Barnaby decided to count the number of ducks and geese flying south for the winter. On the first day he counted 175 ducks and 63 geese. By the end of migration, Barnaby had counted 4,725 geese. If the ratio of ducks to geese remained the same (175 to 63), how many ducks did he count?

9514 1404 393

Answer:

  1/3

Step-by-step explanation:

The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...

  [tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]

In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...

  [tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]

__

You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.

_____

Additional comment

A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...

  y = kx . . . . . . where k is the constant of proportionality.

The line in this problem statement will have the equation ...

  y = (1/3)x

Answer:

Domain: (-∞, 1]

Range: (-∞, 3]

Step-by-step explanation:

The function starts at point (1, 3) and goes to the left and down forever.

Domain: (-∞, 1]

Range: (-∞, 3]

Answer:

Domain: [tex](-\infty, 1][/tex]

Range: [tex](-\infty, 3][/tex]

Step-by-step explanation:

The domain of a function represents the range of x-values that are part of the function, read left to right. We can see that the function goes forever to the left and stops at [tex]x=1[/tex] when we read left to right. Therefore, the domain of this function is [tex]\boxed{(-\infty, 1]}[/tex].

The point at [tex]x=1[/tex] is a filled-in solid dot so it is included as part of the function. Use square brackets to denote inclusive.

The range of a function represents all y-values that are part of the function, read bottom to top. The function continues down forever and stops at [tex]y=3[/tex] when read bottom to top. Therefore, the range of this function is [tex]\boxed{(-\infty, 3]}[/tex]. Similar to the domain, we use a square bracket on the right to indicate that [tex]y=3[/tex] is included in the function. If the dot was not filled-in, then we would use a parenthesis to indicate that [tex]y=3[/tex] would not be part of the function.

Answer: 32 room

Step-by-step explanation:

[tex]7\frac{3}{4} =\frac{4(7)+3}{4} =\frac{28+3}{4} =\frac{31}{4}=7.75[/tex]

If 1 room = 7.75 yd of carpet ⇒ x rooms = 250 yd of carpet

Use proportions & cross-multiply to solve:

[tex]\frac{1}{7.75} =\frac{x}{250}\\7.75x=250\\x=\frac{250}{7.75} =32.258[/tex]

So 250 yd of carpet can cover about 32 rooms.

Answer:

The slope is the cost per hour.

$5 per hour

Answer:

2w<23

Step-by-step explanation:

The product of w and 2 mean that w multiplied by 2

Answer:

E. by the SAS similarity theorem.

Step-by-step explanation:

Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)

DC/BC = 240/150 = 1.6

EC/AC = 320/200 = 1.6

This implies that the ratio of two corresponding sides of both triangles are the same.

Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.

Answer:

Step-by-step explanation:

[tex]h(t)=-16t^2+96t\\\\h(t)=-t(16t-96)[/tex]

[tex]96=2^5*3\\\\16=2^4\\\\h(t)=-t(2^5*3*t-2^4)=-2^4t(2^1*3*t-1)\\\\h(t)=-16t(6t-1)[/tex]

the b) part is easy do it!

Step-by-step explanation:

Since an interior angle is 150 degrees, its adjacent exterior angle is 30 degrees.  Exterior angles of any polygon always add up to 360 degrees.  With the polygon being regular, we can just divide 360 by 30 to get 12 sides.

Answer:

m = 4

n = 5

Step-by-step explanation:

[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]

[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]

Answer:

-192

Step-by-step explanation:

it is a geometric progression

r=-4

Answer:

x= -3

Step-by-step explanation:

2x+14= 8

2x= -6

x = -3

Answer:

-3

Step-by-step explanation:

According to the question,

[tex]\longrightarrow[/tex] CE = CD + DE

[tex]\longrightarrow[/tex] 8 = (x + 10) + (x + 4)

[tex]\longrightarrow[/tex] 8 = x + 10 + x + 4

[tex]\longrightarrow[/tex] 8 = 2x + 14

[tex]\longrightarrow[/tex] 8 ― 14 = 2x

[tex]\longrightarrow[/tex] ―6 = 2x

[tex]\longrightarrow[/tex] ―6 ÷ 2 = x

[tex]\longrightarrow[/tex] –3 = x

Therefore, the value of x is ― 3.

Answer:

a) The margin of error for a 98% confidence interval is of 3.388 people.

b) The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the hypergeometric distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 15 - 1 = 14

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.624

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.624\frac{5}{\sqrt{15}} = 3.388[/tex]

In which s is the standard deviation of the sample and n is the size of the sample. This means that the answer to question a is of 3.388.

Question b:

The lower end of the interval is the sample mean subtracted by M. So it is 24 - 3.39 = 20.61 people

The upper end of the interval is the sample mean added to M. So it is 24 + 3.39 = 27.39 people.

The 98% confidence interval for the population mean is between 20.61 people and 27.39 people.

Answer:

x = 3

y = 8

Step-by-step explanation:

In the given triangle FGH,

m∠F + m∠G + m∠H = 180° [Triangle sum theorem]

60° + 90° + m∠H = 180°

m∠H = 30°

If the given triangles FGH and TUV are congruent, their corresponding sides will be equal in measure.

m∠F = m∠T

7y + 4 = 60°

7y = 56

y = 8

GH ≅ UV

8x - 12 = 12

8x = 24

x = 3

Using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

According to the angle-angle-side congruence theorem (AAS), two triangles are congruent if they have two corresponding congruent angles and one pair of corresponding non-included sides that are congruent.

Thus, by the AAS theorem, we have:

8x - 12 = 12

8x = 12 + 12

8x = 24

x = 3

Also,

7y + 4 = 60

7y = 60 - 4

7y = 56

y = 8

Therefore, using the AAS congruence theorem, the values of x and y that show that both triangles are congruent are: x = 3 and y = 8.

Learn more about AAS congruence theorem on:

https://brainly.com/question/3168048

Answer:

[tex]-2[/tex]

Step-by-step explanation:

Just substitute -3 for all instances of x.

[tex](-3)^{2} + 4(-3) + 1\\\\[/tex]

[tex]9 - 12 + 1[/tex]

[tex]-2[/tex]

Step-by-step explanation:

For an equation of form Ax + By = C, we are given A, B, and C.

The x intercept is when the line/equation is on the x axis, or when y=0.

Therefore, if we plug y=0 into the equation Ax+By=C, and anything multiplied by 0 is equal to 0, we can say that

Ax + 0 = C

Ax = C

divide both sides by A

x  = C/A

Therefore, the x intercept is equal to C/A

Similarly, for the y intercept, or when the line is on the y axis (or when x=0), we have

A*0 + By = C

By = C

divide both sides by B

y= C/B at the y intercept

Step-by-step explanation:

I think substitution would be the easiest since you already have one of the variables solved for.

[tex]y=-x^2+4x+5\\y=x+1\\x+1=-x^2+4x+5\\x^2-3x-4=0\\(x-4)(x+1)=0\\x-4=0\\x=4\\x+1=0\\x=-1[/tex]

(You can just set the equations equal to each other since they both equal y).

Now, to get the points, plug in x = 4 and x = -1 into one of the equations (I'm going to plug them into y = x+1 because that one is much simpler)

[tex]y(4)=4+1\\y(4)=5\\y(-1)=-1+1\\y(-1)=0[/tex]

So, your final points are:

(4,5) and (-1,0)

Answer: A

Step-by-step explanation:

We can use substitution to solve this problem. Since we are given y=-x²+4x+5 and y=x+1, we can set them equal to each other.

-x²+4x+5=x+1        [subtract both sides by x]

-x²+3x+5=1            [subtract both sides by 1]

-x²+3x+4=0

Now that we have the equation above, we can factor it to find the roots.

-x²+3x+4=0           [factor out -1]

-1(x²-3x-4)=0         [factor x²-3x-4]

-1(x+1)(x-4)=0

This tells us that x=-1 and x=4.

We can narrow down our answer to A, but let's plug in those values to be sure it is correct.

-(-1)²+4(-1)+5=(-1)+1      [exponent]

-1+4(-1)+5=-1+1              [multiply]

-1-4+5=-1+1                    [add and subtract from left to right]

0=0  

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

-(4)²+4(4)+5=(4)+1      [exponent]

-16+4(4)+5=4+1           [multiply]

-16+16+5=4+1              [add and subtract from left to right]

5=5

Therefore, we can conclude that A is the correct answer.

Answer:

1/2 or 50-50

Step-by-step explanation:

1/4 +1/4 = 1/2 or 50-50

Answer:

Range: { 0,3,5,7,9}

Step-by-step explanation:

The range is the values that y takes

Range: { 0,3,5,7,9}

Now we have to find,

The range of the table of values,

→ Range = ?

Then the range will be the numbers that is in the Y column.

→ Range = ?

→ Range = (value that Y takes)

→ Range = 0,3,5,7,9

Therefore, the range is 0,3,5,7,9.

Answer:

19.3 miles per gallon

Step-by-step explanation:

First, subtract 54,042.8-53,737.7. The answer is 305.1

Then, find the unit rate. 305.1/15.8

You get 19.31012658. The prompt says to round to the nearest tenth, so round, and you get 19.3.

That's your answer!

Answer:

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

1) 0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2) 0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3) 0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4) 0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Step-by-step explanation:

To solve these questions, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The height, X, of all 3-year-old females is approximately normally distributed with mean 38.72 inches and standard deviation 3.17 inches.

This means that [tex]\mu = 38.72, \sigma = 3.17[/tex]

Sample of 10:

This means that [tex]n = 10, s = \frac{3.17}{\sqrt{10}}[/tex]

Compute the probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

This is 1 subtracted by the p-value of Z when X = 40. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{40 - 38.72}{\frac{3.17}{\sqrt{10}}}[/tex]

[tex]Z = 1.28[/tex]

[tex]Z = 1.28[/tex] has a p-value of 0.8997

1 - 0.8997 = 0.1003

0.1003 = 10.03% probability that a simple random sample of size n= 10 results in a sample mean greater than 40 inches.

Gestation periods:

[tex]\mu = 266, \sigma = 16[/tex]

1. What is the probability a randomly selected pregnancy lasts less than 260 days?

This is the p-value of Z when X = 260. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{260 -  266}{16}[/tex]

[tex]Z = -0.375[/tex]

[tex]Z = -0.375[/tex] has a p-value of 0.3539.

0.3539 = 35.39% probability a randomly selected pregnancy lasts less than 260 days.

2. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 20[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{20}}}[/tex]

[tex]Z = -1.68[/tex]

[tex]Z = -1.68[/tex] has a p-value of 0.0465.

0.0465 = 4.65% probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less.

3. What is the probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less?

Now [tex]n = 50[/tex], so:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260 - 266}{\frac{16}{\sqrt{50}}}[/tex]

[tex]Z = -2.65[/tex]

[tex]Z = -2.65[/tex] has a p-value of 0.0040.

0.004 = 0.4% probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less.

4. What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

Sample of size 15 means that [tex]n = 15[/tex]. This probability is the p-value of Z when X = 276 subtracted by the p-value of Z when X = 256.

X = 276

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{276 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = 2.42[/tex]

[tex]Z = 2.42[/tex] has a p-value of 0.9922.

X = 256

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{256 - 266}{\frac{16}{\sqrt{15}}}[/tex]

[tex]Z = -2.42[/tex]

[tex]Z = -2.42[/tex] has a p-value of 0.0078.

0.9922 - 0.0078 = 0.9844

0.9844 = 98.44% probability a random sample of size 15 will have a mean gestation period within 10 days of the mean.

Answer:

the answer is 50 but I don't know if

[tex]f(x)=\sqrt{x} -2[/tex] is the correct option

Answer:

A is that answer

A) y<2x-3

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

[tex]\frac{vinegar}{oil}[/tex]  If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.

2x = 100 so

x = 50 ml of oil

Answer:

the answer is c

Step-by-step explanation:

the answer is c

Answer:

(D.) 3x^2 + 6x

Step-by-step explanation:

the other options aren't complete and some don't even create a parabola.

Answer:

The answer is the third one below

Answer:

150 dollars. if I am wrong correct me

Answer:

C and D

Step-by-step explanation:

15 to 30 galons at $9.95 to $21.00

the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25

the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630

there are 2 choices that are between 149.25 and 630, C, and D

Answer:

By using a pair of compasses and a ruler you can draw all angles

Answer:

True

Step-by-step explanation:

The statistic is a numerical value which describes the characteristic of a particular sample data. The sample is a set of data which represents a smaller subset randomly selected from the population or a larger dataset.

The sample mean, refers to the mean or average value of a sample data, therefore, a sample mean is a numerical characteristic of the sample dataset and it is therefore a statistic. On the other hand, numerical characteristics of a population data is called the parameter.