In 1995, wolves were introduced into Yellowstone Park.



The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.



By what percent does the number of wolves change each year?

The point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

To find the location of a point on the number line that is a certain fraction of the way from one point to another, we can use the concept of linear interpolation.

In this case, we want to find the point that is 5/7 of the way from A = -4 to B = 17.

To calculate this point, we can use the formula:

Point = A + (Fraction × Distance)

where A is the starting point, Fraction is the desired fraction, and Distance is the total distance between the two points.

In this case, A = -4, B = 17, and the desired fraction is 5/7. The distance between A and B can be calculated as:

Distance = B - A = 17 - (-4) = 21

Plugging in these values, we have:

Point = -4 + (5/7 × 21)

Simplifying the expression, we get:

Point = -4 + (15/7) = -4 + 2.1429 ≈ -1.8571

Therefore, the point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

Among the given options, none of them match the calculated value. However, the closest option is C. 9.

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Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Answer:

-------------------

Divide 1/6 by 4:

Each piece is 1/24 of a pound.

The absolute maximum and minimum values obtained from the graph of the functions are;

Absolute maximum of g; [1, 4]

Absolute minimum of g; [4, -3]

Absolute maximum h; [4, 3]

Absolute minimum of h; (-4, -5)

The absolute maximum and minimum of a function are the coordinates of the highest and lowest points on the graph of the function, within the specified domain.

The points on the graph of the functions indicates that the maximum and minimum values of the functions are;

Graph of g; Absolute maximum of g = (1, 4)

Absolute minimum of g ; [4, -3]

Graph of h

Absolute maximum of h; [4, 3]

Absolute minimum of h; (-4, -5)

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Answer: - 27

Step-by-step explanation:

Plug in for x = 3 and y = -6

I'll start with x to make it easier.

Plugging in x =3

[tex]\sqrt{x^4}[/tex]

Means that first we find x^4, and take the square root of that result.

1. Find x^4

x = 3

3^4 = 3 * 3 * 3 *3  = 81

2. Take the square root of x^4

Square root of 81 = 9

So [tex]\sqrt{x^4}[/tex]  = 9

Plugging in y = -6

Let's move onto plugging in y, which appears in the expression  as y²

y = -6

so y²  = -6 * -6 = 36

Putting this together into the expression

[tex]\sqrt{x^4}[/tex] - y²

9 - 36 = -27

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

[tex]w(x)=14\cdot 1.08^{x}[/tex]

w(25) =

[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

The volume of concrete required is

The volume of concrete required is solved by area * thickness

Area of the figure

First section = 20 * 8 = 160

second section = π(R² - r²)/4 = π(16² - 8²)/4 ≈ 151

Third section = 12 * 8 = 96

sum of areas = 160 + 151 + 96 = 407 ft

Volume of concrete required = volume of the shape

= sum of areas * thickness

thickness = 6'' = 0.5

= 407 * 0.5

= 203.5 cubic ft

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The limit of the function As x → - ∞, f(x) → 2.

The limit of a function is the value the function tends to as the independent variable tends to a given value.

Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows

Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.

So, As x → - ∞, f(x) → 2.

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Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.

From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:

12C + 5S = 28 ----(Equation 1)

From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:

14C + 6S = 33 ----(Equation 2)

To solve this system of equations, we can use a method like substitution or elimination.

Let's use the elimination method to eliminate the variable C:

Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:

24C + 10S = 56 ----(Equation 3)

-42C - 18S = -99 ----(Equation 4)

Add Equation 3 and Equation 4:

-18C - 8S = -43

Solve for S:

8S = 43 - 18C

S = (43 - 18C)/8 ----(Equation 5)

Now substitute Equation 5 into Equation 1:

12C + 5((43 - 18C)/8) = 28

Multiply through by 8 to eliminate the fraction:

96C + 215 - 90C = 224

6C = 9

C = 9/6 = 1.5

Substitute the value of C back into Equation 5 to find S:

S = (43 - 18(1.5))/8 = 2.75

Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

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The canoe's actual speed is approximately 9.66 mph at a bearing of 12° south of east.

To determine the canoe's actual speed and direction, we need to consider the vector addition of the canoe's velocity and the current.

Let's start by drawing a diagram to visualize the problem.

We'll use a scale where 1 cm represents 10 mph.

Draw a line segment representing the canoe's velocity of 10 mph at a bearing of 25° south of east.

From the endpoint of the canoe's velocity vector, draw another line segment representing the current's velocity of 2 mph at a bearing of 80° west of south.

Connect the starting point of the canoe's velocity vector with the endpoint of the current's velocity vector to form a triangle.

Next, we can find the resultant velocity (actual speed and direction) of the canoe by calculating the vector sum of the canoe's velocity and the current's velocity.

Using the law of cosines, we can find the magnitude of the resultant velocity:

c² = a² + b² - 2ab [tex]\times[/tex] cos(C)

Where:

a = 10 mph (canoe's velocity)

b = 2 mph (current's velocity)

C = 80° (angle between the velocities)

Substituting the values:

c² = 10² + 2² - 2 [tex]\times[/tex] 10 [tex]\times[/tex] 2 [tex]\times[/tex] cos(80°)

c² = 100 + 4 - 40 [tex]\times[/tex] cos(80°)

Solving for c, the magnitude of the resultant velocity:

c ≈ √(100 + 4 - 40 [tex]\times[/tex] cos(80°))

c ≈ √(104 - 40 [tex]\times[/tex] cos(80°))

To find the direction, we can use the law of sines:

sin(A) / a = sin(C) / c

Where:

A = 25° (angle of the canoe's velocity)

a = 10 mph (magnitude of the canoe's velocity)

C = 80° (angle between the velocities)

c ≈ √(104 - 40 [tex]\times[/tex] cos(80°)) (magnitude of the resultant velocity)

Substituting the values:

sin(25°) / 10 = sin(80°) / √(104 - 40 [tex]\times[/tex] cos(80°))

Solving for sin(80°):

sin(80°) ≈ (sin(25°) [tex]\times[/tex] √(104 - 40 [tex]\times[/tex] cos(80°))) / 10

Finally, we can use the inverse sine function to find the direction:

Direction ≈ arcsin((sin(25°) [tex]\times[/tex]√(104 - 40 [tex]\times[/tex] cos(80°))) / 10)

Calculating the numerical values using a calculator will give us the actual speed and direction of the canoe.

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Answer:

324 cm^3

Step-by-step explanation:

Because this is a triangular prism, we can take the base area times the height. The base area is 9*8/2=36.

The height is 9.

So 36*9=324.

Answer:

324 cm³

Step-by-step explanation:

Area of triangle = 1/2 × base × height

Area of triangle = 1/2 × 9 cm × 8 cm

Area of triangle = 36 cm²

The height of the triangular prism is given as 9 cm.

To find the volume of the triangular prism, we multiply the area of the base triangle by the height of the prism:

Volume of triangular prism = area of base × height

Volume of triangular prism = 36 cm² × 9 cm

Volume of triangular prism = 324 cm³

Therefore, the volume of the triangular prism is 324 cubic centimeters (cm³).

Answer:  Choice 3.

The number of people purchasing coffee each day in a coffee shop

Reason:

It's not possible to have a decimal or fractional amount of people. So we select the value from the set {0,1,2,3,4,...}

On the other hand, it is possible to have a decimal temperature like 98.6 degrees, which means we rule out choice 1. Choices 2, 4, and 5 are a similar story.

The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58

From the question, we have the following parameters that can be used in our computation:

zeros =  5+2i, 5-2i, -1

One such polynomial P(x) can be defined as

P(x) = x³ - 9x² + x + 29.

When this polynomial is multiplied by a costant, the roots and zeros remain the same

Let the constant be 2

So, we have

New P(x) = 2(x³ - 9x² + x + 29)

Evaluate

New P(x) = 2x³ - 18x² + 2x + 58

Hence, the function is P(x) = 2x³ - 18x² + 2x + 58

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Answer:

Yes

Step-by-step explanation:

Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

The width of a rectangle with a length of 72 is 90 inches.

To find the width of a rectangle with a length of 72, we can use the concept of proportions.

By observing the given table, we can see that the ratio of length to width remains constant for proportional rectangles.

Let's calculate the common ratio:

[tex]\( \text{Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{8}{10} = \frac{12}{15} = \frac{24}{30} = \frac{32}{40} \)[/tex]

Now, we can set up a proportion to find the width for a length of 72:

[tex]\( \frac{72}{\text{Width}} = \frac{8}{10} \)[/tex]

Cross-multiplying, we have:

[tex]\( 72 \times 10 = 8 \times \text{Width} \)[/tex]

Simplifying, we get:

[tex]\( 720 = 8 \times \text{Width} \)[/tex]

Dividing both sides by 8, we find:

[tex]\( \text{Width} = \frac{720}{8} = 90 \)[/tex]

Therefore, the width of a rectangle with a length of 72 is 90 inches.

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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(F - G)(x) is equal to -2x - 3 when we subtract G(x) from F(x). Option B

To find (F - G)(x), we subtract G(x) from F(x). Let's substitute the given functions into the expression:

(F - G)(x) = F(x) - G(x)

F(x) = x + 2

G(x) = 3x + 5

Substituting these values, we have:

(F - G)(x) = (x + 2) - (3x + 5)

Now, let's simplify the expression:

(F - G)(x) = x + 2 - 3x - 5

Combining like terms, we get:

(F - G)(x) = -2x - 3

Therefore, the correct answer is -2x - 3.

Option B (-2x - 3) is the correct answer.

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True, the surface area of the cylinder is 100units²

The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.

The surface area of a cylinder is expressed as;

SA = 2πrh + 2πr²

where 2πr² is the area of the bases

2πrh = lateral area

75 = 2 × 3.14 × 6 × r

r = 75/37.68

r = 1.99 unit

base area = 2 × 3.14 × 1.99²

= 25 units ( nearest whole number)

The surface area = 75+25

= 100units²

Therefore the surface area of the cylinder to nearest whole number is 100units².

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The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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Step-by-step explanation:

100% = 575

1% = 575÷100 = 5.75

60% = 5.75 × 60 = 345

The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.

To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.

From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.

Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.

To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.

Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:

18 units * $200 * 2 = $7,200.

Therefore, the cost is $7,200.

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

Answer:

180 marbles in a 7-pound bag.

Answer:

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

Step-by-step explanation:

Para calcular el capital final, utilizaremos la fórmula del interés compuesto:

Capital Final = Capital Inicial * (1 + Tasa de Interés)^Tiempo

Donde:

Capital Inicial = $1200

Tasa de Interés = 8% = 0.08 (expresada como decimal)

Tiempo = 8 años

Sustituyendo los valores en la fórmula:

Capital Final = $1200 * (1 + 0.08)^8

Calculando el resultado:

Capital Final = $1200 * (1.08)^8 ≈ $2061.68

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

Answer:

  both are rectangles

Step-by-step explanation:

You want to know what two quadrilaterals each having four right angles have in common.

A quadrilateral with four right angles is called a "rectangle." Each of the figures is a rectangle.

__

Additional comment

There are more general classifications that also apply. The figures are made from line segments connected end-to-end that enclose a space, so they are simple polygons. The adjacent right angles mean the figures have opposite sides parallel, so are parallelograms.

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Type the expressions as radicals y^5/2.

[tex] \sqrt{ {y}^{5} } [/tex]

Radical:- The ( √ ) symbol that is used to denote square root or nth roots...

It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-

[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]

Generally, using the power rule of exponents:

[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]

Let's take an example to understand better:

• convertion between radicals and rational exponents:

[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]

Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..

[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]

As , √ denotes ½ ..

The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).

The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

To explain this, let's break it down:

The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.

Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).

Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].

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