All categories

3 days ago

6. Charlie can spend up to $8 on lunch. He wants to buy a tuna sandwich, a bottle of

Mathematics

1 answer:

PIT_PIT [9.1K]3 days ago

3 0

Response:

Charlie can purchase a maximum of 0.375 pounds of potato salad

Detailed explanation:

Refer to the figure provided for improved clarity on the issue

Let

a ----> the price of one tuna sandwich

b ----> the price of a bottle of apple juice

c ----> the cost per pound of potato salad

x ----> pounds of potato salad

we have

$a=\$4.25$

$b=\$2.25$

$c=\$4.00/lb$

he intends to buy a tuna sandwich, a bottle of apple juice, and x pounds of potato salad, and his spending limit is $8

The corresponding inequality for this scenario is

$a+b+cx \leq 8$

substituting the known values

$4.25+2.25+4.00x \leq 8$

Solving for x

Combine similar terms

$6.50+4.00x \leq 8$

Decrease 6.50 from both sides

$4.00x \leq 8-6.50$

$4.00x \leq 1.50$

Divide both sides by 4

$x \leq 1.50/4.00$

$x \leq 0.375\ lbs$

thus

Charlie can acquire a maximum of 0.375 pounds of potato salad

You might be interested in

The diagram shows two objects made of the same kind of glass. At left, a 3 dimensional figure labeled X with 2 triangular sides

Zina [9171]

Response:

A solid qualifies as a polyhedron if it consists solely of polygonal facets, with the faces converging at... polygons, and an equivalent number of faces converging at each vertex.... referred to as a right prism).... 1. 2. 3. The visuals below depict a 3-dimensional shape that does not meet the criteria... Example 10: The solid illustrated below is categorized as a rectangular prism or cuboid

Detailed explanation:

6 0

16 days ago

Read 2 more answers

At what point of the curve y = cosh(x does the tangent have slope 2?

Svet_ta [9500]

The hyperbolic cosine function (cosh) is defined as
cosh (x) = (e^x + e^-x) / 2
The tangent line's slope at any given point on a function is determined by the derivative of that function at that specific point.
d/dx [cosh(x)] = d/dx[(e^x + e^-x) / 2] = (e^x - e^-x) / 2 = sinh(x)
Assuming the slope equals 2, we have
sinh(x) = 2
thus,
x = sinh^-1 (2) = 1.444
Consequently, the curve of y = cosh(x) has a slope of 2 at the coordinate x = 1.44

5 0

4 days ago

12x+7<−11 AND5x−8≥4012

Svet_ta [9500]

Answer:

No solution

Step-by-step explanation:

Given: $12x+7$ and $5x-8\geq 40$

Handle each inequality separately.

$12x+7$ Utilizing the subtraction property of inequalities

$12x$

$x$

and

$5x-8\geq 40$ Utilizing the addition property of inequalities

$5x\geq 40+8$

$5x\geq 48$

$x\geq \dfrac{48}{5}$

Thus, the solution to the combined inequality is the overlap of both solutions.

Refer to the attached image for the number line representation.

No solution

8 0

1 month ago

Read 2 more answers

The savings account offering which of these APRs and compounding periods offers the best APY?

zzz [9080]

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
~~~~~~~~~~~~\textit{4.0784\% compounded monthly}\\\\
~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0784\%\to \frac{4.0784}{100}\to &0.040784\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus twelve}
\end{array}\to &12
\end{cases}
\\\\\\
\left(1+\frac{0.040784}{12}\right)^{12}-1\\\\
-------------------------------\\\\
~~~~~~~~~~~~\textit{4.0798\% compounded semiannually}\\\\
$

$\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2
\end{cases}
\\\\\\
\left(1+\frac{0.040798}{2}\right)^{2}-1\\\\
-------------------------------\\\\
$

$\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\
~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{daily, thus 365}
\end{array}\to &365
\end{cases}
\\\\\\
\left(1+\frac{0.040730}{365}\right)^{365}-1$

7 0

17 days ago

Read 2 more answers

John is filling a bathtub that is 18 inches deep. He notices it takes 2 mins. To fill the tub 3 inches of water. He estimates it

Svet_ta [9500]

The bathtub's depth measures 18 inches

It takes 2 minutes to fill 3 inches of the bathtub

Subsequently

The remaining depth needed for filling with water = (18-3) inches

= 15 inches

The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes

= 30/3 minutes

= 10 minutes

Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.

Hope this clarifies things!

6 0

4 days ago

Read 2 more answers