The snack bar at the game begins with 150 cans of soda. Each hour they sell 30 cans until they have sold out all the cans of soda. Write an equation representing the situation

Answer: 9/2

Step-by-step explanation: Find explanation in the attached file

The amount of the element, Francium, that will remain after 2 hours is 31.25 grams.

To determine how much francium will be left after 2 hours, we need to calculate the number of half-lives that occur within that time period.

Given that the half-life of francium is 22 minutes, we can calculate the number of half-lives in 2 hours (120 minutes):

Number of half-lives = (Total time elapsed) / (Half-life)

Number of half-lives = 120 minutes / 22 minutes ≈ 5.4545

Since we can't have a fraction of a half-life, we take the integer part, which is 5.

Each half-life represents a halving of the amount of francium. So, after 5 half-lives, the remaining amount of francium can be calculated using the formula:

Remaining amount = Initial amount * (1/2)^(Number of half-lives)

Given that the initial amount is 1000 grams, we can calculate the remaining amount after 2 hours:

Remaining amount = 1000 grams * \((1/2)^5\)

Remaining amount ≈ 1000 grams * 0.03125

Remaining amount ≈ 31.25 grams

Therefore, after 2 hours, approximately 31.25 grams of francium will be left.

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The composite function c(x) = 0.8x - 3, and the cost of a $30 item would be $21.

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Let, 'x' be the original cost of the item.

A store offers a 20% discount on all items,

So, f(x) = [(100 - 20)/100]×x.

f(x) = (80/100)×x.

f(x) = 0.8x.

Again, you also have a $3 coupon.

Let, g(x) = x - 3.

Now, The composition of the functions f(x) and g(x) is f(x) + g(x) = C(x).

C(x) = 0.8x - 3.

Now, The cost of an item is $30.

Therefore, C(30) = 0.8×30 - 3.

C(30) = 24 - 3.

C(30) = 21.

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The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments

Degree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45

Mean squares between groups is calculated as follows:

Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58

Mean squares within groups is calculated as follows:

Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places

F ratio is calculated as follows:

F= Mean squares between groups/Mean squares within groups

= 58/8.89

= 6.524184477

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The volume V of the solid obtained by rotating the region bounded by the curves \(y^2=2x\) and \(x=2y\) about the y-axis is 107.168

Given,

The curves are \(y^2=2x...i\) and \(x=2y....ii\)

We need to determine the volume V of the solid obtained by rotating the region bounded by the given curves about y-axis.

Volume of the region can be obtained by using washer method.i.e.

\(V=\int \pi [(f(y)_{outer})^2-(f(y)_{inner})^2]dy\)

From figure, we can observe that the inner curve i.e. \(f(y)_{inner}\) is \(y^2=2x = > x=\frac{y^2}{2}\)

and outer curve i.e. \(f(y)_{outer}\) is \(x=2y\).

To determine the boundaries of the integral, substitute eq.ii in eq.i, we get

\(y^2=2(2y)\\\\y^2=4y\\\\y^2-4y=0\\\\y(y-4)=0\\\\\)

y=0 and y=4

These are the limits of the integral

Now, substituting the equations for volume V,

\(V = \int\limits^4_0 \pi [ (2y)^2 - (\frac{y^2}{2} )^2] dy\\\\ V = \int\limits^4_0 \pi [ 4y^2 - (\frac{y^4}{4} )] dy\\\\V = \pi [ \frac{4}{3} y^3 -\frac{1}{20} y^5 ]\limits^4_0\\\\V=\pi[\frac{4}{3}(4)^3-\frac{1}{20}(4)^5]\\\\V=\pi[\frac{256}{3} - \frac{1024}{20}]\\\\V=\pi[85.33-51.2]\\\\V=\pi [34.13]\\\\V=107.168\)

Hence, the volume of the region bounded by the curve after rotating is 107.168

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Answer:

7 and 1/3

Step-by-step explanation:

The remainder of the polynomial division \(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\) is 2y²

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

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)}\)

When the numerator is expanded, we have

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1) + 2y^2}{y^3 + 1}\)

Split the expanded expression

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = \frac{(y - 1)(y^3 + 1)}{y^3 + 1} + \frac{2y^2}{y^3 + 1}\)

Evaluate

\(\frac{\left(y^4-y^3+2y^2+y-1\right)}{\left(y^3+1\right)} = y - 1 + \frac{2y^2}{y^3 + 1}\)

From the above, we have

Quotient = y - 1

Remainder = 2y²

Hence, the remainder of the polynomial division is 2y²

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A function is what happens even if \($f(-x)=f(x)$\) for all \($x \in \mathbb{R}$\) and A function is what happens odd if \($f(-x)=-f(x)$\) for all \($x \in \mathbb{R}$\) .

Parity of \($\sqrt{\tan ^2(y)}+\sqrt{y^2}, \frac{\pi}{2} < y < \pi$\) : Even .

Defining parity

A function is what happens even if. \($f(-x)=f(x)$\) \(for all $x \in \mathbb{R}$\)                      A function is what happens odd if \($f(-x)=-f(x)$\) for all \($x \in \mathbb{R}$\)

\($$\begin{aligned}& f(-y): \quad \sqrt{y^2}+\sqrt{\tan ^2(y)} \\& -f(y): \quad-\sqrt{\tan ^2(y)}-\sqrt{y^2}\end{aligned}$$\)

Check parity of \($\sqrt{\tan ^2(y)}+\sqrt{y^2}$\)

Equal or equivalentness, as a trait or state. Women have battled for equal pay to males in the workplace, or the equivalent of a commodity's price in one currency to that in another.

An integer's evenness or oddness is defined by its parity. In light of the fact that both 6 and 14 are even, it can be claimed that their parities are the same, but 7 and 12 have the opposite parity (since 7 is odd and 12 is even). the state of equality, particularly the state of equal pay or status Prison guards are want pay parity with the police. Women still lack balance in many occupations, especially at the top levels.

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The polar form of 2+2i is \($2\sqrt{2}(\cos(\frac{\pi}{4}) + i\sin(\frac{\pi}{4}))$\)

We are given that;

The complex number= 2+2i

Now,

To convert a complex number from rectangular form to polar form, we need to find its magnitude and argument.

The magnitude is the distance from the origin to the point (x, y) on the complex plane, and the argument is the angle between the positive x-axis and the line joining the origin and the point.

Using the Pythagorean theorem and the inverse tangent function, we get:

Magnitude = \($\sqrt{x^2 + y^2}$\)

Argument = \($\tan^{-1}(\frac{y}{x})$\)

Plugging in x = 2 and y = 2i, we get:

Magnitude = \($\sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2}$\)

Argument = \($\tan^{-1}(\frac{2}{2}) = \frac{\pi}{4}$\)

Therefore, by pythagoras theorem answer will be \($2\sqrt{2}(\cos(\frac{\pi}{4}) + i\sin(\frac{\pi}{4}))$\).

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Answer:

$1126.16

Step-by-step explanation:

1000(1+2%)^6 is the equation

Answer:

The table represents a linear function.

Step-by-step explanation:

Graphed, the points go in a straight line, and you are able to draw a line through it. The equation for the line is y = 4x + 4.

The measure of m<JMO is 20 degrees

The triangle JOK is a 60 degrees equilateral triangle. Hence the measure of m<O at the center is 60 degrees.

Since the base angles of triangle KOL and OLM are equal hence;

Substitute the base angles and the equilateral angles to get angle JOM

80 + 80 + m<JOM + 60 = 360

m<JOM = 360 - 360 - 220

m<JOM = 140 degrees

Since the sum of angle in the triangle JOM is 180 degrees, hence;

2m<JMO + m<JOM = 180

2m<JMO = 180 - 140

2m<JMO = 40

m<JMO = 20 degrees

Hence the measure of m<JMO is 20 degrees

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Answer:

224

Step-by-step explanation:

the area of a circle is \(\pi\)\(r^{2}\), so for the circle plug in your numbers:

(3.14)(\(14^{2}\)) = 615.44

divide this by 4 because t=in the picture you only have a fourth of a circle:

615.44 / 4 = 153.86

the formula for area of a trapezoid is \(\frac{a + b}{2}\) × h

so plug in your values: \(\frac{14+14}{2}\) × 5

you get 70

add 70 and 153.22

70 + 153.22 = 223.22

this can round to 224

The height of the cylinder whose surface area is given would be = 85 yards.

The cylinder is a type of shape that has three sides which consists of two opposite circles that are joined by a curved surface.

To calculate the height of a cylinder, the formula that should be used is given as follows:

Surface area of cylinder = 2πrh + 2πr²

radius = 29 yards

surface area = 20,761.68 square yards

height = ?

That is ;

20,761.68 = 2×3.14× 29×h + 2×3.14× 29×29

20,761.68 =182.12h + 5281.48

182.12h = 20,761.68-5281.48

182.12h = 15480.2

h = 15480.2/182.12

= 85 yards

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Answer:

the answer is c :1/12....

Least time required to reach the point Q as per the distance and the speed rate is equal to 2 hours.

As given in the question,

Nearest point on the coast is 2 miles far away

rate of the row = 1mile per hour

Walk at the rate of 3 miles per hour

Let 'x' hours be the least time to reach point Q.

Time = distance / speed

Time taken to reach the point Q = [√ 1 + ( 3 - x)² ]/ 3

Time taken to reach the coast = (√ 4 + x² ) / 1

Total  time taken 't' = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

To find least time dt/dx = 0

t  = (√ 4 + x² ) / 1 + [√ 1 + ( 3 - x)² ]/ 3

⇒dt/dx = [ x / √ 4 + x² ] + ( 3 - x) / √( 10 -6x + x² )

⇒x / √ 4 + x² = ( x - 3) / √( 10 -6x + x² )

Squaring both the side we get,

x² / (4 + x²) = ( x - 3)² / ( 10 -6x + x² )

⇒3x² -24x +36 =0

⇒ x² -8x + 12 = 0

⇒ x = 2 or 6 hours

Therefore , the least time taken to reach the point Q is equal to 2 hours.

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Answer:

D

Step-by-step explanation:

The article "an" can only be used with the word "event" so that automatically takes the choices b and c out of the way. An event is something that happens and causes the outcome, it is not the outcome, so it is not A. Thus, the answer is D

A square root function that is represented by the graph include the following: A. f(x) = √(4x + 8).

In Mathematics and Geometry, a square root function can be defined as a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

Therefore, the required square root function is given by;

f(x) = √(4x + 8)

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Answer:

A. Fractions 1 and 4

B. Fractions 1, 2, and 3

Step-by-step explanation:

A negative divided by a positive is a negative.

A positive divided by a negative is a negative.

If the negative symbol is in line with the fraction bar, it is still a negative.

The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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Answer: 22.5

Step-by-step explanation:

math

Answer:

Linear

Step-by-step explanation:

She is spending the same amount per day, so it is linear

Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Combine like terms 4n can only be added with 7n and 14 can only be added to 6

Answer:

11n + 20

Step-by-step explanation:

Because all of the signs are + , the parentheses can be removed.

Next, combine like terms:

4n + 14 + 6 + 7n = 11n + 20

None of the three given possible answers is correct.

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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The possible numbers that Melody could have picked are -4 and 4.

The operation that prevents us from knowing with 100% certainty the number Melody had picked is multiplication which is implied by the phrase "double the number".

Given, Let x be the number Melody had chosen.

Thus, tripling the number will give 3x, and

squaring this will result to (3x)² which is equals to 9x².

Dividing the square of the number by 2 and subtracting 30 from its quotient will give 42:

9x²/2 ₋ 30 = 42

9x²/2 = 42 ₊ 30

9x²/2 = 72

9x² = 72 × 2

9x² = 144

x² = 144/9

x² = 16

x = ±√16

x = ±4

x = ₊4 or x = 4

hence melody could have picked ₊4 or ₋4 numbers.

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The shape of each PDF will be different due to the different standard deviations, with the PDF with the smallest standard deviation being the narrowest and tallest, and the PDF with the largest standard deviation being the widest and shortest.

For our case, since we want to plot four normal distributions with mean zero, we can simplify the formula as:

f(x) = (1/σ√(2π)) * e^-(x^2/(2σ^2))

where µ = 0.

Now, to plot the four normal distributions, we can use the same formula but with different standard deviations. We can choose any values for the standard deviations, but in this case, let's use 1/4, 1/2, 1, and 2.

Thus, the PDFs for the four normal distributions are:

f1(x) = (1/(1/4)√(2π)) x \(e^{-x^2/(2(1/4)^2)}\)

f2(x) = (1/(1/2)√(2π)) x \(e^{-(x^2/(2(1/2)^2))}\)

f3(x) = (1/1√(2π)) x \(e^{-(x^2/(2(1)^2))}\)

f4(x) = (1/2√(2π)) x \(e^{-(x^2/(2(2)^2))}\)

We can then plot these four PDFs on the same graph, with the x-axis representing the data and the y-axis representing the probability density.

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Answer:

About 300 dollars

Step-by-step explanation:

THe best estimate for week one is 300, because 96 rounds to 100, and 100 * 3 equals 300.

The best estimate for week 2 is 600, because 204 rounds to 200, and 200 * 3 equals 600.

600 - 300 = 300, therefore the difference is about 300 dollars.

Hope this helps!

As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Answer:

t = \(\sqrt{63} \\\) or 7.94

Step-by-step explanation:

Yes, you have to use the Pythagorean theorem

A^2+B^2=C^2

So, A=9, B=t, C=12

9^2+t^2=12^2

81+t^2=144

-81        -81

t^2 = 63

t = \(\sqrt{63} \\\)

in decimal 7.94

Hope this helps :)

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