A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water. A. Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation, y, of the loon after x seconds into the dive. B. If the loon is at a depth of 22 feet under the surface of the water, how long was it diving for? Show your work. ​

The number of days that the food will last when an average of 18 people are at the shelter everyday is 50 days.

From the information given, the shelter has enough food to feed an average of 45 hungry people a day for 20 days.

Let the number of days that the people can be fed when 18 people come be Illustrated as x.

Therefore, this will be illustrated as x. This will be:

x = (45 × 20) / 18

x = 900 / 18

x = 50

The number of days is 15 days.

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Complete question

A shelter has enough food to feed an average of 45 hungry people a day for 20 days. If an average of 18 people are at the shelter everyday, how long will the food last?

Answer:

x intercept = (-3/4, 0)

y intercept = (0, 3/7)

Step-by-step explanation:

just ask :))

The height of the sand is changing when the height of the sand is 5 cm is 0.7848 in cm/sec

Volume is a measure of three-dimensional space that is occupied. It is frequently quantified numerically using SI-derived units (such as the cubic metre and litre) or various imperial units (such as the gallon, quart, cubic inch). The definition of length (cubed) is related to volume. The volume of a container is commonly understood to be its capacity; that is, the amount of fluid (gas or liquid) that the container can hold, rather than the amount of space it occupies.

Volume was measured in ancient times using similar-shaped natural containers, and later, standardized containers. Arithmetic formulas can easily calculate the volume of some simple three-dimensional shapes. Volumes of more complicated shapes can be calculated using integral calculus if a formula is provided.

The volume of the cylindrical is,

V = πr²h

V = volume

r = base radius

h = height

Calculate the difference between both sides of the equation in relation to time t. Because the radius r does not change over time, we can consider it a constant:

dv/dt = πr²(dh/dt)

Given,

dv/dt =555 cubic cm per second

r = 15

solve dh/dt:

555 = π(15)²(dh/dt)

dh/dt = 555(7/22)(1/225)

dh/dt =0.7848

The height of the sand is decreasing at a rate of 0.7848 in cm/sec

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Answer:

M/s, km/h, and mph

Step-by-step explanation:

M/s = meters (travelled) per second

km/h = kilometers (travelled) per hour

mph= miles (travelled) per hour

Answer:

m/s

km/h

mph

Step-by-step explanation:

: )

The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.

Thus,

The rule to rotate a point P(x, y)  after a rotation 270° counterclockwise around the origin is:

P(x, y) → P'(y, -x)

From the Graph,

In our case, we have the points

T = (4, -8)

U = (6, -8)

V = (9, -3)

W = (7, -3)

Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

P(x, y)          →        P'(y, -x)

T (4, -8)       →       T'(-8, -4)

U  (6, -8)      →       U'(-8, -6)

V  (9, -3)      →        V'(-3, -9)

W  (7, -3)     →        W'(-3, -7)

Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

 T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)

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Broccoli and peppers occupy 11/12 of the gardenAs a result, 11/12 of the garden is filled with vegetables.

1,Let's add up those two fractions to determine how much of the entire garden contains broccoli and peppers since we know that 1/4 of the garden has broccoli and 2/3 of the garden contains peppers.

Consequently, 1/ 4 + 2/3 =?

It is necessary for the denominator to match.

Consequently, 1/4 x 3/ 3 = 3 / 12.

2/3 × 4 /4 = 8 / 12

Hence, 3 / 12 + 8 / 12 = 11 / 12

2  ,Amount of flour needed to complete both recipes =2+1/4+1

3,  Baked cake 1 /8 +3/4,

6  , Number of birdhouses to be made / Number of bird houses he usually makes x Meters of wood needed for birdhouses Felipe usually makes

= 54 / 12 x 5¹/₄

= 23 ⁵/₈ meters

7,   24 brownies = 9/2 cups of walnuts

    8 brownies =1 1/2 cups of walnuts

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Answer:f(x)=10e^4x

Step-by-step explanation:

f(x)=C*e^4x

f(0)=c*e^4.0

10=C*e^4.0

10=C

f(x)=C*e^kx

f(x)=C*e^4x

Stratified random sampling was the technique employed by Homer to choose his sample.

Given case;

Homer Simpson is fascinated with the proportion of the different sprinkled colors on lard lad doughnuts. Homer buys three of each type of donut they produce and counts the sprinkles on them to perform his research.

The method did homer use to select his sample is stratified random sampling. Because each variety is a stratum.

From there 3 3 samples are collected.

Stratified random sampling:

A crucial aspect of the sampling strategy known as stratified random sampling is the stratification of a population into smaller subgroups known as strata. During stratified random sampling, the strata are created based on the shared traits or features of the participants, such as level of education or income. Numerous uses and advantages of stratified random sampling include examining life expectancy and population demography.

The terms proportionate random sampling and quota random sampling are also used to describe stratified random sampling.

The method did homer use to select his sample is stratified random sampling.

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Bridgette gives 1/10 cans of food to each dog.

According to the question,

We have the following information:

Bridgette has 9 dogs. Every day, she feeds them a total of 9/10 of a can of food, where each dog is fed the same amount of food.

Now, we have the following expression:

9 dogs = 9/10 can

Now, we can easily find the cans given to each dog using division. We will divide the total number of cans of food by the number of dogs.

1 dog = 9/(10*9) cans

1 dog = 1/10 cans of food

Hence, Bridgette gives 1/10 cans of food to each dog.

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The triangle does not exist, as the property, the sum of two sides of a triangle is greater than the third side length of the triangle does not hold true.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric forms is represented by the symbol △ and consists of three connected vertices. Triangles may be categorized into a number of different varieties according to their sides and angles.

It is a triangle's property that the sum of any two sides of a triangle is greater than the third side.

Here sides given are 3 m, 5 m, 9 m.

Let us add the sides length 3 m and 5 m

3 m + 5 m = 8 m

Compare this with the third-side length of the triangle

8 m < 9 m

So, the property does not hold true.

So, the triangle does not exist.

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The number of ribbons that is needed for 7 presents is 73 ribbons.

She needs 5 packages.

An expression is simply used to illustrate the relationship between the variables.

In this case, it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used.

The ribbons needed for 7 presents will be:

= 10p + 3

= 10(7) + 3

= 70 + 3

= 73

Since it's sold in 15 feet packages, the number needed will be:

= 73 / 15

= 5

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The equation of the line parallel to x - y = 3 and passes through pint (2,-4) is y = x - 6.

The equation of line is expressed as;

y = mx + b

The point-slope formula is expressed as;

y - y₁ = m( x - x₁ )

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

Given the data in the question;

Point: (2,-4)

First, reorder the given equation in slope-intercept form and determine the slope.

x - y = 3

x = 3 + y

3 + y = x

y = x - 3

Hence,

The slope m = 1

To find the line parallel to the equation, the slope must be equal.

Find the line using point-slope formula.

y - y₁ = m( x - x₁ )

Plug in slope m = 1 and point: (2,-4)

y - ( -4 ) = (1)( x - 2 )

Simplify and convert to slope intercept form.

y + 4 = x - 2

y = x - 2 - 4

y = x - 6

Therefore, the equation of line is y = x - 6.

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The expected number of customers that get back their own hat is 1.

Utilizing indicator random variables, we resolve this issue. For 1 ≤ i ≤ n,

Let .

Xi = I {Customer 'i' who gets his hat back itself}.

The number of clients that receive their own hats back should be the random variable X. We want to figure out E[X].

Clearly,

      n

X = ∑ Xi

    i=1

It is clear that 1/n represents the likelihood that customer 'I' will receive his own hat.

Due to the fundamental characteristics of indicator random variables, this means that E[Xi] = 1/n.

                   n

  E[X] = E [ ∑ Xi  ]

                  i=1

                   n

           =  ∑ 1/n

                  i=1

Put the limits.

  E[X] = 1

As a result, 1 consumer is anticipated to have their own hats back.

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The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)

A sample mean is the result of a chance experiment. When we sample a random variable, we get one of its possible values. A sample is a specific value. The random variable's probability distribution determines the possible values and the likelihood of each.

Given that,

Point estimate = sample mean = X = 40.7

sample standard deviation = s = 9.2

sample size = n = 19

Degrees of freedom = df = n - 1 = 19 - 1 = 18

At 80% confidence level

α = 1 - 80%

α =1 - 0.80 =0.2

α/2  = 0.1

t  α/2,df = t0.1,18 = 1.330

The margin of error = E = t /2, df x (s/√n)

= 1.330 x (9.2/√19)

= 1.330 x 2.110

= 2.8

Margin of error = E = 2.8

The 80% confidence interval estimate of the population mean is,

X  ±  E

= 40.7  ±  2.8

= (43.5, 37.9)

Therefore The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)

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Answer:

2. ax=m and ​ay=n​

4. mn=a(x+y)

6. power property of logarithms.

I took the quiz.

k12

i took the quiz this is the right answers

Answer: D

Step-by-step explanation: Proportional relationship = relationships between two variables where their ratios are equivalent. 6:15 is equivalent with both 8:20 and 10:25. So D is the correct answer.

The other ways of rewriting the expression are (xˣ)⁽²⁾ or xˣ²

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

x^(x^2)

Rewrite the expression properly

So, we have the following representation:

x⁽ˣ⁾⁽²⁾

The only ways the above expression can be rewriting the expression is by changing the positions of the brackets or removing the brackets entirely

Other than that, there are no other ways of rewriting the expression

So, we have

(xˣ)⁽²⁾ or xˣ²

Hence, the expressions are (xˣ)⁽²⁾ or xˣ²

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In the word problem, if mike has 40 coins consisting of dimes and quarters and if the dimes were quarters and the quarters dimes, he would have 90 cents more, he has 17 quarters.

A word problem refers to a mathematical exercise where significant information on the problem is given in ordinary language and not mathematical notation.  Let x be the number of dimes (10 cents) and y be the number of quarters (25 cents). Hence, the total number of coins is:

x + y = 40

The amount of the total coins would be 0.1x + 0.25y.

If the dimes were quarters and quarters were dimes, he would have 90 cents more than the amount he has now.

Hence,

0.25x + 0.10y = 0.1x + 0.25y + 0.9

Solving,

0.25x – 0.1x = 0.25y – 0.1y +0.9

0.15x = 0.15y + 0.9

As x + y = 40, x = 40 – y

Substituting,

0.15 (40 – y) = 0.15y + 0.9

6 - 0.15 y = 0.15y + 0.9

0.15y + 0.15y = 6 – 0.9

0.3y = 5.1

y = 5.1/0.3 = 17

Hence, the number of quarters are 17.

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Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.

An outcome of a random experiment is a sample. A random variable is sampled when we choose one particular value from its range of potential values. A sample is that precise value. The probability distribution of the random variable determines the possible values and the likelihood of each. Using samples, one can draw conclusions about populations. Since samples are useful, affordable, practical, and manageable, it is simpler to gather data from them. A crucial component of the scientific method is sampling, which enables researchers to demonstrate the validity of generalizable ideas using only a sample of particular facts. Additionally, sampling enables mathematicians to answer challenging paradoxes like the St.

Given,

Exceed relationship will the tolerable rate normally have when compared to the expected rate of deviations in the sample.

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A sample to have a standard deviation of zero means the score has no variability.

When the score has no variability it points towards the standard deviation being zero, This is the case where all the scores in the sample have the exact same value. This means there is no spread in the data set at all. The data set is combined in a single clumped value. Since there is only one value it would be the mean of the data set. The standard deviation measures the spread of a quantitative data set. This number cannot be a non-negative real number.

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Answer:

Home Stores

4.85×5

= 24.25

Paint Supplies

£18

∛128 is  the radius r and height h of the cylinder with minimal surface area .

What is Surface Area?

       V = πr²n

   128π = πr²n

        n = 128/r²

s = 2πrn + 2πr²

s = 2πr 128/r² +  2πr²

s = 256π/r + 2πr²

ds/dt = - 256π/r²  + 2πr

d²s/dt² = -256/(-2) r³ + 2π

d²s/dt² = 128/r³ + 2π

for maxima or minima

ds/dt = 0

- 256 π/r² + 2πr = 0

256 = 2r³

 r = ∛128

d²s/dt² = 128/(∛128)³  + 2π

           = 2π + 1

d²s/dt² > 0

so surface area is minimum

         a + r  = ∛128

  n = 128(∛128)²

   n = ∛128

r = ∛128  ,  n= ∛128

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The deceleration of the train is -3 ms^-2.

Given:

A train is moving along a Straight track with a speed of 30 ms^-1 when it reaches point A. the driver applies the brakes and the train decelerates at a constant speed until it comes to a stop 150 m from point A

we know that:

v^2 - u^2 = 2as

where

v = 0

u = 30 ms^-1

s = 150 m

0^2 - 30^2 = 2a*150

0 - 900 = 300*a

-900 = 300*a

a = -900/300

a = -3 ms^-2

Negative acceleration is nothing but the deceleration so a = -3 ms^-2.

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The cost of publishing the 300 copies of the book is $6500.

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 a small publishing company is planning to publish a new book. Let C be the total os of publishing the book(in dollars). Let N be the number of copies of the book produced. For the first printing, the company can produce up to 300 copies of the book. Suppose that c=20N+500 gives C as a function of N during the first printing.

The cost of 300 copies will be calculated as,

c=20N+500

c = ( 20 x 300 ) + 500

c = 6000 + 500

c = 6500

Therefore, the cost of publishing the 300 copies of the book is $6500.

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Answer:I think $1064

Step-by-step explanation:

First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.

The probability of the selected household will own a dog or a cat can't be determined because there is not enough information to determine the probability

Probability is counted by dividing the event number with the total number of outcomes. In this case, the probability of the selected household will own a dog or a cat will have a formula like this:

P(A ∨ B)=P(A)+P(B)+P(A ∧ B)

Annotation:

P(A ∨ B) = probability own a dog or a cat

P(A) = probability own a dog

P(B) = probability own a cat

P(A ∧ B) = probability own a dog and a cat.

Based on question, we cant find value of the probability own a dog and a cat. Therefore, the best answer for this question there is not enough information to determine the probability

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Considering an exponential function, it is found that:

a) The half-life of the element is of 39.63 days.

b) The time needed is of 51.82 days.

A decaying exponential function is modeled by the equation presented as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which the variables of the equation are:

In this problem, the parameters are given as follows, from the text:

A(0) = 120, A(11) = 99.

Hence the decay rate r is obtained as follows:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]120 = 99(1 - r)^{11}[/tex]

[tex](1 - r)^{11} = \frac{99}{120}[/tex]

[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]

[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]

1 - r = 0.98266367982

Hence the equation is:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

The half-life is the value of t for which:

A(t) = 0.5A(0).

Hence:

[tex]A(t) = A(0)(0.98266367982)^t[/tex]

[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = 0.5[/tex]

[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]

[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]

t = 39.63 days.

For item b, the time is obtained as follows:

[tex]A(t) = 99(0.98266367982)^t[/tex]

[tex]40 = 99(0.98266367982)^t[/tex]

[tex](0.98266367982)^t = \frac{40}{99}[/tex]

[tex](0.98266367982)^t = 0.40404040[/tex]

[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]

t = 51.82 days.

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