The wolf population in a certain region was monitored over several years for a project aimed at
boosting the number of wolves. The number of wolves can be modeled by the function
f(x)=41x +7 where x is the number of years since 2005. Using algebraic techniques, find the
value of x so that f(x) = 89.

a.  There are 4 sample points in the sample space.

a) There are 4 sample points in the sample space.

b) The tree diagram and sample space are:

HH (two heads)

HT (one head, one tail)

TH (one head, one tail)

TT (two tails)

c) The probability that no tails are tossed (two heads) is 1/4 or 0.25.

d) The probability that exactly one tail is tossed (HT or TH) is 1/2 or 0.5.

e) The probability that two tails are tossed is 1/4 or 0.25.

f) The probability that at least one tail is tossed (HT, TH, or TT) is 3/4 or 0.75.

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Answer:

-36

Step-by-step explanation:

-1/2x<18

multiply each term by LCM=2

-1/2x×2<18×2

the 2on the left hand side will cancel each other leaving

-x <36

divide both sides by -1

-x/-1>36/-1

(note the equality sign changes because following the laws when you divide by a negative number the sign will change

X>-36

Answer:

Step-by-step explanation:

x>-36 is the anwser brainlist whould be aprecited and verifed

The number of birds in Mrs. Tillman's yard depends on the number of birdhouses in a linear fashion, with each birdhouse containing 8 birds

To find the number of birds (b) in a given number of bird houses (h), we can use the formula: b = 8h

Now, we can complete the table:

Number of bird houses (h) Number of birds (b)

1 8

2 16

3 24

4 32

5 40

So, the number of birds in Mrs. Tillman's yard depends on the number of birdhouses in a linear fashion, with each birdhouse containing 8 birds.

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Mrs. Tillman has bird houses in her yard, with eight birds living in each bird house. Complete the table to show how the number of birds (b) depends on the number of bird houses (h):

Number of bird houses (h) Number of birds (b)

1

2

3

4

5

The horizontal asymptotes of the function is y = 0 and the y-intercepts is (0, 1).

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In this problem, the graph of the function f(x) = (1/4)ˣ is attached below the question and the characteristics of the graph are;

1. The domain of the function is {x|x ∈ R}

2. The range of the function is {y|y > 0}

3. The horizontal asymptotes is y = 0

4. The x-intercepts does not exists

5. The y-intercepts are (0, 1)

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Answer:

O (x + 1)2 + (y + 2)² = 9

Step-by-step explanation:

This is because the distance between points A and B is 3 units, and the distance between points B and C is 4 units, making the triangle a 3-4-5 right triangle. Point B is located at (-1, 1), which is 3 units away from point A (-1, -2) and 4 units away from point C (-5, 1). Therefore, the circle with center (-1, -2) and radius 3 would pass through point B, and its equation would be:

(x + 1)2 + (y + 2)² = 3²

(x + 1)2 + (y + 2)² = 9

The accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

The accounting equation is:

Assets = Liabilities + Capital

(a) Commenced business with cash of Rs. 1,00,000 and Machine of Rs. 50,000.

Assets = Cash + Machine = Rs. 1,00,000 + Rs. 50,000 = Rs. 1,50,000

(b) Purchased goods for cash Rs. 30,000 and credit Rs. 10,000.

Assets = Cash + Inventory = Rs. 1,30,000

Liabilities = Accounts Payable = Rs. 10,000

(c) Sold goods for cash Rs. 25,000 and credit Rs. 15,000.

Assets = Cash + Accounts Receivable + Inventory = Rs. 1,70,000

Liabilities = Accounts Payable = Rs. 10,000

(d) Goods taken by the owner for private use Rs. 2,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,68,000

(e) Cash paid to creditors Rs 8,000.

Assets = Cash + Accounts Receivable + Inventory - Drawings = Rs. 1,60,000

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

(f) Cash received from debtors Rs. 14,500 in full settlement.

Assets = Cash + Inventory - Drawings = Rs. 1,74,500

Liabilities = Accounts Payable - Rs. 8,000 = Rs. 2,000

Capital = Rs. 1,70,500

(g) Received a loan of Rs. 5,000 from Mr. Dipendra.

Assets = Cash + Inventory - Drawings = Rs. 1,79,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 1,74,500

(h) He introduced additional capital Rs. 40,000.

Assets = Cash + Inventory - Drawings = Rs. 2,19,500

Liabilities = Accounts Payable - Rs. 8,000 + Loan Payable Rs. 5,000 = Rs. 1,000

Capital = Rs. 2,10,500

Therefore, the accounting equation is:

Assets = Rs. 2,19,500

Liabilities = Rs. 1,000

Capital = Rs. 2,10,500

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Answer:

Part A   ---->    2

Part B   ---->     2 (2x - 1) (x + 5)

Part C   ----->    See explanation below

Step-by-step explanation:

Given expression is
4x² + 18x - 10

Part A

The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder

To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5

The  prime factor common to all 3 is 2

Therefore the GCF of the expression is 2

Part B

The factored expression can be obtained by factoring out the GCF

4x² + 18x - 10 = 2(2x² + 9x - 5)

We can further factor the term in parentheses:
2x² + 9x - 5

To do this,

Break the expression into groups:

= (2x² - x) + (10x - 5)

Factor x from 2x² - x:     x(2x - 1)

Factor 5 from 10x - 5:    5(2x - 1)

Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)

Factor out the common term 2x -1 to get
(2x - 1)(x + 5)

Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)

Part C
Checking if factorization is correct

Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5

= 2x² + 10x  -1x -5

= 2x² + 9x - 5

Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5

= 4x² + 18x + 10

which is the original expression

So the factorization is correct

The outlier does not affect the mode

The outlier will increase the mean.

The outlier will not affect the median.

The outlier will increase the mean because  it will significantly increase the sum of the values.

The presence of an outlier will not affect the median, as it only changes the position of the middle value.

The mode is the value that occurs most frequently in a data set. In this case, the mode will not be affected because the outlier is not the most frequent in the data set and only appears once.

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Answer:

see below

Step-by-step explanation:

The Reason for #1 is literally GIVEN to you.

Statement #2: Since the Base Angles of an isosceles triangle are congruent, this statement should be ∠CAB≅∠CBA.

Reason #3: Notice that the statement repeats itself (AB=AB). This demonstrates the REFLEXIVE property.

Reason #4: (Clue) Note which items have been Given or Proven congruent and use it as the triangle congruence property. It helps to actually mark them. Your choices are SSS, SAS, ASA, and AAS.

Reason #5: (Clue) Since the triangles of which AM and BN are of part are now proven congruent, these Corresponding Parts are Congruent as well.

The statement that is not true is: C. The translation of a line is a pair of parallel lines.

In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.

Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.

In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.

The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.

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The probability of landing on red is given by the number of red sections divided by the total number of sections. In this case, there are 2 red sections out of a total of 6 sections. Therefore, the probability of landing on red is:

P(red) = 2/6 = 1/3

So the probability of landing on red is 1/3.

To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.

For the 7 oz bag, the price per ounce is:

1.10 / 7 = 0.1571

For the 9 oz bag, the price per ounce is:

1.46 / 9 = 0.1622

Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.

______________________________

______________________________

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.

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Note tha given the above trigonometric expression, the solution is

x = 2π/3 or 4π/3

We will start by simplifing the equation by moving all the terms involving sin (x/2) to one side..

2sin (x  /2) = √(3)

Then, we can solve for sin(x/2) by dividing both sides by  two  

sin (x /2) = √(3)/2

This is true when x/2 is π /3 or 2π/3, since these are the values where

sin  (  π/3) = √(3)/2 and

sin  (2π/3) = √(3)/2.

To find the values of x, we multiply these solutions by two

x = 2pi/3 or 4pi/3

Since we need to make sure that these solutions are in the given interval (0, 2π)

 both solutions are in the interval, so our final answer is  

x = 2π/3 or 4 π/3

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Stan used 19/40 of a gallon of gasoline.

Given that;

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.

Hence, It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

Now, After he mowed, 1/4 of a gallon was left in the tank.

Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Thus, the total amount of gasoline Stan used is, 19/40 of a gallon

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The surface area of the triangular prism is given as follows:

S = 549.15 m².

The surface area of a prism is given by the sum of the areas of all the parts that compose the prism.

The prism for this problem is composed as follows:

Hence the surface area is obtained as follows:

S = 15 x 13 + 15 x 15.81 + 2 x 0.5 x 9 x 13

S = 549.15 m².

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The triangular prism's surface area is given as follows:

S = 549.15 m².

The total area of all the prism's component components determines the prism's surface area.

The following is the structure of the prism for this issue:

rectangle with 15 and 13 meter sides.

rectangle with measurements of 15 and 15.81 meters.

two right triangles with 9 and 13 meter sides. So, the following is how the surface area is determined:

S is equal to 15 x 13 plus 15 x 15.81 and 2 x 0.5 x 9 x 13

S = 549.15 m².

The claim is: Testing if the time spent completing the obstacle course is improved by the energy drink

The null and the alternate hypotheses are added below

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

The table

Also, we have the following statistical question

Is there sufficient evidence at α = 0.05 to conclude that the students did better the second time?

This means that the null hypothesis are

H1: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

The alternate hypothesis is the opposite of the null hypothesis

So, we have

H2: There is no significant difference in the time spent to complete the obstacle course before and after drinking the new energy drink.

Lastly, the claim is that

Testing if the time spent completing the obstacle course is improved by the energy drink

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Answer:

Sure, I can help you with that.

Given:

   * The box is 24 inches long.

   * The width of the box is seven inches less than the height.

   * The volume of the box is 2,880 cubic inches.

To solve:

   * Complete the equation that models the box's volume in terms of its height, x, in inches.

   * Determine if the height of the box can be 15 inches.

Solution:

Let's define the following variables:

* $h$ = the height of the box (in inches)

* $w$ = the width of the box (in inches)

* $l$ = the length of the box (in inches)

We are given that  l=24 and w=h−7. We can use these values to find the volume of the box:

[tex]V = lwh = 24(h - 7)h[/tex]

We can simplify this expression to get the following equation:

[tex]V = 24h^2 - 168h[/tex]

To determine if the height of the box can be 15 inches, we can substitute 15 for $h$ in the equation and see if we get a positive value for the volume.

[tex]V = 24(15)^2 - 168(15) = 2160 - 2490 = -330[/tex]

Since the volume is negative, the height of the box can't be 15 inches.

Therefore, the equation that models the box's volume in terms of its height, x, in inches is [tex]$V = 24x^2 - 168x$[/tex]. Consequently, the size of the box can't be 15 inches.

Answer:

Yes

Step-by-step explanation:

The only answer is height = 15 because the -8 will be rejected

The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.

To calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.

This gives us:

z(360) = (360-350)/18 = 0.56

z(380) = (380-350)/18 = 1.67

We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.

The probability is approximately 0.24.

Therefore, the answer is option (3), 0.24.

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Answer:

x = 65

Step-by-step explanation:

let the number be 'x'.

If 86 is added to a number, the result is 44 less than three times the number. Therefore the equation will be,

=> 86 + x = 3x - 44

Rearranging,

=> x - 3x = -44 - 86

=> -2x = -130

=> x = 130/2

=> x = 65

Answer:

28

Step-by-step explanation:

i did 7 times 4

Answer:

137 yd2

Step-by-step explanation:

Step-by-step explanation:

m=y1-y2/x1-x2

m=2-8/5-8

m=-6/-3

m=2

y=m(x-x1)+y1

y=m(x-8)+8

y=2x-16+8

y=2x-22

Answer: Y=mx+c

Step-by-step explanation:

The Slope-Intercept Form can be written in the form: y = mx + c Where “m” is the slope of the line “c” is the y-intercept of the equation of the line

Answer:  6

Step-by-step explanation:

you just get those numbers and times them 3 times 2 is 6

a) The probability of selecting exactly 3 award-winners before selecting a SENIOR is  0.078875

b)The probability of selecting more than 2 award-winners before selecting a JUNIOR is 0.135437

c)The probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is 0.252744

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

(a) The probability of selecting a SENIOR is 0.65, and the probability of not selecting a SENIOR is 0.35.

Since we are selecting award-winners until we select a SENIOR, the first two selections must not be SENIORS, and the third selection must be a SENIOR.

the probability of selecting exactly 3 award-winners before selecting a SENIOR is:

P(not SENIOR) x P(not SENIOR) x P(SENIOR) = 0.35 x 0.35 x 0.65 = 0.078875

(b)Therefore, the probability of selecting more than 2 award-winners before selecting a JUNIOR is:

P(not JUNIOR) x P(not JUNIOR) x P(JUNIOR) = 0.77 x 0.77 x 0.23 = 0.135437

To find the probability of selecting more than 2 award-winners, we can subtract this value from 1, since the only other possibility is selecting exactly 2 award-winners before selecting a JUNIOR:

P(more than 2) = 1 - P(exactly 2) = 1 - (P(not JUNIOR) x P(JUNIOR) x P(not JUNIOR)) = 1 - (0.77 x 0.23 x 0.77) = 0.567911

(c) The probability of selecting a SOPHOMORE is 0.12, and the probability of not selecting a SOPHOMORE is 0.88.

Since we are selecting award-winners until we select a SOPHOMORE, we can keep selecting SENIORS and JUNIORS until we select a SOPHOMORE.

Therefore, the probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is:

P(SOPHOMORE) + P(not SOPHOMORE) x P(JUNIOR) x P(SOPHOMORE) + P(not SOPHOMORE) x P(not JUNIOR) x P(JUNIOR) x P(SOPHOMORE) = 0.12 + (0.88 x 0.23 x 0.12) + (0.88 x 0.77 x 0.23 x 0.12) = 0.252744

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Answer:

Your answer is E) 1/2 , -6 , 5

Step-by-step explanation:

Find the slope between (-6,5) then simplify and you will get 1/2

the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.

what is  vertical asymptotes  ?

Vertical asymptotes are vertical lines on a graph where a function approaches infinity or negative infinity as the input (x) approaches a certain value. In other words, vertical asymptotes occur when the denominator of a function becomes zero and the function is undefined at that point

In the given question,

To find the horizontal and vertical asymptotes of the function f(x) = 3x²/[(x+1)(x-4)], we need to analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the vertical asymptotes (if any).

Vertical asymptotes occur at the values of x that make the denominator of the fraction equal to zero. In this case, we have vertical asymptotes at x = -1 and x = 4.

To find the horizontal asymptote, we need to divide the leading term of the numerator by the leading term of the denominator when x approaches infinity or negative infinity. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, we can use long division or synthetic division to write the function in the form of a polynomial plus a proper fraction:

f(x) = 3x²/[(x+1)(x-4)] = (3x + 15)/(x² - 3x - 4)

As x approaches infinity or negative infinity, the fraction approaches the value of 3/1 (the ratio of the leading terms of the numerator and denominator), but there is no horizontal asymptote.

Therefore, the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.

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