Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with = 0.40 gram.
(a)
Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)
lower limit
upper limit
margin of error
(b)
What conditions are necessary for your calculations? (Select all that apply.)
normal distribution of weights
is unknown
uniform distribution of weights
is known
n is large
Correct: Your answer is correct.

(c)
Interpret your results in the context of this problem.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.
We are 20% confident that the true average weight of Allen's hummingbirds falls within this interval.
We are 80% confident that the true average weight of Allen's hummingbirds falls within this interval.
The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.
Correct: Your answer is correct.
(d)
Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.13 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)

Incorrect: Your answer is incorrect.
hummingbirds

(x,y) --> (x, y-2)

=======================================================

Explanation:

Choice A can be ruled out because of the jump from x to 2x, and from y to 2y. This is a dilation with a scale factor 2. Meaning the preimage enlarges to a bigger image. Specifically the larger image has side lengths twice as long as the smaller preimage. The larger image of course cannot possibly be congruent to the smaller preimage. Congruent figures must have the same corresponding side lengths.

We'll come back to choice B.

Choice C and choice D are ruled out for similar reasoning as choice A was eliminated.

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

To summarize the previous section: We ruled out choices A, C, and D. The only thing left is choice B.

Choice B is a translation. The jump from y to y-2 means we shift the point 2 units down. There is no left or right shifting because x stays the same.

For example, the point (5,12) moves to (5,10).

Notice that dilation is not being applied for choice B.

With any geometric translation, aka shifting, the side lengths will remain intact. Something that is 5 units long will stay 5 units long. No amount of shifting will change the distance.

Therefore, a translation preserves distances and lengths. We consider it a rigid transformation. This is why choice B will have the preimage congruent to the image.

Answer:B) (x, y) → (x, y − 2)

Step-by-step explanation:

Answer: False, False, True, False, True

Step-by-step explanation: JUST DO IT! MAKE YOUR DREAMS COME TRUE!

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

The term "proportionate" refers to relationships that always have the same ratio. For instance, the average number of apples per tree influences how many trees there are in an orchard and how many fruits there are in a harvest of apples. A linear relationship between two numbers or variables is referred to in mathematics as being proportionate. In the same way as the first quantity doubles, so does the other. The other decreases as well when one of the variables is reduced to 1/100th of its previous value.

When two quantities are proportional, it means that when one rises, the other rises as well and that the ratio between the two quantities is constant at all values. As an example, consider a circle's diameter and circumference.

given

2000 pounds make up a ton.

Snowmobile owned by John weighs 600 pounds or 0.3 tons.

The difference between Mike's snowmobile's 500 and 600 pound weights is 100 pounds.

= 600 - 500 = 100 pounds

Since the Johns snowmobile weighs 600 pounds, the weight difference between the two vehicles is 100 pounds.

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Answer:

slope = - [tex]\frac{8}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope- formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, - 4) ← 2 points on the line

m = [tex]\frac{-4-4}{4-(-1)}[/tex] = [tex]\frac{-8}{4+1}[/tex] = [tex]\frac{-8}{5}[/tex] = - [tex]\frac{8}{5}[/tex]

All the correct expression are;

⇒ 2x + 6 = 2

⇒ 2(x - 4) = 6x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We have to check all the expression which has x = - 2 as a solution.

So, For first expression;

⇒ 2x + 6 = 2

Put x = -2;

LHS = 2×- 2 + 6

       = - 4 + 6

       = 2

       = RHS

Hence, This expression has a solution x = - 2

For second expression;

⇒ 2(x - 4) = 6x

Put x = -2;

LHS = 2×(- 2 - 4)

       = 2 × - 6

       = -12

RHS = 6x

       = 6×-2

       = - 12

Hence, This expression has a solution x = - 2

For third expression;

⇒ 3x + 1/2 = 1/4x + 6

Put x = -2;

LHS = 3×-2 + 1/2

       = - 6 + 1/2

       = - 11/2

RHS = 1/4x + 6

       = 1/4 × - 2 + 6

       = - 1/2 + 6

       = 11/2

Hence, This expression does not a solution x = - 2.

So, For fourth expression;

⇒ 7 - 3x = 5x + 11

Put x = -2;

LHS = 7 - 3×-2

       =  7 + 6

       = 13

RHS = 5x + 11

       = 5×-2 + 11

       = - 10 + 11

       = 1

Hence, This expression does not a solution x = - 2.

So, For fifth expression;

⇒ 3x + 15 = 2x + 9

Put x = -2;

LHS = 3×- 2 + 15

       = - 6 + 15

       = 9

RHS = 2x + 9

       = 2×-2 + 9

       = - 4 + 9

       = 5

Hence, This expression does not a solution x = - 2.

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The 10th term of the arithmetic sequence is T₁₀ = a + 9d. a is the first term and d is the common ratio.

What is a sequence?

A sequence in mathematics is an enumerated collection of items in which repetitions are permitted and order is important. It has members, just like a set. The length of the sequence is defined as the number of items.

An arithmetic sequence follows a pattern.

Arithmetic progression or arithmetic sequence is a number sequence in which the difference between subsequent terms is constant.

The formula for nth term of the sequence is

Tn = a + (n - 1)d

Where a is the first term, d is the common ratio, and n is the number of terms.

Putting n = 10 in Tn = a + (n - 1)d

T₁₀ = a + (10- 1)d

T₁₀ = a + 9d

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Answer:

[tex] \sqrt{1693} [/tex]

The slope of a line perpendicular to the original line is then the negative reciprocal of 4/3, or -3/4.

Reciprocity is a reciprocal exchange of goods, services, or privileges between two parties. It is often used in business transactions and in politics to create beneficial relationships and agreements between parties.

The slope of a line perpendicular to 4x-3y=12 is calculated by finding the negative reciprocal of the slope of the original line. To find the slope of the original line, we need to rewrite the equation in the form y = mx + b, where m is the slope.
In this case, we can rewrite the equation as:
3y = 4x - 12
Yielding the slope of the original line as m = 4/3.
The slope of a line perpendicular to the original line is then the negative reciprocal of 4/3, or -3/4.

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Answer:

Step-by-step explanation:

45 peaches + 55 peaches + 60 peaches = 160 peaches total

17 pounds + 21 pounds + 25 pounds = 63 pounds total

63 pounds / 160 peaches = about 0.39 pounds per peach

The increase in Lupita's retirement savings from June to July to the nearest percentage is 44%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred.

It is given that the initial amount of money Lupita had in June is $115

In July the amount of money Lupita saved increased to $165

We are asked to find this increase in money as a percentage.

Increase in percentage

= {(Final amount of money - Initial amount of money) / Initial amount of money } × 100

=  {(165 - 115) / 115 } × 100 = 43.48%. ≈ 44%

Therefore the increase in amount of money saved as percentage is 44%.

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Answer:

44.3

Step-by-step explanation:

47 - 2.7 = 44.3

Taking away 2.7 from 47 gives us 44.3.

Hope this helped!

Answer:

2x+12

Step-by-step explanation:

We can re-write (2x+8)+4 using the associative property of addition. The associative property states that you can move around the parenthesis in an addition problem.

We can write (2x+8)+4 as 2x+(8+4).

2x+(8+4) = 2x+12.

Answer: 40.5 cm.

Step-by-step explanation:

first the formula for a parallelogram is base times height and we know the height is 4.5 cm and the base is twice the height and 4.5+4.5=9 and then 9x4.5= 40.5

42 , 16 values of sin and cos

Let's review some information regarding the sin function before learning the sin formula. The sine function, often known as the sin function, is a periodic function in trigonometry. The ratio of the hypotenuse's length to the perpendicular's length in a right-angled triangle is another way to describe the sine function. Sin is a periodic function that has a period of 2 and a domain and range of (, ), respectively. To determine the sides of a triangle, use the sin formula.

The Sin Formula: What Is It? The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse

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So on solving the provided question, we can say that by equation , y = 5/8x; it makes a vertical line.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Let y be the number of gallons of fertilizer produced by combining x tsp of fertilizer powder.

5 litres of liquid fertilizer are created by combining 8 tsp of fertilizer powder.

Therefore, the amount of liters of liquid fertilizer produced by combining 1 tsp of fertilizer powder = 5/8

gallons of LF by mixing x tsp of powder fertiliser  = 5/8x

the required equation is => y = 5/8x

so by graph it makes a vertical line.

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10.1 g of fluorine is required to produce 20.0 grams of FeF3

first, we have to balance the equation:

2Fe+3F₂⇒2FeF₃

The molar mass of FeF₃ is 112.84g/mol. so the num of mol(n) of FeF₃ present in 20.0g of mass is calculated as shown below:

n=20.0g/112.84g/mol

n=0.1772mol

According to the balanced equation on the macroscopic scale, 2 mol of FeF₃ is produced from 3 mol of F₂.

so, 0.1772 mol of FeF₃ is produced from X mol of F₂. where X is calculated as shown below:

X=3 mol/2mol*0.1772 mol

X=0.2658 mol

Hence, 0.2658 mol of F₂ is required. The molar mass of F₂ is 38.0g/mol

so, the mass of 0.2658 mol of F2 is calculated as:

m=0.2658 mol*38.0g/mol

m=10.1g

Hence, 10.1 g of fluorine is required.

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Therefore , the solution of the given problem of circumference of the given figure is 15.7 ft.

The circumference of a circle or other curved geometric object refers to length. It is the boundary across any two-dimensional circular surface measured linearly in one dimension.

Here,

in the given question

first find the length of the diameter

in the figure

Perpendicular = 3ft

Base = 4ft

using Pythagoras rule

(hypotenuse)

(base)2 + (perpendicular)2

(hypotenuse)2=42+32

(hypotenuse)2=16+9

(hypotenuse)2=25

hypotenuse = √25

hypotenuse = 5

in the given figure hypotenuse diameter of the circle

radius(r) =

diameter

== 2.5

circumference of the circle is given by

circumference = 2πr

circumference = 2*3.14 * 2.5

circumference = 15.7ft

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Answer: The fourth data set (bottom right corner).

Step-by-step explanation: In the graph shown the dots represent a value in the data set. In the graph, there are 4 data sets above 2 meaning that there should be 4 values of 2 in the data set. A quick scan will show that the only logical answer is the fourth set since this is the only set with 4 2s. You can repeat this process for the rest of the dots to check your work.

Answer:

25

Step-by-step explanation:

25 because i used a calculator

The measure of angle a is given as 94 degrees.

In order to get the value of a, we have to use the formula for the sum of angles in a straight line.

The sum of angles that are in a straight line is given as 180

this is summed up and equated to 180

From the figure,

m∠1 = 86 degrees

m∠2 = a

we have to sum this up and equate the value to 180 degrees

86 degrees + a = 180 degrees

a = 180 - 86

a = 94 degrees

Therefore the measure of the angle a is given as 94 degrees

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600 mL of solution B and 3(600) = 1800 mL of solution A are used by Chau.

Let x = the amount of Solution B used

3x = the amount of Solution A used

Knowing that 13% = 0.13 and 18% = 0.18, we can create the equation shown below:

3x(0.13) + x(0.18) = 342 (Remember that the concentration of pure alcohol is 100%, or 1.00).

0.39x + 0.18x = 342

0.57x = 342

x = 600 mL

600 mL of solution B and 3(600) = 1800 mL of solution A are used by Elsa.

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The limits to the function are given as follows:

a) lim x -> -5 f(x) = 10.

b) lim x -> 5 f(x) = -5.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

As the function in this problem does not have discontinuities at the values of x = -5 and x = 5, the limits are in fact given by the numeric values at these points.

The limits are given as follows:

a) lim x -> -5 f(x) = 10. -> as the graph passes through the point (-5,10).

b) lim x -> 5 f(x) = -5. -> as the graph passes through the point (5,-5).

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The linear function's missing data values are x = 0 and y = 1, which is the right response (B).

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = mx + b, where m and b are real values.

Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b.

When given as a graph, information about a function is assumed to be linear if the graph is a line.

If the function's details are provided in algebraic form, then f(x) = mx + b indicates that the function is linear.

According to our question-

Using two specified pairs of points from the table, (-9, 3) and (-6, 2), one may calculate the slope as follows:

Let

x₁ = -6, y₁ = 2

x₂ = 95, y₂ = 3

Slope (m) equals (3 – 2)/(-9 – (-6))

Slope (m) equals 1/-3, or 1/3.

By substituting (x, y) = (-9, 3) and m = -1/3 into y = mx + c, it is possible to find c:

⇒ 3 = -1/3(-9) + c

⇒ 3 = 3 + c

⇒ 3 - 3 = c

⇒ c = 0

Change y = mx + c to m = -1/3 and c = 0.

⇒ y = -1/3x

Now, calculate the values of the missing data using the equation:

Please use y = 0.

Hence, x would be:

⇒ 0 = -1/3x

⇒ x = 0

Replace x with -3,

Y then would be:

⇒ y = -1/3(-3) (-3)

⇒ y = 1

Hence, The linear function's missing data values are x = 0 and y = 1, which is the right response (B).

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The equation of the line in slope intercept form is y = - 1 / 2 x + 4.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through the points (2, 3) and the y-intercept is 4.

Hence,

y = mx + 4

let's find slope using (2, 3)

3 = 2m + 4

3 - 4 = 2m

2m = -1

divide both sides by 2

m = - 1 / 2

Therefore, the equation of the line is y = - 1 / 2 x + 4.

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Answer:

18. y = -2x + 6

19. y = -1/2x -1/2

Step-by-step explanation:

y = mx + b

18. The point (0,6) 0 is the x-intercept and 6 is the y-intercept

For now, all we care about is 6

-2 is the slope which means the line will go down 2 and right 1

m = slope

b = y-intercept

y = -2x + 6

19.

-1/2 is the slope which means the line will go down 1 and right 2

For the y-intersept, I just played with it on a graphing calculater until I got it right.

m = slope

b = y-intercept

y = -1/2x -1/2

Answer:

36 -12 = 24

Step-by-step explanation:

24 / 12 × 100

= 2 × 100

= 200 %

On solving the provided question we can say that from the provided quadrilateral ABCD, ∠ BAD and ∠BCD are supplementary, ∠ABC and ∠ADC are supplementary.

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

from the provided quadrilateral ABCD,

∠ BAD and ∠BCD are supplementary,

∠ABC and ∠ADC are supplementary.

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Answer:

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

Given expression:

Simplify it in steps:

Answer:

[tex] \sf \: - g - 6[/tex]

Step-by-step explanation:

The expression is,

→ -2 + 2g - (3g + 4)

Let's simplify the expression,

→ -2 + 2g - (3g + 4)

→ -2 + 2g - 3g - 4

→ (-3g + 2g) + (-2 - 4)

→ (-g) + (-6)

→ -g - 6

Hence, the answer is -g - 6.