A park began with a population of 8 rabbits. Every year, the rabbit population triples. How long will it take for the population to reach 1,944 rabbits?

Answer: Yes. On average, it takes about 455 days for 1 person to throw away 1 ton of garbage, so just over 1 year.

Step-by-step explanation: The average person throws away 4.4 pounds of trash daily. So, the way to figure this out is 2,000 divided by 4.4 to find out the number of days it would take to throw away 2,000 pounds of trash.

Answer:

Choice B is correct

Step-by-step explanation:

The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.

Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;

[tex]r=\frac{k}{1-4sin(theta)}[/tex]

The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;

k= 4*6 = 24

The polar equation is thus given by alternative B

Answer:

b on edge

Step-by-step explanation:

Answer:

<1:88

<2:65

<3:115

Step-by-step explanation:

Since we know that a line and the inside of a triangle equals 180 than we can use that to identify the missing angles.Using what we know about a line we can subtract 92 from 180 and we get 88, knowing that angle 1(<1)is the only angle that rest on that line than we know that <1 is 88.(to check this you can add 92 plus 88 and you get 180)Then switching hands,we can now figure out the interior missing angle 2(<2).There are two ways you can do this,Add all the interior angles together and then subtract from 180(88+57=145 then 180-145=35)or you can subtract all the known interior angles and then the answer is your missing angle(180-57-88=35).Now switching again, in order to find <3 then you have to find which number falls on the angle which we are looking for.Which would be 35 or <2.Now all you have to do is subtract 180-35=145

Part B:

I agree with the other person below⬇⬇⬇

Answer:

Step-by-step explanation:

(A) From the given figure, we have

[tex]{\angle}1+92^{\circ}=180^{\circ}[/tex] (Linear pair)

⇒[tex]{\angle}1=180^{\circ}-92^{\circ}[/tex]

⇒[tex]{\angle}1=88^{\circ}[/tex]

Thus, the measure of [tex]{\angle}1[/tex] is [tex]88^{\circ}[/tex].

Also, using the angle sum property in the given triangle, we get

[tex]{\angle}1+{\angle}2+57^{\circ}=180^{\circ}[/tex]

⇒[tex]88^{\circ}+{\angle}2+57^{\circ}=180^{\circ}[/tex]

⇒[tex]{\angle}2+145^{\circ}=180^{\circ}[/tex]

⇒[tex]{\angle}2=35^{\circ}[/tex]

Thus, the measure of [tex]{\angle}2[/tex] is [tex]35^{\circ}[/tex].

And, [tex]{\angle}2+{\angle}3=180^{\circ}[/tex]

⇒[tex]35^{\circ}+{\angle}3=180^{\circ}[/tex]

⇒[tex]{\angle}3=145^{\circ}[/tex]

Thus, the measure of [tex]{\angle}3[/tex] is [tex]145^{\circ}[/tex].

(B) Exterior angle theorem states that the exterior angle is equal to the sum of the two interior angles, thus from the given figure, we have

[tex]{\angle}1+{\angle}2=123^{\circ}[/tex]

Therefore, the relationship between the measure of [tex]{\angle}1[/tex] and  [tex]{\angle}2[/tex] to exterior angle is [tex]{\angle}1+{\angle}2=123^{\circ}[/tex].

Answer:

False

Step-by-step explanation:

We have the serie:

[tex]\frac{1}{49}+ \frac{1}{64} + \frac{1}{81}+...[/tex]

To test whether the series converges or diverges first we must find the rule of the series

Note that:

[tex]7^2 = 49\\\\8^2 = 64\\\\9^2 = 81[/tex]

Then we can write the series as:

[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+...[/tex]

Then:

[tex]\frac{1}{7^2}+ \frac{1}{8^2} + \frac{1}{9^2}+... = \sum_{n=7}^{\infty}\frac{1}{n^2}\\\\\sum_{n=7}^{\infty}\frac{1}{n^2} = \sum_{n=1}^{\infty}\frac{1}{(n+6)^2}[/tex]

The series that have the form:

[tex]\sum_{n=1}^{\infty}\frac{1}{n^p}[/tex]

are known as "p-series". This type of series converges whenever [tex]p > 1[/tex].

In this case, [tex]p = 2[/tex] and [tex]2 > 1[/tex]. Then the series converges

Step-by-step answer:

Angle ECF = 110 = angle of intercepted (minor) arc EF.

The inscribed angles (angles EDF and EHF) are equal to half the angle of the inscribed arc, namely 110/2 = 55 degrees.

For your information, an inscribed angle is an angle with its vertex on (circumference of) the circle, formed by two intersecting chords, with a base on the inscribed arc.

Answer:

Step-by-step explanation:

Look at the pictures.

(the picture 1)

Inscribed angle and central angle.

(the picture 2)

In a circle, central angle is two times larger than inscribed angle that intercept the same arc.

In a circle, inscribed angles that intercept the same arc are congruent.

We have the central angle C = 110°. The inscribed angle EHF is two times smaller than ∠C. Therefore m∠EHF = 110° : 2 = 55°.

The inscribed angles EHF and EDF that intercept the same arc. Therefore are congruent. m∠EHF = m∠EDF.

Answer:

Choice D is correct

Step-by-step explanation:

The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;

[tex]r=\frac{3}{1-cos(theta)}[/tex]

The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.

The value of the directrix is determined as;

d = k/e = 3/1 = 3

The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;

x = -3

Thus, the polar equation represents a parabola that opens towards the right with a directrix located at  x = -3. Choice D fits this criteria

Answer:

10.1

Step-by-step explanation:

i divided the numbers now mark brainliest if its wrong or right

Find the midpoint of the chord:

9 / 2 = 4.5 cm

Now we can find the radius:

Radius = √(4.5^2 + 3.7^2)

Radius = √(20.25 + 13.69)

Radius = √33.94

Radius = 5.8 cm

Answer:

The horizontal distance from the plane to SCCA is [tex]32,708.5\ ft[/tex]

Step-by-step explanation:

Let

x-----> the horizontal distance from the plane to SCCA

we know that

see the attached figure to better understand the problem

[tex]tan(17\°)=\frac{10,000}{x}[/tex]

[tex]x=\frac{10,000}{tan(17\°)}[/tex]

[tex]x=32,708.5\ ft[/tex]

Answer:

M = 4S

In three years

M + 3 = 3(S + 3)

So you put the 4S in to substitute for the M.

4S + 3 = 3(S + 3)

4S + 3 = 3S + 9

S = 6

If the son is 6, the father must be 24.

We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.

Step-by-step explanation:

Answer:

p score = 0.031

Step-by-step explanation:

We will be running a hypothesis test to find the p-value.  See attached photo for the work needed and the running of the test.

Our hypothesis are:

H0: µ = 1500

HA: µ > 1500 (claim)

They say that the life of the light bulbs are more than 1,500 hours, so that is the alternate hypothesis since it's strictly more than, not equal to or greater.

we have a sample mean of: 1509.5

we have a sample standard deviation of: 24.27

We just need to find the p-value, we don't need to make a conclusion about the test results.

The p-value of the hypothesis test that the light bulbs last more than 1500 hours is estimated to be less than 0.05, supporting the company's claim. The calculation involved computing a t-statistic from the sample data and then finding the probability of getting a t-statistic larger than the computed value.

The question involves conducting a hypothesis test for the claim that the company's light bulbs last more than 1500 hours. The null hypothesis H0 for this test would indicate that the population mean longevity is less than or equal to 1500 hours (H0: μ ≤ 1500), while the alternative hypothesis H1 posits that the mean exceeds 1500 hours (H1: μ > 1500). The company collected a sample (n=25) and computed the sample mean ( = 1509.5 hours) and the sample standard deviation (s = 24.27 hours). To calculate the p-value for this test, we need to first calculate the test statistic (z or t) by using the given sample data and then find the area to the right of this test statistic in the relevant distribution.

Using the formula for calculating the test statistic in t-tests: t = ( - μ0)/(s / √n), where μ0 is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size. Here, t = (1509.5 - 1500)/(24.27 / √25) = approximately 1.96.

Since the alternative hypothesis is looking for values greater than 1500, we seek the probability that a test statistic is greater than what we observed (i.e., t > 1.96). This probability is equal to the p-value. To obtain it, we use the t-distribution with n-1 = 24 degrees of freedom. Since exact p-values can be challenging to retrieve without a statistical software or detailed tables, it's typically adhered to note if the p-value is less than or greater than the significance level, which is 0.05 in this case. Due to the calculated t-statistic, our p-value is approximately less than 0.05. Hence, this result supports rejecting the null hypothesis and lends credibility to the company's claim that its light bulbs typically last more than 1500 hours.

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Answer:

Option C

Step-by-step explanation:

The first number is - 3, then we have a blank and the third number is - 1 1/8

In order for the numbers to be arranged from least to greatest, the number in the center should be greater than -3, and lesser than -1 1/8

Note that for negative numbers, the larger the constant, the smaller the number. i.e. -5 is smaller than -4.

So from the given options, the only number that is greater than -3 and lesser than -1 1/8 is - 2 1/4

So, option C gives us the correct answer to have the numbers ordered from least to greatest.

Answer:

B

Step-by-step explanation:

first you wanna multiply and sehow many mutiplesof 4 will go into 8.

The equal amount of bird food put into the 4 feeders is 7 / 32 pounds.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Mia has 7/8 pounds of bird food. She puts an equal portion into 4 bird feeders.

The amount of bird food for each feeder will be calculated as,

Bird food = (7/8) / (4)

Bird food = [ 7/ (8 x 4 )]

Bird food =  7 / 32 pounds

Therefore, the equal amount of bird food put into the 4 feeders is 7 / 32 pounds.

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Answer:

10 × 4 – (5 – 3) + 2

10 × 4 – 2 + 2

40 – 2 + 2

38 + 2

40

Step-by-step explanation:

To solve;

10 × 4 – (5 – 3) + 2

We use BODMAS

We start by removing brackets, to get

10 × 4 – 2 + 2

Then we proceed to multiplication to get;

40 – 2 + 2

Then subtraction to get;

38 + 2

The answer is 40

The correct answer to evaluate  is  10 × 4 – (5 – 3) + 2 is 40

The correct way to evaluate the expression 10 × 4 – (5 – 3) + 2 is as follows:

10 × 4 – (5 – 3) + 2

= 40 – (5 – 3) + 2

= 40 – 2 + 2

= 38 + 2

= 40

Therefore, the correct evaluation is 40.

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it should be the radius

Answer:

x = 69  and  y = [tex]23\sqrt{3}[/tex]

Step-by-step explanation:

Firstly the hypotenuse is the side opposite the 90 degree angle. So hypotenuse is [tex]46\sqrt{3}[/tex]

Since the angle given is 30 degree, with respect to this angle, the side length y is opposite and the side length x is adjacent.

Now, we can use trigonometric ratios to solve for x and y. Sine is defined as  [tex]sin\theta=\frac{Opposite}{Hypotenuse}[/tex] and Cos is defined as  [tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]

Hence, we can write:

[tex]Sin(30)=\frac{y}{46\sqrt{3} }\\y=46\sqrt{3}*Sin30 \\y=46\sqrt{3}*\frac{1}{2}\\y=23\sqrt{3}[/tex]

Also, we can figure out:

[tex]Cos(30)=\frac{x}{46\sqrt{3} }\\Cos(30)*46\sqrt{3}=x\\ x=\frac{\sqrt{3} }{2}*46\sqrt{3} \\x=\frac{46*3}{2}\\x=69[/tex]

2nd answer choice is right.

ANSWER

[tex]x = 69,y = 23 \sqrt{3} [/tex]

EXPLANATION

Recall and use the mnemonics SOH CAH TOA.

We use the cosine ratio to find x.

[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex] \cos(30 \degree) = \frac{x}{46 \sqrt{3} } [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{x}{46 \sqrt{3} } [/tex]

Cross multiply,

[tex]2x = 46 \sqrt{3} \times \sqrt{3} [/tex]

[tex]2x = 46(3)[/tex]

[tex]x = 23(3)[/tex]

[tex]x = 69[/tex]

We use the sine ratio, to find y.

[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex]\sin(30 \degree) = \frac{y}{46 \sqrt{3} } [/tex]

[tex] \frac{1}{2} = \frac{y}{46 \sqrt{3} } [/tex]

Solve for y.

[tex] \frac{1}{2} \times 46 \sqrt{3} = y[/tex]

[tex]23 \sqrt{3} = y[/tex]

Therefore,

[tex]x = 69,y = 23 \sqrt{3} [/tex]

Answer:

I am assuming it is the same table as mine. So it would be 0.56

Step-by-step explanation:

79-y=2y+22

Add y on both sides

79=3y+22

Subtract 22 from both sides

57=3y

Divide by 3 on both sides

19=y

Answer:

it is A) No, there is not an overlap between the two data setsStep-by-step explanation:

i did it on usatestprep

Answer:

A-No, there is not an overlap between the two data sets.

Step-by-step explanation:

Step-by-step explanation:

Inverse is x · y = k

Since k = 20, then you are looking for x,y coordinates whose product is 20.

Answer:

The following are possible solutions:

[tex]\left\begin{array}{c|c|c}\underline{\quad x\quad }&\underline{\quad y\quad }&\underline{\qquad k\qquad }\\1&20&1\cdot 20=20\\2&10&2\cdot 20=20\\4&5&4\cdot 5=20\\10&2&10\cdot 2=20\\20&1&20\cdot 1=20\end{array}\right[/tex]

(See attached for graph)

Answer:

384√3 in²

Step-by-step explanation:

Given in the question a regular 6 sided polygon

To find it's area you have to use the following formula

Perimeter = the sum of the lengths of all the sides

Suppose length of one side = x

Apothem = a segment that joins the polygon's centre to the midpoint of any side that is perpendicular to that side = 8√3

Since the polygon have 6 sides so

perimeter = 6x

x = 2(8)

x = 16

perimeter = 6(16) = 96 in

plug values in the formula of area

384√3 in²

Answer:

= 384√3 In²

Step-by-step explanation:

The polygon is a hexagon ; thus the angle subtended by each side at the center will be given by;

θ = 360/6

 = 60°

Therefore; we can calculate the length of each side;

Tan θ = opp/Adj

Tan θ = x /8√3

 Tan 30 = x /8√3

Therefore; 1/√3 =x /8√3

x = 8√3× 1/√3

   = 8

The length of each side is 8 × 2 = 16 In

The area of the polygon will be;

Area of one triangle multiplied by the number of a triangle;

= 1/2 × 16 × 8√3 ×6

Trigonometric ratios are vital in real-world applications such as construction for measuring building heights, in navigation or aviation for determining distances, and in physics for predictions and descriptions of natural phenomena.

Trigonometry and special right triangles are fundamental in various real-world scenarios, especially in fields such as engineering, astronomy, and construction. One example where trigonometric ratios are crucial is in construction when determining the height of a building using a measured baseline and the angles of elevation. If a surveyor knows the distance from his point of observation to the base of the building (the adjacent side in a right triangle) and the angle of elevation to the top of the building, they can use the tangent ratio (opposite over adjacent) to calculate the building's height.

Another scenario involves navigation or aviation, where knowing the distance between two locations is necessary. By measuring the angle from two different points to a third point, one can apply the basic problem of trigonometry to find the distance to the third point using a known baseline and the measured angles, a process often referred to as triangulation.

Lastly, in physics, the principles of special right triangles like the Pythagorean theorem are used to predict certain outcomes. Whether a calculation is made using trigonometry or some other physics principle, the predictions must agree and accurately describe natural phenomena. The Pythagorean theorem is always reliable as long as the algebra and arithmetic are correctly done, illustrating the logic and interconnectedness of mathematical postulates.

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The probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz is approximately 60%.

To find the probability that a randomly selected person is 41-55 in age or prefers drinking Dr. Fizz, we need to sum the frequencies for the 41-55 age group and the frequency for Dr. Fizz, and then divide by the total number of people.

From the table:

- Frequency of 41-55 age group = 30

- Frequency of Dr. Fizz preference = 30

Total number of people = 100

Therefore, the probability is:

[tex]\[ \text{Probability} = \frac{\text{Frequency of 41-55 age group} + \text{Frequency of Dr. Fizz}}{\text{Total number of people}} \][/tex]

[tex]\[ = \frac{30 + 30}{100} \][/tex]

[tex]\[ = \frac{60}{100} \][/tex]

[tex]\[ = 0.60 \][/tex]

Converting to a percentage, rounded to the nearest whole percent:

[tex]\[ \text{Probability} \approx 60\% \][/tex]

So, the correct answer is: 60%.

Answer:

A total of zero softballs will fit into the container

Step-by-step explanation:

step 1

Find the dimensions of the base  of the prism

we know that

The volume of the prism is equal to

[tex]V=Bh[/tex]

where

B is the area of the base

h is the height of the prism

In this problem we have

[tex]V=99\ in^{3}[/tex]

[tex]h=11\ in[/tex]

substitute in the formula and find the area of the base B

[tex]99=B(11)[/tex]

[tex]B=99/11=9\ in^{2}[/tex]

the length side of the square base is the square root of the area

so

[tex]\sqrt{9}=3\ in[/tex]

we have that

The diameter of the softball 3.8 inches will fit (11/3.8=2.89 )  2 times  in the length of the container

The diameter of the softball 3.8 inches will fit  0 times  in the width of the container

so

A total of 0 times of softballs will fit  in the width of the container

therefore

A total of zero softballs will fit into the container

Answer:

Zero softballs with a diameter of 3.8 inches will fit into the container as length of the container is less the diameter of the softball.

Zero softballs can fit in length and zero softballs will fit in width.

Step-by-step explanation:

Length of the square base in rectangular pyramid = s

Breadth of the square base in rectangular pyramid = s

Height of the square base in rectangular pyramid ,l = 11 inches

Volume of the square base in rectangular pyramid ,V=[tex]99 inches^3[/tex]

Volume of the cuboid =  l × b × w

V= s × s × l

[tex]99 inches^3=s^2\times 11 inches[/tex]

s = 3 inches

Softballs with a diameter of 3.8 inches.

But the length of the container is less the diameter of the softball which means not even single ball will not be able to get into the container. So zero softballs can fit in length and zero softballs will fit in width.

Wouldn't he be making $1,000 a week again? Since it was reduced by 10% but then raised by 10%.....

Answer:

Option B. 36

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

The graph of the figure represent an inverse variation

so

In this problem

Constant=Height*Width

Take any point in the graph

example -----> the point (4,9)

Constant=4*9=36

Answer:

The radius is 98

Step-by-step explanation:

The circumference of a circle is the distance around the edge of the circle. To find the circumference, we use the formula C = 2πr. You have the circumference so substitute C = 615.44. Then solve for r.

C = 2πr

615.44 = 2πr

98 = r

Answer: 98 units

Step-by-step explanation:

Factor 3x^3−12x

3x^3−12x

=3x(x+2)(x−2)

Answer:

3x(x+2)(x−2)

3x^3 - 12x //Common factor: 3x

3x (x^2 - 4)

3x (x - 2) (x + 2)

Answer: C

//Hope this helps.

The cost per package depends on the weight of the package.

We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.

Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.

Here from the graph we may observe that the cost of the package depends on the weight of the package.

The cost per package depends on the weight of the package.

We know that a dependent variable is one which depends on some other variable or the value of the variable is calculated corresponding to the independent variable.

Generally we consider the values on the y-axis or the vertical axis as the dependent values because they are dependent upon the x-value or the value on the horizontal axis.

Here from the graph we may observe that the cost of the package depends on the weight of the package.