Plz help8 Pamela is shopping for bottled water at the supermarket. Which is the best buy?

47,448/12=$3954

As, 28/36 rule states that maximum of 28% of your monthly expenditure should be spent on housing finances.

0.28*3954=$1107,12

Answer: $1107.

Answer:

(1.5, 1.5)

Step-by-step explanation:

To solve the system of equations, use elimination, substitution, or graphing to find the solution. The solution is the point (x,y) where they intersect.

Graph 2x + 12y = 21 and 2x + 2y = 6.

See attached picture.

The solution is (1.5, 1.5).

Final answer:

To find the inverse function of a given function, interchange x and F(x) and solve for x. The steps involve replacing F(x) with y, interchanging x and y, and then solving for y.

Explanation:

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and F(x) and solve for x. Step by step:

Replace F(x) with y: y = (8 - 2x)²

Interchange x and y: x = (8 - 2y)²

Solve the resulting equation for y: y = 4 - √(x) / 2

The function F(x) = (8 - 2x)² does not have an inverse function because it's not one-to-one. Instead, for all x, the inverse is a constant function [tex]\( F^{-1}(x) = 4 \)[/tex].

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and y and then solve for y. So, let's start by writing y instead of F(x):

y = (8 - 2x)²

Now, our goal is to solve this equation for x. First, we'll expand the expression:

y = (8 - 2x)(8 - 2x)

y = 64 - 16x - 16x + 4x²

y = 4x² - 32x + 64

Now, to find the inverse, we switch x and y and solve for y :

x = 4y² - 32y + 64

This is a quadratic equation in terms of y, so we need to solve it. To do that, we can use the quadratic formula:

[tex]\[ y = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where a = 4, b = -32, and c = 64. Plugging in these values:

[tex]\[ y = \frac{{32 \pm \sqrt{{(-32)^2 - 4(4)(64)}}}}{{2(4)}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{{1024 - 1024}}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{0}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm 0}}{{8}} \][/tex]

[tex]\[ y = \frac{{32}}{{8}} \][/tex]

y = 4

So, the inverse function of F(x) is [tex]\( F^{-1}(x) = 4 \)[/tex].

This result suggests that the function F(x) is not one-to-one, meaning it doesn't have an inverse that's a function. Instead, it suggests that for every value of x, the function F(x) produces the same output, which is 4. Therefore, F(x) doesn't have a unique inverse function.

Answer:

The first option i.e a

Step-by-step explanation:

- 2.5 + (-1) = - 2.5 -1 = -3.5

and the arrow indicating towards -3.5 is first option

Answer:

3x=$20

Step-by-step explanation:

well first you divide    3x/3=$20/3                      

3 can go into 20 6 times that                                                                                                          would 18 and then u would have a remainder of 2 dollars and 3 cant go into 2 so it would be .67 so x=6.67

Answer:

Part A) Option B. [tex]-4n^{3}+24n^{2}-12n[/tex]

Part B) Option A. [tex]4n^{4}-24n^{3}+12n^{2}[/tex]

Step-by-step explanation:

Part A) we have

[tex](n^{2}-6n+3)(-4n)[/tex]

the product is equal to

[tex]=(n^{2})(-4n)-6n(-4n)+3(-4n)\\=-4n^{3}+24n^{2}-12n[/tex]

Part B) When this product is multiplied by -n, the result is

we have

[tex](-4n^{3}+24n^{2}-12n)(-n)[/tex]

[tex]=(-4n^{3})(-n)+24n^{2}(-n)-12n(-n)\\=4n^{4}-24n^{3}+12n^{2}[/tex]

Answer:

f(x) = -|x - 3| + 2.

Step-by-step explanation:

f(x) = |x| is shaped like a V and the vertex is at (0, 0). f(x) = -|x| is  a reflection  in the x-axis so will be an inverted V , opening down. f(x) = - |x - 3|  will be the  -|x| moved 3 units to the right with the vertex at (3, 0). To bring the vertex  to (3, 2)   it will move upwards 2 units.

So it is f(x) = -|x - 3| + 2.

f(x)=-|x-3|+2

Negative before the abs value inverts the graph and it moves right 3 and up 2

Answer:First one is D

Step-by-step explanation:

The graph passses through the pints neccessary for it to decrease by 300

➷ tanR = 20/29

tanR = 0.689655

The correct option would be 0.6897

➶ Hope This Helps You!

➶ Good Luck (:

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The value of tan R using trignonometic values is 0.9524.

Tan is used to determine the value of an angle given the opposite side and the adjacent side. Tan R is the opposite side divided by the adjacent side.

Tan = opposite / adjacent

Tan = 20/21

Tan = 0.9524.

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Why this is so easy

Ok so, 75/5=15

15*7 =105 so the answer is 105 pages

Answer:A translation then rotation then reflection

Step-by-step explanation:

In the context of the Side-Side-Side (SSS) theorem in geometry, the rigid transformations referred to are typically translation, rotation, and reflection. By strategically applying these transformations, one can map one triangle onto another, thereby demonstrating their congruence according to the SSS theorem.

Rigid transformations in the context of geometry often refer to transformations that preserve the shape and size of geometric figures. The characterization quoted as 'SSS proof' likely refers to the Side-Side-Side congruence theorem in geometry, which states that if the three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. This congruence can be proven through certain rigid transformations, most commonly, translation, rotation and reflection.

In the case of the SSS proof, one or a combination of these three transformations can be used to map one triangle onto another. For example, you can translate one triangle so that a vertex matches a corresponding vertex on the other triangle. Then rotate the translated triangle if necessary so that one side matches the direction of the corresponding side on another triangle, this is rotation. Finally, if the triangle is flipped relative to the other one, reflect along the appropriate axis to match the final side. Again, this is the most common example and sometimes you may need to combine the transformations.

The inquiry about Einstein's postulate and other references seems unrelated to rigid transformations in Geometry and the SSS proof specifically.

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let's say hight of tree is x.

from figure attached , using trigonometry we can say

tan 37 = x / 26

multiplying by 26 both side

tan 37 × 26 = x/26 × 26

tan 37× 26 = x

putting value of tan 37

x = tan 37 × 26 = 0.7535 × 26

x = 19.592 meters

Answer:

The dependent variable is the total cost "t"

Explanation:

The given equation is:

3n + 10 = t

where n is the number of yards and t is the total cost

We have two variables in this equation, n and t

We know that the total cost "t" will depend on the number of yards of fabric she buys

This means that the total cost will change by changing the number of yards bought

For example:

If she bought 1 yard: t = 10 + 3(1) = $13

If she bought 3 yards: t = 10 + 3(3) = $19

Therefore, the total cost "t" depends on the number of yards which means that "t" is the dependent variable in the equation

Hope this helps :)

Answer:

{0.16807, 0.36015, 0.3087, 0.1323, 0.02835, 0.00243}

Step-by-step explanation:

The expansion of (p+q)^n for n = 5 is ...

(p+q)^5 = p^5 +5·p^4·q +10·p^3·q^2 +10·p^2·q^3 +5·p·q^4 +q^5

When the probability p=0.3 and q = 1-p = 0.7 the terms of this series correspond to the probabilities of 5, 4, 3, 2, 1, and 0 favorable outcomes out of 5 trials.

For example, p^5 = 0.3^5 = 0.00243 is the probability of 5 favorable outcomes in 5 trials where the probability of each favorable outcome is 0.3.

___

The attachment shows the calculation of these numbers using a graphing calculator. It lists them in reverse order of the expansion of (p+q)^5 shown above, so that they are the probabilities of 0–5 favorable outcomes in the order 0–5.

See the attached pictures for the answers.

Since he has four cuts for each pizza, jason has 8 pizzas

Answer:

89

Step-by-step explanation:

86+78+80+99+99+92+86 = 620

620/7 = 88.57142857

And since you requested the nearest whole number the 88 turns into an 89 due to the fact that the tenth place is a 5 (or greater).

Answer:

The correct answer option is P (S∩LC) = 0.16.

Step-by-step explanation:

It is known that the probability if someone is a smoker is P(S)=0.29 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.552.

So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.552 = P(S∩LC) / 0.29

P (S∩LC) = 0.552 × 0.29 = 0.16

The area of the ellipse [tex]E[/tex] is given by

[tex]\displaystyle\iint_E\mathrm dA=\iint_E\mathrm dx\,\mathrm dy[/tex]

To use Green's theorem, which says

[tex]\displaystyle\int_{\partial E}L\,\mathrm dx+M\,\mathrm dy=\iint_E\left(\frac{\partial M}{\partial x}-\frac{\partial L}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

([tex]\partial E[/tex] denotes the boundary of [tex]E[/tex]), we want to find [tex]M(x,y)[/tex] and [tex]L(x,y)[/tex] such that

[tex]\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]

and then we would simply compute the line integral. As the hint suggests, we can pick

[tex]\begin{cases}M(x,y)=\dfrac x2\\\\L(x,y)=-\dfrac y2\end{cases}\implies\begin{cases}\dfrac{\partial M}{\partial x}=\dfrac12\\\\\dfrac{\partial L}{\partial y}=-\dfrac12\end{cases}\implies\dfrac{\partial M}{\partial x}-\dfrac{\partial L}{\partial y}=1[/tex]

The line integral is then

[tex]\displaystyle\frac12\int_{\partial E}-y\,\mathrm dx+x\,\mathrm dy[/tex]

We parameterize the boundary by

[tex]\begin{cases}x(t)=5\cos t\\y(t)=17\sin t\end{cases}[/tex]

with [tex]0\le t\le2\pi[/tex]. Then the integral is

[tex]\displaystyle\frac12\int_0^{2\pi}(-17\sin t(-5\sin t)+5\cos t(17\cos t))\,\mathrm dt[/tex]

[tex]=\displaystyle\frac{85}2\int_0^{2\pi}\sin^2t+\cos^2t\,\mathrm dt=\frac{85}2\int_0^{2\pi}\mathrm dt=85\pi[/tex]

###

Notice that [tex]x^{2/3}+y^{2/3}=4^{2/3}[/tex] kind of resembles the equation for a circle with radius 4, [tex]x^2+y^2=4^2[/tex]. We can change coordinates to what you might call "pseudo-polar":

[tex]\begin{cases}x(t)=4\cos^3t\\y(t)=4\sin^3t\end{cases}[/tex]

which gives

[tex]x(t)^{2/3}+y(t)^{2/3}=(4\cos^3t)^{2/3}+(4\sin^3t)^{2/3}=4^{2/3}(\cos^2t+\sin^2t)=4^{2/3}[/tex]

as needed. Then with [tex]0\le t\le2\pi[/tex], we compute the area via Green's theorem using the same setup as before:

[tex]\displaystyle\iint_E\mathrm dx\,\mathrm dy=\frac12\int_0^{2\pi}(-4\sin^3t(12\cos^2t(-\sin t))+4\cos^3t(12\sin^2t\cos t))\,\mathrm dt[/tex]

[tex]=\displaystyle24\int_0^{2\pi}(\sin^4t\cos^2t+\cos^4t\sin^2t)\,\mathrm dt[/tex]

[tex]=\displaystyle24\int_0^{2\pi}\sin^2t\cos^2t\,\mathrm dt[/tex]

[tex]=\displaystyle6\int_0^{2\pi}(1-\cos2t)(1+\cos2t)\,\mathrm dt[/tex]

[tex]=\displaystyle6\int_0^{2\pi}(1-\cos^22t)\,\mathrm dt[/tex]

[tex]=\displaystyle3\int_0^{2\pi}(1-\cos4t)\,\mathrm dt=6\pi[/tex]

The areas of the ellipse and curve interior can be calculated using Green's Theorem and the respective parametrizations, x(t) = 5cos(t) and x(t) = 4cos3(t), followed by integrating.

To compute the area inside the ellipse using Green's Theorem, we use the fact that the area can be written as ∬ dxdy = 1/2 ∫ d(−y dx+x dy). Using the hint, x(t) = 5cos(t), we parametrize the ellipse and integrate over the boundary to compute the area.

Similarly, for the parametrization of the curve x2/3 + y2/3 = 42/3, we could use the hint x(t) = 4cos3(t), which is a cube root form representation. After this, compute the area of the interior using the proper integration methods.

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The equations are classified as follows: 1. 2nd order non-linear differential equation, 2. 2nd order linear differential equation, 3. 3rd order non-linear differential equation, 4. 1st order non-linear differential equation.

The task given is to classify each differential equation into one of several categories: whether the order of the equation is first, second, third, fourth or fifth, and whether or not it is a linear differential equation.

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Answer:

3.7  liters

Step-by-step explanation:

The required amount of water in each bottle is 0.5 gallon.

Given that,
2.5 gallons of water are poured into 5 equally sized bottles, how much water is in each bottle is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Total volume = 2.5 gallon,
Number of bottle = 5,
Gallon per bottle = 2.5 / 5 = 0.5 gallon per bottle

Thus, the required amount of water in each bottle is 0.5 gallons.

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Answer:

Step-by-step explanation:

Answer is G

Graph [G] will be the correct graph representing the  lifeguard’s weekly earnings in dollars for working [h] hours over 40.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week.

For over 40 hours of work, the graph on the y - axis will start from the point (0, 320). Of the two possible graphs, we have to find the find whose slope will be 12 since, the lifeguard receives $12 per hour.

Slope of graph [F] = (400 - 320)/(10 - 0) = 80/10 = 8

Now, slope of graph [G] = (500 - 320)/(15 - 0) = 180/15 = 12

Graph [G] is the correct choice.

Therefore, Graph [G] will be the correct graph representing the  lifeguard’s weekly earnings in dollars for working [h] hours over 40.

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y=×^2+23

Answer letter B

×=y-23

233÷11=21.18

for a total of 22 pieces of wood

[tex] ln( \sqrt{ex {y}^{2} {z}^{5} } ) \\ = ln{(ex {y}^{2} {z}^{5} ) }^{ \frac{1}{2} } \\ = \frac{1}{2} ln(ex {y}^{2} {z}^{5} ) \\ = \frac{1}{2} ln(e) + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) \\ = \frac{1}{2} + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) [/tex]

Answer:

Answer A  B and D

Step-by-step explanation:

This one requires and eagle eye. You have to be a bit careful with it.

The one you checked (D) is correct. There are a couple more and one is really tricky.

The first one is actually correct.

So is the second one, which I'll show first. Only C is incorrect.

======

B]

ln(e^(1/2) + ln(x^(1/2)) + ln(y^(2/2) + ln(z^(5/2))

1/2 + ln(x^(1/2)) + ln(y) + (5/2) ln(z)

1/2 + 1/2 ln(x) + ln(y) + 5/2 ln(z)

A]

(1/2) * Ln(ex*z) + ln(yz^2)

(1/2)ln(e) + (1/2)ln(x) + (1/2)ln(z) + ln(y) + lnz^2

ln(e) = 1;   ln(z^2) = 2 ln(z)

1/2 + 1/2 ln(x) + 1/2 ln(z) + ln(y) + 2ln(z)

1/2 ln(z) + 2ln(z) = 5/2 ln(z)

So put all this together

1/2 + 1/2 ln(x) + 5/2 ln(z) + ln(y) which is Exactly like B

Answer:

Step-by-step explanation:

Let x be the amount of colored pencils she buys, and let y be the number of jelly beans that she buys. We have the following inequalities..

4x + 2y ≤ 20     (the cost times the amount has to be less than or equal to 20)

4x + 2y > 8       (she spends more than $8)

We can rewrite the inequality like this...

8 < 4x + 2y ≤ 20

Now reduce since all coefficients are even, they can be divided by 2

4 < 2x + y ≤ 10

We want values of x and y that can satisfy the situation.  

There are many points,

If x = 1, then you can have y =3 to 8

If x = 2,  then you can have y = 1 to 6  

If x = 3, then you can have y = 1 to 4

If x = 4, then you can have y = 1 or 2

x = 5,  the y = o

Final answer:

To find the possible number of pounds of jelly beans Cindy could purchase, we set up a compound inequality considering the $4 spent on colored pencils and the $2 per pound cost of jelly beans. Solving the inequality 4 < 4 + 2x < 20 gives us the range 0 < x < 8, meaning Cindy could have bought more than 0 pounds but less than 8 pounds of jelly beans.

Explanation:

To solve the problem involving Cindy's shopping at the store, let's create a compound inequality with the following conditions: she has $20 to spend, she has already spent $4 on colored pencils, and the jelly beans cost $2 per pound. Cindy wants to spend more than $8 in total at the store, which includes the cost of the pencils and the jelly beans.

Let's define x as the number of pounds of jelly beans that Cindy can purchase. The cost of the jelly beans is $2 per pound, so the total cost for the jelly beans is $2x.

Since she spent $4 on pencils, adding the cost of the jelly beans needs to be more than $4 (to exceed the $8 total spending) but less than $20 (to stay within her budget). Hence, the compound inequality will be:

4 < 4 + 2x < 20

Now let's solve for x:

First, subtract 4 from all parts of the inequality:

0 < 2x < 16

Next, divide all parts by 2:

0 < x < 8

The solution tells us that Cindy could have purchased more than 0 but less than 8 pounds of jelly beans.

Final answer:

To find the length (c) of a rectangle when the perimeter is 30 inches, we use the formula c = (P - 2w) / 2, with P representing the perimeter and w the width.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that the perimeter (P) is 30 inches, and we are looking to find the formula that shows the length of side c assuming c represents either the length or the width of the rectangle. Let's say c represents the length for this context. Therefore, the formula rearranges to c = (P - 2w) / 2. We use this formula when we know the perimeter and the width (w), and we want to find the length (c).

Answer:

4.24

Step-by-step explanation:

You can use the formula d=sqrt(2a to calculate this with ease.

Answer:

[tex]f(a^{2})=7(a^{4})-8[/tex]

Step-by-step explanation:

we have

[tex]f(x)=7x^{2}-8[/tex]

we know that

[tex]f(a^{2})[/tex]

Is the value of f(x) for [tex]x=a^{2}[/tex]

so

substitute the value of x in the function

[tex]f(a^{2})=7(a^{2})^{2}-8[/tex]

[tex]f(a^{2})=7(a^{4})-8[/tex]