The cosine ratio is the ___ side over the hypotenuse

Exponential functions model growth patterns such as population growth under ideal conditions, while the logistic model accounts for resource limits. The standard exponential equation is Y=abˣ, while logistic growth has a more complex form that includes the carrying capacity.

Exponential functions model various real-world phenomena in which growth occurs at a rate proportional to the current amount. For example, in natural populations, exponential growth is observed when resources are abundant and organisms can reproduce without constraints.

The standard form of an exponential function is Y = abx, where 'a' is the initial amount, 'b' is the growth factor, and 'x' represents time or another independent variable. In the context of population growth, 'a' would be the initial population size, 'b' is the growth rate per time period, and 'x' is the time elapsed.

Logistic growth is another pattern that is observed when resources become limited. It starts off similar to exponential growth but eventually slows down as the population reaches the carrying capacity of the environment.

Environmental conditions represented by the exponential growth model imply unlimited resources and space, whereas the logistic growth model includes the effects of limiting factors such as space, food, and other resources.

Answer: 120 people

Step-by-step explanation: To do this problem, you want to find common denominators. The lowest common denominator is 900. So to get the denominator to 900 from 30, multiply it by 30. 30 x 30=900. Multiply 4 by 30. 4 x 30=120. Another way to do this is to set up a proportion. It would be 4/30=x/900. Cross multiply and solve for x. 3600=30x. X=120.

Answer:

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x

Step-by-step explanation:

Let

EM -----> the distance between the Earth and the Moon.

y -----> the distance between the Sun and the Moon.

we know that

In the right triangle of the figure

The sine of angle x is equal to divide the opposite side to angle x (distance between the Earth and the Moon.) by the hypotenuse ( distance between the Sun and the Moon)

so

sin(x)=EM/y

Solve for EM

EM=(y)sin(x)

therefore

The distance between the Earth and the Moon is equal to the distance between the Sun and the Moon multiplied by the sine of angle x

Answer:

C. (4y -1)(3y+2)

Step-by-step explanation:

12 y^2 + 5 y - 2

12 y^2 + (-3+8) y - 2

12 y^2 - 3y + 8y - 2

3y(4y-1)+2(4y-1)

(4y-1)(3y+2)

Answer:

6

Step-by-step explanation:

Because AD and BC Are congruent so when you add them that would equal the diameter of the rapper.

Option D is correct. The smallest diameter of wrapper that will fit the candy bar is 6

According to the attached figure - the cross-sectional view of candy bar ABC. If a cylindrical container is created from the cross-section, then the diameter of the cylindrical container formed from the cross-section will be the side AC.

From the figure, AD = DC and AC = AD + DC

Given the segment AD = 3cm

AC = AD + AD (Since AD = DC)

AC = 2AD

AC = 2(3)

AC = 6

This shows that the smallest diameter of wrapper that will fit the candy bar is 6. Option D is correct

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Answer:

f(x) = -1.25

Step-by-step explanation:

Substitute x with -5, so our equation would look this:

Note: We were already given the value of x

f(x) = 1/4(-5)

Multiply 1/4 and -5:

1/4 * -5 = -1.25

So, our answer would be -1.25

-1.25

In order to find the answer to your question, we're going to need to plug in a number to the variable x.

We know that x = -5

This means that whenever you see x, you would replace it with what it equals to. In this case, we would plug in -5 to x, since that's what it equals to.

Your equation would look like this:

[tex]\frac{1}{4}( -5)[/tex]

Now, you would solve to get your answer.

[tex]\frac{1}{4} (-5)=-1.25\\\\\text{1/4 is the same as 0.25} \\\\0.25(-5)=-1.25[/tex]

Once you're done solving, you should get -1.25

This means that f(x) = -1.25

For this case we must factor the following expression:[tex]x ^ 2-12x-20[/tex]

We have that the expression cannot be factored with rational numbers.

On the other hand, we can find the zeros, applying the quadratic formula we have:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -12\\c = -20[/tex]

[tex]x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}[/tex]

Thus, the roots would be:

[tex]x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}[/tex]

Answer:

the expression cannot be factored with rational numbers.

The factors of the given quadratic expression are: (x - 2) and (x - 10)

The quadratic expression is given as:

x² - 12x - 20

Now, to get the factors, we need to write as follows:

x² - 10x - 2x + 20

This can be factorized to get:

x(x - 10) - 2(x - 10)

= (x - 2)(x - 10)

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Answer:

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Step-by-step explanation:

The sum of two rational expressions is done in the following way:

[tex]\frac{a}{b}+\frac{c}{d} = \frac{a*d + c*b}{b*d}[/tex]

In this case we have the following rational expressions

[tex]\frac{3x}{x+9} + \frac{x}{x-4}[/tex]

So:

[tex]a=3x\\d=(x+9)\\c=x\\d=(x-4)[/tex]

Therefore

[tex]\frac{3x}{x+9} + \frac{x}{x-4}=\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}[/tex]

simplifying we obtain:

[tex]\frac{3x(x-4)+x(x+9)}{(x+9)(x-4)}=\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}\\\\\frac{3x^2-12x+x^2+9x}{(x+9)(x-4)}=\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Answer:

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

Step-by-step explanation:

We are given the following expression and we are to find the sum of this rational expression below:

[tex] \frac { 3 x } { x + 9 } + \frac { x } { x - 4 } [/tex]

Taking LCM of it to get:

[tex]\frac{3x}{x+9} =\frac{3x(x-4)}{(x+9)(x-4)}[/tex]

[tex]\frac{x}{x-4} =\frac{x(x+9)}{(x-4)(x+9)}[/tex]

[tex]\frac{3x(x-4)}{(x+9)(x-4)}+\frac{x(x+9)}{(x-4)(x+9)}[/tex]

[tex]\frac{3x(x-4)+x(x-9)}{(x+9)(x-4)}[/tex]

[tex]\frac{4x^2-3x}{(x+9)(x-4)}[/tex]

let's recall that, arc's angle measures come from the central angle they're in.

if this intercepted arc is 80°, and is intercepted by an angle stemming from the center, namely a central angle, then the angle is also 80°.  Check the picture below.

If angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is  80°.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that angle with its vertex at the center of a circle intercepts an 80° arc of that circle

We have to find the measure of the angle.

When an angle is formed at the center of a circle, it intercepts an arc of the circle that is equal in measure to the angle.

Since the given angle intercepts an 80° arc of the circle, we know that its measure is also 80°. so the measure of the angle is 80°.

Hence, if angle with its vertex at the center of a circle intercepts an 80° arc of that circle then the measure of the angle is  80°.

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Answer:

10a-4b+2c

Step-by-step explanation:

Answer:

10a -4b +2c

Step-by-step explanation:

6a-4b+c and 4a+c

6a-4b+c + 4a+c

Combine like terms

6a+4a   + (-4b) + c+c

10a -4b +2c

Answer:

QT = RT

Step-by-step explanation:

When drawing triangle PQR the perpendicular bisector cuts the triangle in half, which results in two sides that are congruent. This makes QT and RT congruent.

Based on the triangle QPR  option C) PQ = PR and A) QT = RT

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In QPR

∠Q = ∠R (∵ PT is a bisector)

∴QT = RT (∵ PT is a bisector of QR)

PT is a common  between PQT and RQT

∴PQ = PR ( by congruent part of congruent triangle)

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Answer:

1/34 or 2.94%

Step-by-step explanation:

There is only one paper that has your name on it out of 34 papers. So there is a 1 out of 34 chance your name is drawn.

You have write this as a fraction 1/34 or as a percentage 2.94%

Final answer:

The probability that your name will be drawn first in a contest with 34 entrants is 1 in 34, based on the principle of equally likely outcomes in a random selection process.

Explanation:

The probability of any one person being chosen first in a random draw from a group of 34 people is based on the principle that each person has an equal chance of being selected. To determine this probability, we use the concept of equally likely outcomes, which suggests that each person has 1 chance in the total number of people competing. Therefore, the probability that your name will be drawn first from a group of 34 people is 1 in 34.

Answer:

The correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Step-by-step explanation:

It is given that,

(x² - 1)² - (x² - 1) + 24 = 0

To find the correct answer

Substitute u = x² - 1

The equation becomes,

u² - 11u + 24 = 0 Where u = (x² - 1)

Therefore the correct answer is first option

u² - 11u + 24 = 0

When u = (x² - 1)

Answer:

u² - 11u + 24 = 0 is equivalent to (x²-1)² - 11(x²-1) + 24 = 0

Step-by-step explanation:

(x²-1)² - 11(x²-1) + 24 = 0

Evaluate each equation by substituting the value of u to match the equation above.

1) u² - 11u + 24 = 0 where u = (x² - 1)

(x²-1)² - 11(x²-1) + 24 = 0

This equation matches (x²-1)² - 11(x²-1) + 24 = 0

2) (u²)² - 11(u²) + 24 where u = (x² - 1)

[(x²-1)²]² - 11(x²-1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

3) u² + 1 - 11u +24 = 0 where u = (x² - 1)

(x² - 1)² + 1 - 11(x²-1) + 24 = 0

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

4) (u² - 1)² - 11(u² - 1) + 24 where u = (x² - 1)

[(x²-1)²-1]² - 11(u² - 1)² + 24

This equation does not match (x²-1)² - 11(x²-1) + 24 = 0

Therefore, the first quadratic equation is equivalent to (x²-1)² - 11(x²-1) + 24 =0.

!!

Answer:

[tex]a_{20} = 12+3(20-1)[/tex]

Step-by-step explanation:

Given a quadratic equation [tex]ax^2+bx+c=0[/tex], the two solution (if they exist) are given by the formula

[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In your case, the coefficients are

[tex]a=3,\quad b=5,\quad c=2[/tex]

So the quadratic formula becomes

[tex]x_{1,2}=\dfrac{-5\pm\sqrt{25-24}}{6} = \dfrac{-5\pm 1}{6}[/tex]

So, the two solutions are

[tex]x_1 = \dfrac{-5+1}{6}=-\dfrac{4}{6}=-\dfrac{2}{3}[/tex]

[tex]x_2 = \dfrac{-5-1}{6}=-\dfrac{6}{6}=-1[/tex]

Answer:

Mechanic A worked for 5 hours and Mechanic B worked for 15 hours

I hope my answer and explanation helped!

okay to get started you need to make a system of equations:

x= number of hours worked by mechanic A

y= number of hours worked by mechanic B

x + y= 20

95x + 60y= 1375

substitute in an equation:

x + y= 20

y= 20- x

95x + 60(20-x)=1375

Solve for x

95x + 1200 - 60x=1375

35x =175

x= 5

plug in x to solve for y

x + y= 20

5 + y= 20

y=15

Check work

then you're done :D

WHAT IS A COMPLEMENTARY ANGLE?

Complementary comes from the word complement. When two angles sum a total of 90°, they 'complement' each other. A complementary angle is a combination of two angles whose sum is equal to 90°.

BACK TO THE QUESTION

The question is asking what the measure of the other angle is. The given angle is 28°.

HOW TO FIND YOUR ANSWER

When you're given the measure of one of the angles, it's easy to find the other. All you have to do is subtract the measure of the angle from 90°.

In this question, you are given that the angle is 28°. That means you have to subtract 28 from 90.

[tex]90\°-28\°=62\°[/tex]

a. 14° ✘

b. 28° ✘

c. 62° ✓

d. 152° ✘

The answer to your question is 62°, also known as choice c.

Answer:

that the linear scale factor is  4:3 which can be written as 4/3

the volume scale factor will be:

(4/3)^3

D. 64:27

Step-by-step explanation:

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Put the given y-intercept b = 7 and the coordinates of the point (-2, 1) to the equation:

[tex]1=-2m+7[/tex]          subtract 7 from both sides

[tex]-6=-2m[/tex]       divide both sides by (-2)

[tex]3=m\to m=3[/tex]

We have the equation:

[tex]y=3x+7[/tex]

Convert it to the general form [tex]Ax+By+C=0[/tex]:

[tex]y=3x+7[/tex]              subtract 3x and 7 from both sides

[tex]-3x+y-7=0[/tex]           change the signs

[tex]3x-y+7=0[/tex]

Answer:

C. anus

Step-by-step explanation:

The digestive system ends at the anus.

Therefore, it does not end in the colon, large intestine, or small intestine.

The digestive system starts when you take in food and ends in the anus.

Answer:

Radius of circle is 4

Step-by-step explanation:

The standard equation of circle is

(x-h)^2+(y-k)^2=r^2

where (h,k) is the center and r is the radius.

We are given:

(x² - 10x + 25) + (y² - 16y + 64) = 16

we know that a^2-2ab+b^2 =(a-b)^2

Using the above formula and converting the given equation into standard form, we get:

(x-5)^2+(y-8)^2=(4)^2

So, radius of circle is 4.

Answer:

125.59 feet

Step-by-step explanation:

(see attached)

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2[/tex]

Answer:

A = 95.03in² or 95.03 ( rounded to the nearest hundredth )

Step-by-step explanation:

The approximate area of a circle that has a diameter of 11 inches, rounded to the nearest hundredth is 95.03.

Formula: A=1/4πd²

A=1

4πd^2=95.03.

4·π·11^2≈95.03318in²

[tex]

-3(2x-5)<5(2-x) \\

-6x+15<10-5x \\

-x<-5 \\

\boxed{x>5}

[/tex]

Hope this helps.

r3t40

Answer:

611.04 mm³

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 30.4 and h = 20.1, hence

A = 30.4 × 20.1 = 611.04 mm³

Answer:

611.04 mm³

Step-by-step explanation:

Formula for finding the area of a parallelogram: A = B * H

B is base, H is height, * is multiply.

_________________________________________________

The area of the parallelogram pictured: 611.04 mm³

A=bh=30.4·20.1=611.04

_________________________________________________

Answer:

its a)the first sequence is geometric bc of the common ratio of 2. the second sequence is arithmetic bc of the common difference of 7.

Option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. A recursive pattern rule is a pattern rule that tells you the start number of a pattern and how the pattern continues.

For the given situation,

First sequence: 5, 10, 20, 40..

Second sequence: 8, 15, 22, 29, ...

Now consider the first sequence: 5, 10, 20, 40..

Here, when we divide the second number by first number, we get the common ratio as 2.

⇒ [tex]\frac{10}{5}=2[/tex]

⇒ [tex]\frac{20}{10}=2[/tex]

⇒ [tex]\frac{40}{20}=2[/tex]

Thus the first sequence follows a geometric progression with common ratio 2.

Now consider the second sequence: 8, 15, 22, 29, ...

Here, when we subtract the first term is subtracted from the second term, the common difference is 7.

⇒ [tex]15-8=7[/tex]

⇒ [tex]22-18=7[/tex]

⇒ [tex]29-22=7[/tex]

Hence we can conclude that option (A) the first sequence is geometric because there is a common ratio of 2 and the second sequence is arithmetic because there is a common difference of 7 is the correct answer.

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Answer:

It shows that  h varies directly with V and inversely with l and w.

Step-by-step explanation:

The given equation is:

h = V/lw

It shows that  h varies directly with V and inversely with l and w.

Inversely means if the value of one entity increases, the value of second entity decreases or vice versa. Directly related means as one quantity increases, another quantity increases at the same rate

We can show it as h=1/lw which means  h is in inverse relation with l and w and in direct relation with V....