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3 years ago

9

A small garden measures 8 ft by 7 ft. A uniform border around the garden increases the total area to 110 ft 2. What is the width

of the border?

1 answer:

Alik [6]3 years ago

8 0

Answer: 3

Step-by-step explanation:

You can answer this question by using the equation

(8+x)(7+x)=110

The x represents the width, as we do not know the area. If you simplify the equation, it becomes 56+15x+x2=110.

If you move all the terms to the left side, and rearrange it, it can become x^2+15x-54=0

This can be simplified into (x-3)(x+18)=0

This equation makes it so that x is either 3 or -18. It is not possible for a width to be -18, so the width must be 3.

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Suppose a large shipment of telephones contained 21% defectives. If a sample of size 498 is selected, what is the probability th

grandymaker [24]

Answer:

$P(-3\% < x < 3\%) = 0.901$

Step-by-step explanation:

Given

$p = 21\%$

$n = 498$

Required

$P(-3\% < x < 3\%)$

First, we calculate the z score

$z = \sqrt{p * (1 - p)/n}$

$z = \sqrt{21\% * (1 - 21\%)/498}$

$z = \sqrt{21\% * (79\%)/498}$

$z = \sqrt{0.1659/498}$

$z = \sqrt{0.000333}$

$z = 0.0182$

So:

$P(-3\% < x < 3\%) = P(-3\%/0.0182 < z$

$P(-3\% < x < 3\%) = P(1.648 < z$

From z probability, we have:

$P(-3\% < x < 3\%) = 0.901$

6 0

2 years ago

..................................

yanalaym [24]

Answer:

The answer is a² .

Step-by-step explanation:

You have to substitute x and y into the expression :

$let \: x = a \cos(θ) \\ let \: y = a \sin( θ)$

${x}^{2} + {y}^{2} = {(a \cosθ )}^{2} + {(a \sinθ) }^{2}$

${x}^{2} + {y}^{2} = {a}^{2}( {cos}^{2}θ) + {a}^{2} ({sin}^{2}θ)$

Next, you have to apply Basic Trigonometric Identity :

${sin}^{2} θ + {cos}^{2} θ = 1$

${x}^{2} + {y}^{2} = {a}^{2} ( {cos}^{2} θ + {sin}^{2} θ)$

${x}^{2} + {y}^{2} = {a}^{2} (1)$

${x}^{2} + {y}^{2} = { a}^{2}$

8 0

3 years ago

X^4=15 <br> is an exponential equation?

miskamm [114]

Answer:

No. It is not an Exponential Equation.

Step-by-step explanation:

Given $x^{4} =15$

By the Definition of Exponential Equation which states.

"The equation is said to be an exponential equation when it has a variable occurred in the exponent and which have the same base."

For Example:

All given below are said to be exponential equations.

$5^{x} =5^{2} \\7^{x}=49\\$

which can be rewritten as

$7^{x}=7^{2}$

Now in the given equation $x^{4}=15$ it doesn't have same base neither any means the base can be made same,hence the given equation is not an exponential equation

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3 years ago

Difference 77/8 -31/4=

ad-work [718]

The answer is 15/8
simplified: 1 7/8

3 0

2 years ago

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3 years ago