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`.



According to the model, about how many years will it take for the population to reach `500` wolves?

Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.

Answer:

y = (2x + 5)(2x + 3)

Step-by-step explanation:

y = 4x² + 16x + 15

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 4 × 15 = 60 and sum = + 16

the factors are + 10 and + 6

use these factors to split the x- term

y = 4x² + 10x + 6x + 15 ( factor the first/second and third/fourth terms )

y = 2x(2x + 5) + 3(2x + 5) ← factor out (2x + 5) from each term

y = (2x + 5)(2x + 3)

since multiplication is commutative , then could be

y = (2x + 3)(2x + 5)

a : 10<x<=20

b: 20<x<=30

4048 yards is the answer

Step-by-step explanation:

2.3 × 1760

The linear function for this case is:

f(x) = 5,000*x + 7,000

The general linear function is written as:

f(x) = a*x + b

Where a is the slope and b is the y-intercept.

Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:

f(x)= a*x + 7,000

Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:

f(x) = 5,000*x + 7,000

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Answer:

V = (3.14)(4.25)²(6)

Step-by-step explanation:

Answer:

y = 5

Step-by-step explanation:

[tex]14y-7y=35\\7y=35\\y=5[/tex]

14 minus 7 is 7

7Y is equal to 35

divide both sides by 7 is equal to 5

Answer:

The formula for calculating the future value (VF) of a periodic sum of money is:

VF = P * [(1 + r) n - 1] / r

where:

   VF is the future value (the total amount in the savings account)

   P is the periodic amount (monthly deposit)

   r is the periodic interest rate (annual interest rate divided by the number of periods in the year)

   n is the total number of periods (months)

In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).

Using these values in the formula, we can calculate the future value (VF):

VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025

Now let’s calculate this:

VF = 110 * [(1.0025) 36 - 1] / 0.0025

110 * (1.0965726572 - 1) / 0.0025

110 * 0.0965726572 / 0.0025

So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.

Step-by-step explanation:

WU is the perpendicular bisector of TV and W is the midpoint of TV.

Statements:

WU is the perpendicular bisector of TV.

W is the midpoint of TV.

TW = VW.

∠ZTWU and ∠ZVWU are right angles.

∠ZTWU ≅ ∠LVWU.

WU = WU.

∠ATWU ≅ ∠AVWU.

TU = VU.

Reasons:

Given.

Definition of the perpendicular bisector: It divides a segment into two congruent parts, and W is the midpoint of TV.

Definition of midpoint: The segment TW is congruent to VW because W is the midpoint of TV.

Given that WU is the perpendicular bisector, it means that ∠ZTWU and ∠ZVWU are right angles.

All right angles are congruent.

Reflexive property of congruence: Any segment or angle is congruent to itself.

Corresponding parts of congruent triangles are congruent (CPCTC): Since ∠ATWU and ∠AVWU are corresponding parts of congruent triangles, they are congruent.

Corresponding parts of congruent triangles are congruent (CPCTC): Since TU and VU are corresponding parts of congruent triangles, they are congruent.

Therefore, the correct statements and reasons are:

Statements:

WU is the perpendicular bisector of TV.

W is the midpoint of TV.

TW = VW.

∠ZTWU and ∠ZVWU are right angles.

∠ZTWU ≅ ∠LVWU.

WU = WU.

∠ATWU ≅ ∠AVWU.

TU = VU.

Reasons:

Given.

Definition of the perpendicular bisector.

Definition of midpoint.

Given.

All right angles are congruent.

Reflexive property of congruence.

CPCTC.

CPCTC.

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a. The open interval on which the function is increasing is [-2/3, 0].

The open intervals on which the function is decreasing are [-∞, -2/3] and [0, -∞].

b. The function's has a local maximum at (0, 0) and a local minimum at (-2/3, -4/27).

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of the given function, we can reasonably infer and logically deduce that it is decreasing over the following open intervals:

increasing = [-2/3, 0].

decreasing = [-∞, -2/3] and [0, -∞].

Part b.

The local minimum of a graph is the point on the graph of a function where it changes from a decreasing function to an increasing function, which is given by this ordered pair (-2/3, -4/27);

h(x) = -x³ - x²

h'(x) = -3x² - 2x

0 = -3x² - 2x

3x² = -2x

3x = -2

x = -2/3

h(-2/3) = -(-2/3)³ - (-2/3)²

h(-2/3) = -4/27.

For the local maximum, we have:

(0, 0)

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Case 1: SE = s / √500

Case 2: SE = s / √5,000

Case 3: SE = s / √50,000

To find the standard error of the mean in each of the given cases, we can use the formula:

Standard Error (SE) = population standard deviation / square root of sample size

However, since the population standard deviation is not provided, we'll need to use an estimated value. We'll assume the population standard deviation is unknown and use the sample standard deviation as an estimate.

Given that the sample size is 44 and the population mean (μ) is 8, we'll calculate the standard deviation for each case:

Case 1: Sample size (n) = 500

The sample size (500) is larger than 5% of the population (44), so we can assume it's a large enough sample. In this case, we'll use the standard formula for the standard error of the mean without the finite population correction factor:

SE = sample standard deviation / square root of sample size

= s / √n

Case 2: Sample size (n) = 5,000

Similar to Case 1, the sample size (5,000) is larger than 5% of the population (44), so we'll use the standard formula without the finite population correction factor:

SE = s / √n

Case 3: Sample size (n) = 50,000

In this case, the sample size (50,000) is much larger than the population size (44), which means we have a large enough sample. Therefore, we'll also use the standard formula without the finite population correction factor:

SE = s / √n

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Answer:

77 units^2

Step-by-step explanation:

Since the formula for the area of a parallelogram is Area = Base x Height, you can multiply the Base (11) by the Height (7)

So, A = (7) x (11) = 77 units^2

The 8 in this case is not necessary. You only need the base and height. Hope this helps!

Answer:

The solutions to the quadratic equation 0 = -3x² - 4x + 5 in simplest radical form are x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

To find the solutions to the quadratic equation 0 = -3x² - 4x + 5, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Comparing the equation to the standard quadratic form ax² + bx + c = 0, we have a = -3, b = -4, and c = 5.

Plugging these values into the quadratic formula, we get:

x = (-(-4) ± √((-4)² - 4(-3)(5))) / (2(-3))

= (4 ± √(16 + 60)) / (-6)

= (4 ± √76) / (-6)

= (4 ± 2√19) / (-6)

= -2/3 ± (1/3)√19

Therefore, the solutions to the quadratic equation are:

x = -2/3 + (1/3)√19 and x = -2/3 - (1/3)√19

In simplest radical form, the solutions are:

x = (-2 + √19) / 3 and x = (-2 - √19) / 3.

These expressions cannot be further simplified since the square root of 19 is not a perfect square.

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Answer:

[tex]3^{-14}[/tex] or [tex]\displaystyle \frac{1}{3^{14}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{3^{-10}}{3^4*3^0}=\frac{3^{-10}}{3^4}=3^{-10-4}=3^{-14}[/tex]

[tex]{\huge{\blue{\tt{Step\:by\:step\:solution}}}}[/tex]

4.1 To convert the mass of the self-raising flour to kg, we can divide the mass by 1000, since there are 1000 grams in a kilogram:

2 500 g ÷ 1000 = 2.5 kg

So the mass of the self-raising flour is 2.5 kg.

4.2 To determine the number of cups of bran flour needed to bake 400 g of rusks, we can use a proportion:

800 g of rusks requires 10 cups of bran flour

400 g of rusks requires x cups of bran flour

We can set up the proportion as:

800 g ÷ 10 cups = 400 g ÷ x cups

Cross-multiplying, we get:

800 g x cups = 10 cups x 400 g

Simplifying, we get:

x = 5 cups

So 5 cups of bran flour are needed to bake 400 g of rusks.

4.3 To write the ratio of raisins to butter in simplified form, we can divide both quantities by their greatest common factor. The greatest common factor of 200 g and 1 000 g is 200 g, so we can divide both by 200 g:

200 g ÷ 200 g = 1

1 000 g ÷ 200 g = 5

So the simplified ratio of raisins to butter is 1:5.

4.4 The rusks were placed in the oven to bake at 14:40. In words, this time is "twenty to three in the afternoon" (assuming that the time is given in a 12-hour clock format).

f(0) = -3

I believe, since the graph has a closed circle/point at (0,-3), f(0) should equal -3. Also, the graph 3x-3 has a domain of x>=0.

However, in terms of limits, the limit approaching x-->0 does not exist since the left and right limits do not equal one another.

Hope this helps.

Answer:

y=2x-6

Step-by-step explanation:

y+4=-2(x-1)

Since the slope intercept form is in the form of:

y=mx+c

Making above equation in this form.

y+4=-2(x-1)

opening bracket

y+4=2x-2

subtracting both side by 4.

y+4-4=2x-2-4

y=2x-6

This equation is the slope intercept form.

Answer:

A scale is just another way of saying what we want to count by on our graph.

Step-by-step explanation:

A "scale" is just another way of saying what we want to count by on our graph. The scale is the range of values that are shown on the axis of a graph. It helps to determine the size and spacing of the intervals or ticks on the axis. The scale can be in different units, such as time, distance, weight, or any other measurable quantity depending on the type of data being represented in the graph.

The x-coordinate of the vertex is given by h = -2 and the equation of the axis of symmetry is x = -2.

Given function is H(x) = -(x + 2)² + 8.

The axis of symmetry of a quadratic function y = ax² + bx + c is defined by x = -b/2a.

So, let's solve the problem as follows:

To find the axis of symmetry, we need to convert the given function into standard form y = a(x - h)² + k.

We can do this by completing the square.

For that, we have

H(x) = -(x + 2)² + 8H(x)

= -1(x² + 4x + 4) + 8H(x)

= -1(x + 2)² + 8

The standard form is y = a(x - h)² + k, so the given function is y = -1(x + 2)² + 8.

The vertex form of a quadratic equation is y = a(x - h)² + k

Where(h, k) is the vertex.

The vertex form of the given function H(x) = -(x + 2)² + 8 can be calculated as follows:  

y = a(x - h)² + k

The vertex form is y = a(x - h)² + k.

Where the vertex form of the given function is:

y = -1(x + 2)² + 8.

Since the vertex form is y = a(x - h)² + k the vertex form of the given function is y = a(x + 2)² + 8 and (h, k) = (-2, 8).

Vertex is given by h = -2.

Axis of symmetry is x = -2.

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Step-by-step explanation:  

C

Answer:

y = (-1/6)x represents a proportional relationship.

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90

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