by-step explanation:

80 divided by three = 26.666666

26 times 3 = 78

2 leftover

The number sticker each student get is 26 and the number stickers teacher got is 2.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, three friends buy one pack of 80 stickers.

Now, number of stickers each friend = 80/3

3|80|26

  78
_____
   2

Therefore, the number sticker each student get is 26 and the number stickers teacher got is 2.

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The large dog and small boy working together will take 2/3 hour to destroy Mr McGregor's garden.

To solve this problem, we can add the rates at which the large dog and the small boy work together:

Large dog's rate = 1 garden / 2 hours = 1/2 garden per hour

Small boy's rate = 1 garden / 1 hour = 1 garden per hour

Combined rate = 1/2 garden per hour + 1 garden per hour = 3/2 gardens per hour

Now, we can use the combined rate to find the time it would take for the large dog and the small boy to destroy Mr. McGregor's garden:

Time = 1 garden / Combined rate = 1 garden / (3/2 gardens per hour) = 2/3 hour

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Answer:

D. 2(√{x} + √{x - 2})

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{4}{\sqrt{x} - \sqrt{x - 2} } * \frac{\sqrt{x} + \sqrt{x - 2}}{\sqrt{x} - \sqrt{x - 2}} = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} }[/tex]

Then we simplify:

[tex]\frac{4(\sqrt{x} + \sqrt{x - 2})}{(\sqrt{x} )^{2} - (\sqrt{x - 2} )^{2} } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{(x) - (x - 2) } = \frac{4(\sqrt{x} + \sqrt{x - 2})}{ 2 } = 2(\sqrt{x} + \sqrt{x - 2})[/tex]

Answer is D. 2(√{x} + √{x - 2})

Answer:

F. Hyperbola

Step-by-step explanation:

In each napped, you'll have a parabola, combined they form an hyperbola.

It's one of the various shapes that can be produced by a plane intercepting a right circular cone, as you can see in the attached picture.

Each plane intersection is different, based on the angle and the position it passes through.

I hope that helps.

Answer:

hyperbola

Step-by-step explanation:

apeex

Answer:

What school you go to

Step-by-step explanation:

step by step go catch friend and step by step friends

Answer:

4.6

Step-by-step explanation:

We are given the results of a survey of patients at a hospital of their blood type, categorized by their gender.

We are to find the percentage of patients with blood type AB among all patients.

Number of patients with blood type AB = 33

Total number of patients = 714

Percent of patients with blood type AB = [tex] \frac { 3 3 } { 7 1 4 } \times 100 [/tex] = 4.6