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13 days ago

11

Bob wants to plant a 7 foot by 10 foot garden with a uniform border of petunias around the outside and still have 28 square feet

to plant tomatoes and roses in the middle. How wide should the border of petunias be?

2 answers:

tester [3.9K]13 days ago

5 0

Answer:

The petunia border width is 1.5 feet.

Step-by-step explanation:

Let’s define x as the border width in feet,

Given,

The garden measurements are 7 feet by 10 feet,

Thus, the dimensions of the central area without the border are (7 - 2x) feet by (10 - 2x) feet.

Therefore, the central area = (7 - 2x)(10 - 2x)

According to the problem,

$(7 - 2x)(10 - 2x)=28$

$70 -14x-20x + 4x^2=28$

$4x^2 -34x+70-28=0$

$4x^2 -34x+42=0$ ( Combine like terms )

$4x^2-(28+6)x+42=0$ ( Middle term splitting )

$4x^2-28x-6x+42=0$

$4x(x-7)-6(x-7)=0$

$(4x-6)(x-7)=0$

By applying the zero product principle,

4x - 6 or x - 7 = 0

⇒ x = 1.5 or x = 7

Since the width cannot equal the garden dimensions,

It follows that the border width would be 1.5 feet.

lawyer [4K]13 days ago

4 0

Answer:

1.5 feet

Step-by-step explanation:

Bob is planning to create a garden that measures 7 feet by 10 feet.

Area = $7\times10=70$ square feet

He intends to plant petunias in a uniform border around the garden while ensuring there is a leftover area of 28 square feet for tomatoes and roses in the center.

This requires factoring 28 so that both the length and width remain under 10 and 7 feet.

28 = 2 x 2 x 7

This indicates that the width can be 4 feet and 7 feet the length for the area meant for tomatoes.

Thus, we find that the garden reduces $10-7=3$ feet on every side, meaning the deduction on each side is $3/2=1.5$ feet.

Similarly, the width is also reduced by $7-4=3$ feet, resulting in a width reduction of 1.5 feet on each side.

Consequently, the petunia border should be 1.5 feet wide throughout.

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12 days ago

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As part of Kayla's exercise program, she either runs 6 miles/day or rides her bike 10 miles/day. Her new goal is to cover a mini

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To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.

200 miles = (6 miles/day)x + (10 miles/day)y

where x signifies the days she spent running and y represents the days bike riding.

If the minimum biking days are set to be 15, indicated by y = 15, we have:

200 miles = (6 miles/day)x + (10 miles/day)(15 days)

Solving for x gives:
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Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.

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8 days ago

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In a circle, an arc 60 centimeters long subtends an angle of 5 radians. What is the radius of the circle?

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Got it!
There are 2π radians in a complete circle.

Now, let's calculate the circumference.
5/2π = 60/circumference.
Next, solve for the circumference.
By multiplying both sides by 2π, we have: 5 * circumference = 120π.
Now divide both sides by 5, and we find: circumference = 24π.

Using the formula c = 2πr,
we set 24π = 2πr.
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10 days ago

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Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his sc

AnnZ [3877]

1) 4.55

2) Short hit

Step-by-step explanation:

1)

The score and corresponding probabilities are shown in the following table:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let us define

X = Miguel's score on the Water Hole

The expected value of the variable X can be represented as:

$E(X)=\sum x_i p_i$

where

$x_i$ represents the different possible outcomes of X

$p_i$ denotes the associated probabilities

Accordingly, the expected value of Miguel's score is calculated as follows:

$E(X)=3\cdot 0.15 + 4\cdot 0.40 + 5\cdot 0.25 + 6\cdot 0.15 + 7\cdot 0.05=4.55$

2)

Here, we will again consider:

X = Miguel's score on the Water Hole

In this case:

- For a successful long hit, the expected value of X is

$E(X)=4.2$

- Conversely, if the long hit isn't successful, the expected value of X becomes

$E(X)=5.4$

We also know that the likelihood of succeeding with a long hit is

$p(L)=0.4$

Consequently, the chance of failure in a long hit is

$p(L^c)=1-p(L)=1-0.4=0.6$

Thus, the expected value of X when opting for the long hit strategy is:

$E(X)=p(L)\cdot 4.2 + p(L^C)\cdot 5.4 = 0.4\cdot 4.2 + 0.6\cdot 5.4 =4.92$

In the first part of this question, we calculated the expected value using the short hit strategy, yielding:

$E(X)=4.55$

Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.

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10 days ago

A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same sized cand

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Answer:

Step-by-step explanation:

I'm fairly certain that addition is needed here.

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In this case, the denominators match, so we straightforwardly combine 3+3 to get 6/4. The denominator remains the same.

answer:

3/4 + 3/4 = 6/4

Hope this helps!

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7 days ago