A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundredSix hundred and sixtyand sixty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum​ area?

Answer:

length = 50 + 50 = 100 yards

width = 50 yards

Step-by-step explanation:

The area of parking lot for the the ice cream stand is given as  5000 yard². The length of the yard is 50 yard longer than its width.

Let

width = a

length = 50 + a

The parking lot is definitely a rectangle .

Area of a rectangle = length × width

area =  (50 + a)a

5000 = (50 + a)a

5000 = 50a + a²

a² + 50a - 5000 = 0

The numbers that can be multiply together to give you -5000 is -50 and 100 and this same number can be added to give 50. Therefore,

a² - 50a + 100a - 5000 = 0

a(a - 50) + 100(a - 50) = 0

(a + 100)(a - 50) = 0

a = -100 or 50

We can't use negative value so we use 50.

length = 50 + 50 = 100 yards

width = 50 yards

Answer:

16

Step-by-step explanation:

The midpoint theorem says that if a line bisects the two sides of the triangle , it is parallel to the third side and half of it

Thus the x = 1/2 × 32 = 16

Answer:

a) 92% probability that a randomly selected mortgage will not​ default

b) 47.22% probability that nine randomly selected mortgages will not default

c) 52.78% probability that the derivative from part​ (b) becomes​ worthless

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening

Suppose a randomly selected mortgage in a certain bundle has a probability of 0.08 of default.

This means that [tex]p = 0.08[/tex]

(a) What is the probability that a randomly selected mortgage will not​ default?

Either it defaults, or it does not default. The sum of the probabilities of these outcomes is 1. So

0.08 + p = 1

p = 0.92

92% probability that a randomly selected mortgage will not​ default

(b) What is the probability that nine randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the​ others?

This is P(X = 0) when n = 9. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{9,0}.(0.08)^{0}.(0.92)^{9} = 0.4722[/tex]

47.22% probability that nine randomly selected mortgages will not default.

​(c) What is the probability that the derivative from part​ (b) becomes​ worthless? That​ is, at least one of the mortgages defaults

Either none defect, or at least one does. The sum of the probabilities of these events is 100%. So

p + 47.22 = 100

p = 52.78

52.78% probability that the derivative from part​ (b) becomes​ worthless

Answer:

(a) True

(b) False

(c) True

(d) False

(e) False

(f) True

(g) False

(h) True

(i) True

(k) True

Step-by-step explanation:

(a) Two lines parallel to a third line are parallel

True

(b) Two lines perpendicular to a third line are parallel

Only for  lines on the same plane

Therefore, false

(c) Two planes parallel to a third plane are parallel

True

(d) Two planes perpendicular to a third plane are parallel

The two planes can be at an angle to each other and so intersect

Therefore, false

(e) Two lines parallel to a plane are parallel

Where the two lines are on a plane parallel to the first plane but the lines are not themselves parallel to each other they intersect

Therefore, false

(f) Two lines perpendicular to a plane are parallel

True

(g) Two planes parallel to a line are parallel

Where the planes are not parallel to each other, they will intersect

Therefore, false

(h) Two planes perpendicular to a line are parallel

True

(i) Two planes either intersect or are parallel

True

(k) A plane and a line either intersect or are parallel

True.

Answer:

  105 seconds

Step-by-step explanation:

We can use the relation ...

  distance = speed · time

to write equations for the distance each girl travels as a function of time t since Jillian started.

  Jillian's distance = (6 ft/s)(t)

  Samantha's distance = (7 ft/s)(t -15) . . . . Samantha starts 15 seconds after the clock starts running

These distances are the same when ...

  6t = 7(t -15)

  6t = 7t -105 . . . . eliminate parentheses

  105 = t . . . . . . . . add 105-6t

Jillian had been walking 105 seconds when the two girls met.

Answer:

P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Step-by-step explanation:

Let P(n) be the proposition that 2n-1 ≤ n!. for n ≥ 3

Basis: P(3) is true since 2(3) - 1 = 5  < 3! = 6.  

Inductive Step: Assume P(k) holds, i.e., 2k - 1 ≤ k! for an arbitrary integer k ≥ 3. To show that P(k + 1) holds:

2(k+1) - 1 = 2k + 2 - 1

≤ 2 + k! (by the inductive hypothesis)

= (k + 1)! Therefore,2n-1 ≤ n! holds, for every integer n ≥ 3.

Answer:

The probability is P=0.9545.

The empirical rule is consistent, as it would have estimate a probability of 95%.

Step-by-step explanation:

We have a random variable with mean 31.8 in. and standard deviation of 2.4 in.

We have to find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 in.

If we assumed a normal-like distribution, we can calculate the z-score for both values:

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{27-31.8}{2.4}=\dfrac{-4.8}{2.4}=-2\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{36.6-31.8}{2.4}=\dfrac{4.8}{2.4}=2[/tex]

That can be interpreted as an interval that is 2 standard deviations wide, centered on the mean.

This interval has a probability of:

[tex]P(27.0<x<36.6)=P(-2<z<2)=0.9545[/tex]

If we apply the empirical rule, with 2 standard deviations from the mean, we would have estimate a probability of 95%, which is accurate.

Answer:

True

Step-by-step explanation:

Multiply the top the same as the bottom

6*2=12

10*2=20

Answer:

The answer is true.

Step-by-step explanation:

6/10 = 12/20 because if you multiply 2 to the numerator and the denominator of 6/10, then the resulting fraction is 12/20. Because 12/20 = 12/20, the answer is true.

Answer:

9.5 ft

Step-by-step explanation:

The perimeter is equal to

P =2(l+w)

29.6 = 2(5.3+z)

Divide each side by 2

29.6 /2 =2/2(5.3+z)

14.8 = 5.3 +z

Subtract 5.3 from each side

14.8-5.3 = z

9.5 =z

Answer:

Z=9.5

Step-by-step explanation:

Perimeter(of a triangle)=2(5.3+z)

29.6=10.6+2z

2z=29.6-10.6

2z=19(then divide both sides by 2 to find the value of z)

z=19/2

z=9.5 ft

To check your answer

29.6=2(5.3+9.5)

29.6=2(14.8)

29.6=29.6 so your answer is correct.

Answer:

(-1, 3)

Step-by-step explanation:

5x + 3y = 4

2x + y = 1 ⇒ y=1-2x

Answer:

The first graph

Step-by-step explanation:

when x is equal to something it is always up

y = 2 would be #4

Answer:

The first graph

Step-by-step explanation:

Personally, I use the acronym HAY and VAX to remember this rule. This means that horizontal lines always correlate with y and vertical lines always correlate with x. A horizontal equation (y=#) is valid, so to say, whereas vertical (x=#) is undefined. It is undefined because there are multiple values of y for the same value of x. You can remember this with the following scenario: A person will always be able to walk in a straight line without getting injuries, but if a person tries to walk up the wall, they will fall and can break their bones, making their body "undefined"

Answer:

4/r -1      

Step-by-step explanation:

i did khan

but sorry if its pooop

Answer:

  none of the options shown

Step-by-step explanation:

You can add 2x+2 to the inequality and get ...

  8 ≥ 2x

  4 ≥ x . . . . . divide by 2

This means that there should be a solid circle at x=4, and shading should be to the left of that.

None of the three graphs shown here is appropriate. (We don't see Option 2.)

__

Attached is the output of a graphing calculator. The solid line at x=4 corresponds to a filled dot on a number line plot.

Answer:

[tex]49/12[/tex]

Step-by-step explanation:

[tex]6\frac{1}{3} -2\frac{1}{4}[/tex]

[tex]\frac{19}{3} -\frac{9}{4}[/tex]

[tex]\frac{49}{12}[/tex]

Answer:

4 1/12

Step-by-step explanation:

6 1/3 - 2 1/4

Get a common denominator of 12

6 1/3*4/4   - 2 1/4*3/3

6 4/12 - 2 3/12

4 1/12

One way to do this is to exploit the Pythagorean identity,

[tex]\cos^2x+\sin^2x=1[/tex]

to rewrite

[tex]\cos^3(3x)=\cos(3x)\cos^2(3x)=\cos(3x)(1-\sin^2(3x))[/tex]

so that

[tex]\displaystyle\int\cos^3(3x)\sin^7(3x)\,\mathrm dx=\int\cos(3x)\left(\sin^7(3x)-\sin^9(3x)\right)\,\mathrm dx[/tex]

Then substitute [tex]u=\sin(3x)[/tex] and [tex]\frac{\mathrm du}3=\cos(3x)\,\mathrm dx[/tex] to get the integral

[tex]\displaystyle\frac13\int u^7-u^9\,\mathrm du=\frac13\left(\frac{u^8}8-\frac{u^{10}}{10}\right)+C[/tex]

[tex]=\boxed{\dfrac{\sin^8(3x)}{24}-\dfrac{\sin^{10}(3x)}{30}+C}[/tex]

which is one correct form of the antiderivative. There's no reason we can't use the identity from before to express the integrand in terms of powers of cos(3x) instead.

Answer:

12.5 feet

Step-by-step explanation:

He only needs 10/12 of a 15 foot long piece of wood. We need to find 10/12 of the length of the wood.

That is:

10/12 * 15 = 12.5 feet

He only needs 12.5 feet of the piece of wood.

Step-by-step explanation:

5/6f=20apples. that means the total number of fruits is 6/6 which is whole thus

if 5/6=20

6/6=?

that is 6/6x20 divide by 5/6

=24fruits

Answer:

The equation can be y = -7x+11

Answer:

See explanation and attachment.

Step-by-step explanation:

One of the ways to represent polynomial is the use of algebraic tiles.

To represent the polynomial x²-5x-1, we would use algebraic tiles to represent each of the three terms.

Algebra tiles come with different colors and sizes. Each size is equivalent to a degree of different monomials.

The x² tile is a monomial with degree of 2, the x tile is a monomial with degree of 1 and the unit tile (constant) is a monomial with degree of 0.

Let the shaded tiles represent the positive tiles and the unshaded tile represent the negative tiles.

Find attached the diagram for the tiles.

To represent the polynomial x² - 5x - 1, we would need 1 shaded x² tile, 5 unshaded x tiles and 1 unshaded unit tile. Then we would arrange the tiles to correspond with the polynomial.

Answer:

Answer:

(drag one tile) +x 2 into the product then click check.

(drag five) -x    into the product then click check.

(drag one) - tile into the product and click check..

Step-by-step explanation:

Answer:

B:

Step-by-step explanation:

P(A or B) = P(A)+P(B)-P(A and B)

0.5 = 0.4 + P(B) -0.2

P(B) = 0.5-0.4+0.2

P(B) = 0.3

Answer: it is a right tailed probability

Step-by-step explanation:

Population proportion = 26.9/100 = 0.269

We are dealing with the fact that the probability that the mean bond percent for the sample will be at least 28. This means that the sample proportion is 0.28 or above. This means that it is greater than the population proportion of 0.269

The hypothesis would be

For null hypothesis

p = 0.269

For alternative hypothesis,

p > 0.269

The inequality sign means that it is right tailed.

Answer:

Step-by-step explanation:

Find the characteristic polynomial of the​ matrix, using either a cofactor expansion or the special formula for 3times3 determinants.​ [Note: Finding the characteristic polynomial of a 3times3 matrix is not easy to do with just row​ operations, because the variable lambda is​ involved.]

[tex]\texttt {let} A = \left[\begin{array}{ccc}4&-4&0\\-4&7&0\\4&6&5\end{array}\right][/tex]

The characteristics polynomial of A is [tex]|A- \lambda I|[/tex]

[tex]\to|A-\lambda I|=\left[\begin{array}{ccc}(4-\lambda)&-4&0\\-4&(7-\lambda)&0\\4&6&(5-\lambda)\end{array}\right][/tex]

[tex]=(4-\lambda)[7-\lambda)(5-\lambda)-0]+4[-4(5-\lambda)-0]+0[-4\time 6-4(7-\lambda)]\\\\=(4-\lambda)[35-7\lambda-5\lambda+\lambda^2]+4[-20+4\lambda]+0\\\\=(4-\lambda)[35-12\lambda+\lambda^2]-80+16\lambda\\\\=140-48\lambda+4\lambda^2-35\lambda+12\lambda^2-\lambda^3-80+16\lambda\\\\=-\lambda^3+16\lambda^2-67\lambda+60[/tex]

Find the probability of each one:

Taffy would be 1/6

Chips would be 1/3

Soda would be 1/3

For the probability of all three multiply them together:

1/6 x 1/3 x 1/3 = 1/54

Diameter of round bud is 22.29 m.

Given that,

The circumference of round bud = 70 m

We have to calculate its diameter,

Since we know that,

Its shape is circular,

Since,

The circumference of the circle, also known as the perimeter of the circle, is the measurement of the circle's boundary. The area of a circle, on the other hand, specifies the territory it occupies. If we open a circle and draw a straight line through it, the length of the line equals the circumference.

S,

⇒ Circumference = 2πr

Where r is radius of circle,

⇒ 70 = 2πr

⇒   r = (70/2x3.14)

⇒   r = 11.14

Here we know that,

Diameter = 2r

Hence,

Diameter = 22.29 m

To learn more about circle visit:

https://brainly.com/question/29288238

#SPJ2

Answer:

a. Option D

b. H₀ : p₁ = p₂, H₁: p1 ≠ p₂

Step-by-step explanation:

a. A hypothesis test regarding the difference between two population proportions from independent samples. This type of test is used to compare the proportions of two populations. This test is usually appropriate under the conditions that:

The sampling method for each population is simple random sampling.

The samples are independent.

Each sample includes at least 10 successes and 10 failures.

Each population is at least 20 times as big as its sample.

b. Null hypothesis: H₀ : p₁ = p₂

   Alternative hypothesis: H₁ : p₁ ≠ p₂

Answer:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

101.5 98.7 95.4 92.3 109.8 104.7

We can calculate the mean with the following formula:

[tex] \bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X = 100.4[/tex]

And we can calculate the deviations from each value like this:

[tex] |101.5-100.4 |=1.1[/tex]

[tex] |98.7-100.4 |=1.7[/tex]

[tex] |95.4-100.4 |=5.0[/tex]

[tex] |92.3-100.4 |=8.1[/tex]

[tex] |109.8-100.4 |=9.4[/tex]

[tex] |104.7-100.4|=4.3[/tex]

And the mean absolute deviation would be:

[tex] MAD =\frac{1.1+1.7+5.0+8.1+9.4+4.3}{6}= 4.93[/tex]