Can someone explain? I Dont Get It

a rectangular dog kennel is to be constructed alongside a house with 60m of fencing. If the house serves as one side of the kenn

Basile [38]

Answer:

$450\text{ m}^2$ .

Step-by-step explanation:

Let x represent side of kennel opposite to house and y represent other sides.

We have been given that a rectangular dog kennel is to be constructed alongside a house with 60 m of fencing.

Since fencing will cover 3 sides of kennel, so perimeter of kennel would be:

$x+y+y=60$

$x+2y=60$

Let us solve for x.

$x+2y-2y=60-2y$

$x=60-2y$

The area of the kennel would be product of its sides that is:

$\text{Area}=x\cdot y$

Now, we will substitute $x=60-2y$ in area equation as:

$A(y)=(60-2y)\cdot y$

$A(y)=60y-2y^2$

Let us find the derivative as shown below:

$A'(y)=60-4y$

Now, we will set derivative equal to 0 and solve for y.

$60-4y=0$

$60=4y$

$\frac{60}{4}=\frac{4y}{4}$

$y=15$

Upon substituting $y=15$ in area function, we will greatest possible area.

$A(y)=60y-2y^2$

$A(15)=60(15)-2(15)^2$

$A(15)=900-2(225)$

$A(15)=900-450$

$A(y)=450$

Therefore, the greatest possible area that can be enclosed by 60 m of fencing is 450 square meters.

5 0

3 years ago

Jaqueline buys 4 bracelets and 2 necklaces each bracelet cost $8 and jaqueline’s total is $70

lisabon 2012 [21]

Answer:

1 necklace is $19!

Step-by-step explanation:

4•$8=$32

$70-$32=$38

$38/2=$19

5 0

4 years ago

Read 2 more answers

The XO Group Inc. conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of

slavikrds [6]

Answer:

a) 0.0392

b) 0.4688

c) At least $39,070 to be among the 5% most expensive.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 29858, \sigma = 5600$

a. What is the probability that a wedding costs less than $20,000 (to 4 decimals)?

This is the pvalue of Z when X = 20000. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.0392.

b. What is the probability that a wedding costs between $20,000 and $30,000 (to 4 decimals)?

This is the pvalue of Z when X = 30000 subtracted by the pvalue of Z when X = 20000.

X = 30000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30000 - 29858}{5600}$

$Z = 0.02$

$Z = 0.02$ has a pvalue of 0.5080.

X = 20000

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{20000 - 29858}{5600}$

$Z = -1.76$

$Z = -1.76$ has a pvalue of 0.0392.

So this probability is 0.5080 - 0.0392 = 0.4688

c. For a wedding to be among the 5% most expensive, how much would it have to cost (to the nearest whole number)?

This is the value of X when Z has a pvalue of 0.95. So this is X when Z = 1.645.

$Z = \frac{X - \mu}{\sigma}$

$1.645 = \frac{X - 29858}{5600}$

$X - 29858 = 5600*1.645$

$X = 39070$

The wedding would have to cost at least $39,070 to be among the 5% most expensive.

5 0

3 years ago

All zeros of polynomial function 3x^4 +14x^2 -5

Marizza181 [45]

Answer:

Correct answer: x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

Step-by-step explanation:

Given:

3 x⁴ + 14 x² - 5 = 0 biquadratic equation

this equation is solved by a shift x² = t and get:

3 t² + 14 t - 5 = 0

t₁₂ = (-14 ± √14² - 4 · 3 · 5) / 2 · 3 = (-14 ± √196 + 60) / 6

t₁₂ = (-14 ± √256) / 6 = (-14 ± 16) / 6

t₁ = -5 or t₂ = 1 / 3

the solution t₁ = -5 is not accepted because it cannot be x² = -5

we accepted t₂ = 1 / 3

x² = 1 / 3 ⇒

x₁ = 1 / √3 = √3 / 3 or x₂ = - 1 / √3 = - √3 / 3

God is with you!!!

5 0

3 years ago

Which of the following statements is true about any sphere ? It has only two dimensions . Its cross section is in the shape of a

ser-zykov [4K]

Answer:

1) It has only two dimensions . FALSE

2). Its cross section is in the shape of a circle . TRUE

3) Its surface area is measured in cubic units. FALSE

4) It has a radius that is always a perfect square. FALSE.

Step-by-step explanation:

Sphere: Sphere is a 3 dimensional perfectly round object.

Here, all point lying at the circumference are at equal distance from the center.

The given statements are:

1) It has only two dimensions .

FALSE, a 2 D figure is a circle not a sphere. Sphere is 3 D.

2). Its cross section is in the shape of a circle .

TRUE, any cross section of a sphere is always a circle.

3) Its surface area is measured in cubic units.

FALSE, Surface area of a sphere = $4 \pi r^2$ sq. units

4) It has a radius that is always a perfect square.

FALSE. A sphere can be of any possible radius.

8 0

3 years ago