It took Ivan 7 1/2 hours to drive 412.5 miles at a constant speed. How fast was he driving? Show how you know.

Jane is going to walk once around the edge of a rectangular park. The park is 300 yards long and 200 feet wide. How far will Jan

vova2212 [387]

Jane will walk 2200 feet

4 0

2 years ago

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A hexagonal pyramid is cut by a plane as shown in the diagram. What is the shape of the resulting cross section? see diagram

Alenkasestr [34]

From the diagram you can see that plane cuts each lateral face of hexagonal pyramid and do not cut the base. A hexagonal pyramid has six lateral faces. The intersection of each of these lateral faces with given cutting plane is segment. The figure which consists of these segments is hexagon. This hexagon is not the same as base and even is not similar to the base because the cutting plane is not parallel to the base.

Answer: resulting cross section is a hexagon, correct choice is option 4.

9 0

2 years ago

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a lunch stand makes a $.75 profit on each chef's salad and $1.20 profit on each caesar salad. On a typical weekday, it sells bet

tangare [24]

Answer:

50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

Step-by-step explanation:

Suppose, the number of Chef's salad is $x$ and the number of Caesar salad is $y$

On a typical weekday, it sells between 40 and 60 Chefs salads and between 35 and 50 Caesar salads.

So, the two constraints are: $40\leq x\leq 60$ and $35\leq y\leq 50$

The total number sold has never exceed 100 salads. So, another constraint will be: $x+y\leq 100$

According to the graph of the constraints, the vertices of the common shaded region are: $(40,35), (60,35), (60,40), (50,50)$ and $(40,50)$ (Refer to the attached image for the graph)

The lunch stand makes a $.75 profit on each Chef's salad and $1.20 profit on each Caesar salad. So, the profit function will be: $P=0.75x+1.20y$

For (40, 35) , $P=0.75(40)+1.20(35)=72$

For (60, 35) , $P=0.75(60)+1.20(35)=87$

For (60, 40) , $P=0.75(60)+1.20(40)=93$

For (50, 50) , $P=0.75(50)+1.20(50)=97.5$ (Maximum)

For (40, 50) , $P=0.75(40)+1.20(50)=90$

Profit will be maximum when $x=50$ and $y=50$

Thus, 50 Chef's salads and 50 Caesar salads should be prepared in order to maximize profit.

6 0

2 years ago

A gardener wants to replant a circular bare spot in a yard with grass. The bare spot has a radius of 8 inches. What is the area

ch4aika [34]

The area of the bare spot the gardener needs to replant is 201 square feet

Step-by-step explanation:

We have to find the area of the circular bare spot

Given

Radius of bare spot = r = 8 inches

The formula for area of a circle is given by:

$Area=A = \pi r^2$

putting the value

$A = 3.14 * (8)^2\\= 3.14 * 64\\=200.96$

Rounding off to nearest foot

201 ft^2

Hence,

The area of the bare spot the gardener needs to replant is 201 square feet

Keywords: Area, radius

Learn more about area of circle at:

#LearnwithBrainly

7 0

1 year ago

What is the approximate area of the shaded sector in the circle shown below

Akimi4 [234]

$\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
r=4.5\\
\theta =150
\end{cases}\implies A=\cfrac{(150)(\pi )(4.5)^2}{360}\\\\\\ A=\cfrac{3037.5\pi }{360}$

8 0

1 year ago

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