Jeremiah wants to set aside enough money for lunch during the coming year. How much money will he need to save assuming he eats four days a week for 32 weeks and spends​ $3 per​ lunch? ​$
nothing

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer: 0.41666666...

Step-by-step explanation: 5/12 is the exact same as 5 divided by 12 (hard to show that on computer) 5 divided by 12 is 0.4166....

Given:

The length of all sides of the given shape.

8.2 ft, 6.6 ft, 6.6 ft, 6.6 ft, 6.6 ft, 2 ft, 2 ft, 6.6 ft, 6.6 ft, 12.4 ft, 12.4 ft, and 8.2 ft.

Aim:

We need to find the perimeter of the given shape.

Explanation:

Recall that the perimeter of the shape is the sum of the lengths of all sides of the shape.

Final answer:

Answer:

The most common units of distance are inches, feet, yards, and miles.

Step-by-step explanation:

Hope this helped you :) N read my 9 poems I have written :)

Answer:

first and third expressions

Step-by-step explanation:

using the rule of exponents

\(\frac{a^{m} }{a^{n} }\) = \(a^{m-n}\)

then

\(\frac{3^{\frac{4}{9} } }{3^{\frac{2}{9} } }\)

= \(3^{\frac{4}{9}-\frac{2}{9} }\) ← first expression

= \(3^{\frac{2}{9} }\) ← third expression

The directed distance from point A to the curve at the angle theta = 5\(\pi\)/6 is:

\(\sqrt(192 + 48\sqrt(3))\)

To find the directed distance from point A to the curve at the angle theta = 5\(\pi\)/6, we first need to find the equation of the tangent line to the curve at point A.

To do this, we can take the derivative of the curve equation with respect to x:

\(2x + 2y * dy/dx + 8 = 0\)

Solving for dy/dx, we get:

\(dy/dx = -x / (y + 4)\)

At point A, we have x = -4 and y = 4, so:

\(dy/dx = -(-4) / (4 + 4) = 1/2\)

Therefore, the equation of the tangent line to the curve at point A is:

\(y - 4 = (1/2) * (x + 4)\)

Simplifying, we get:

\(y = (1/2) * x + 6\)

Now we can find the intersection point of the tangent line with the line passing through point A and making an angle of 5π/6 with the positive x-axis.

The line passing through point A with angle 5π/6 has slope:

\(tan(5\pi /6) = -\sqrt(3)\)

So the equation of this line is:

\(y - 4 = -\sqrt(3) * (x + 4)\)

Simplifying, we get:

\(y = -\sqrt(3) * x + 4\sqrt(3) + 4\)

Now we can solve for the intersection point of the two lines. Setting the equations for y equal to each other, we get:

\((1/2) * x + 6 = -\sqrt(3) * x + 4\sqrt(3) + 4\)

Solving for x, we get:

\(x = -8 / (2 + \sqrt(3))\)

Now we can find the corresponding value of y using either equation for the tangent line or the line with angle 5π/6. Using the equation for the tangent line, we get:

\(y = (1/2) * (-8 / (2 + \sqrt(3))) + 6 = 11 - 4\sqrt(3) / (2 + \sqrt(3))\)

The directed distance from point A to this intersection point is the distance between these two points along the line with angle 5π/6. This distance can be found using the distance formula:

\(d = \sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Plugging in the values, we get:

\(d = \sqrt((-4 - (-8 / (2 + \sqrt(3))))^2 + (4 - (11 - 4\sqrt(3) / (2 + \sqrt(3))))^2)\)

Simplifying, we get:

\(d = \sqrt(192 + 48\sqrt(3))\)

Therefore, the directed distance from point A to the curve at the angle theta = 5π/6 is:

\(\sqrt(192 + 48\sqrt(3))\)

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The directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

What is curve?

In mathematics, a curve refers to a continuous and smooth line that has no corners or edges. Curves can be described using equations or parametric equations, and they can be represented in a two-dimensional or three-dimensional space.

To find the directed distance when θ = 5π/6, we first need to find the corresponding point on the curve.

The equation \(x^2 + y^2 + 8x = 0\) can be rewritten as \((x + 4)^2 + y^2 = 16\), completing the square. This is the equation of a circle with center (-4, 0) and radius 4.

To find the point on the circle corresponding to θ = 5π/6, we can use polar coordinates. Let r be the radius of the circle (r = 4), and let θ be the angle from the positive x-axis to the point we want to find. Then we have:

x = r cos(θ) = 4 cos(5π/6) = -2√3

y = r sin(θ) = 4 sin(5π/6) = 2

So the point on the curve corresponding to θ = 5π/6 is (-2√3, 2).

To find the directed distance from point A (-4, 4) to this point, we can use the distance formula:

distance = √[\((x2 - x1)^2 + (y2 - y1)^2\)]

= √[\((-2\sqrt3 - (-4))^2 + (2 - 4)^2\)]

= √[12 + 4]

= 2√4

= 4

Therefore, the directed distance from point A to the point on the curve corresponding to θ = 5π/6 is 4 units.

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Answer:

Step-by-step explanation:

Given:

We know that the sum of squares of diagonals of the parallelogram is equal to twice the sum of the squares of the sides:

Substitute the values and solve for b:

\(\sqrt{25*7x^{4}*x^{1} } \\=\sqrt{25*x^{4}*7 *x^{1} } \\=\sqrt{25x^{4} } *\sqrt{7x}\\=5x^{2} \sqrt{7x}\)

Option B is the answer.

Answer: C

i hope you can see my handwriting

The Solution:

Given the figure:

We are asked to show that DE and AB are parallel.

So, by the similarity theorem, we have

If a segment is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original and the segment that divides the two sides it intersects is proportional.

Thus, the two triangles are similar. So, it follows that line DE is parallel to line AB since the ratios of the two corresponding sides are equal.

Answer:

15 cups of flour

Step-by-step explanation:

if the vanilla is going from 2 - 6 then it is being multipled by 3. Therfore you should multiply the flour (5) by 3, which makes the total flour to be 15 cups.

Answer:

15

Step-by-step explanation:

CUPS TEASPOONS

5 2

10 4

15 6

The Central Limit Theorem states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of the underlying distribution of the variable. In this case, we have a sample size of 42, which is large enough for the Central Limit Theorem to apply.

The mean of the sampling distribution of the mean is equal to the population mean, which is $100. The standard deviation of the sampling distribution of the mean is equal to the population standard deviation divided by the square root of the sample size, which is $20 / sqrt(42) ≈ $3.08.

We can standardize to find the z-score for a sample mean of $90: z = ($90 - $100) / $3.08 ≈ -3.25. Using a z-table, we find that the probability of getting a z-score less than -3.25 is approximately 0.0006. Therefore, the probability that the mean coffee expense of a randomly selected sample of 42 college students is greater than $90 is approximately 1 - 0.0006 = 0.9994.

The width of the shape is 4.2 units

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

Surface Area = 54 square units

Length = 2 units

Height = 3 units

The surface area of the shape can be calculated using the following formula

Surface Area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

2 * (2 * Width + 2 * 3 + Width * 3) = 54

Divide both sides by 2

So, we have

2 * Width + 2 * 3 + Width * 3 = 27

Subtract 6 from both sides

2 * Width + Width * 3 = 21

This gives

Width * 5 = 21

Divide both sides by 5

Width = 4.2

HEnce, the width is 4.2 units

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Answer:

30

Step-by-step explanation:

hope it helps <3

Answer: 5/2

Step-by-step explanation:

slope equation: (y2-y1)/(x2-x1)

13-3/5-1 = 10/4 or 5/2

Answer:

2.5

Step-by-step explanation:

Gradient (slope) =

\(m = \frac{y2 - y1}{x2 - x1} = \frac{13 - 3}{5 - 1} = \frac{10}{4} = 2 \frac{1}{2} \)

Answer: 6 1/6

Step-by-step explanation:

6 can go into 37 6 times

6x6=36

with 1 left over

The fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fraction is:

= 37/6

We can write the above number as:

= (36 + 1)/6

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 36/6 + 1/6

= 6 + 1/6

Or

= 6 1/6 (mixed fraction)

Thus, the fraction 37/6 can be changed to the mixed number​ as 6 1/6 if the fraction is 37/6.

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The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer:

3x + 8y = 60 ; x + 3y = 22

Step-by-step explanation:

Answer:

Analysis for these data will be based on a __survey__ design.

Step-by-step explanation:

A survey design is a process through which surveys are conducted to acquire enough insight about a given situation or matter of interest.  In this case, the National Park Service's interest is finding out the amount of money that visitors in the two different national parks spend.  Visitors are sampled from each park to get the required information.  The mean spends are calculated and then compared.

Brooklyn needs to invest $432.43, rounded to the nearest ten dollars.

To determine how much Brooklyn needs to invest in an account that pays a continuously compounded interest rate, we can use the formula:

A = \(Pe^(^r^t^)\)

where A is the future value of the account, P is the principal investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.

In this case, we want the future value of the account to be $640, the interest rate is 3.5% (or 0.035 as a decimal), and the time is 9 years. We can substitute these values into the formula and solve for P:

640 = \(Pe^(^0^.^0^3^5^*^9^)\)

640 = Pe^0.315

P =\(640/e^0^.^3^1^5\)

P = 432.43

Therefore, to have a future value of $640 in 9 years with a continuously compounded interest rate of 3.5%.

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Answer:

216.

Step-by-step explanation:

To solve this expression, you can first simplify the expression inside the parentheses:

45 - (25 + 8) = 45 - 33 = 12

Then you can substitute this simplified expression back into the original equation and multiply by 18:

(12) X 18 = 216

The relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

Is a function, because each element in the domain is mapped to a single element in the range.

A relation maps elements from one set, called the domain, into another set, called the range.

For example, the element x mapped into element y is written as (x, y).

Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.

So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).

Here the relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.

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Answer:

Step-by-step explanation:

First, we solve any operations inside of parentheses or brackets. Second, we solve any exponents. Third, we solve all multiplication and division from left to right. Fourth, we solve all addition and subtraction from left to right.

Answer:

3 feet

Step-by-step explanation:

Answer:

3 feet

Step-by-step explanation:

A dilation is changing the size of a figure. A factor of 2.5 would mean to multiply it by 2.5.

1.2 x 2.5 is 3

3 ft is the answer

The estimate of 179% of 41 by rounding is about 73.19.

To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.

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No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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Answer:

e^-x + e^x  + c

Step-by-step explanation:

∫e^x  dx   -  ∫e^-x dx

= e^x - -e^-x

= e^x + e^-x

= e^-x + e^x + c

Answer:

Q1 = 32.5

Q3 = 50

D2 = 29

D8 = 52

67th percentile = 46.5

Step-by-step explanation:

Given the ordered data:

13, 13, 13, 20, 26, 29, 32, 33, 34, 34, 35, 35, 36, 37, 38, 41, 41, 41, 45, 46, 47, 47, 48, 52, 54, 55, 56, 62, 67, 82

The first quartile :

Q1 = 1/4(n+1)th term

n = sample size = 30

Q1 = 1/4(31) = 7.75 = (7th + 8th) / 2 = (32+33) / 2 = 32.5

Q3 = 3/4(n+1)th term

n = sample size = 30

Q3 = 3/4(31) = 23.25 = (23rd + 24th) / 2 = (48+52) / 2 = 50

D2 = 2nd decile

2 * 10% = 20%

20% * n

0.2 * 30 = 6th = 29

D8 = 8th decile

8 * 10% = 80%

80% * 30 = 24th = 52

67th percentile :

0.67 * 30 = 20.1 th

(20th + 21th) / 2

(46 + 47) / 2

= 46.5

The Relative Maximum will be (7, 50) and minimum is (12, 0).

We have the graph showing average low temperatures in international falls minnesota.

From the graph the maximum y coordinate is 50.

So, the Relative Maximum will be (7, 50).

and, the minimum y coordinate is 0.

So, the Relative minimum is (12, 0)

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Answer:

2 : 18

Step-by-step explanation:

to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.

1 : 9 ( multiply both parts by 2 )

= 2 : 18

or

1 : 9 ( multiply both parts by 3 )

= 3 : 27

and so on...