Of all rectangles with a perimeter of 29​, which one has the maximum​ area? (Give the​ dimensions.) Let A be the area of the rectangle. What is the objective function in terms of the width of the​ rectangle, w? Aequals 14.5 w minus w squared ​(Type an​ expression.) The interval of interest of the objective function is nothing. ​(Type your answer in interval notation. Use integers or simplified fractions for any numbers in the​ expression.) The rectangle that has the maximum area has length nothing and width nothing. ​(Simplify your​ answer.)

Answer:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Step-by-step explanation:

The information given we have the following info given:

[tex] n = 1019[/tex] represent the sampel size

[tex] \hat p=0.6[/tex] represent the sample proportion of interest

The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

Replacing the info given we got:

[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]

[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]

The 95% confidence interval for the true proportion would be given by (0.570;0.630) .

And if we convert this into % we got (57.0%, 63.0%)

Answer:third term=14 twelfth term=59

Step-by-step explanation:

first term=a=4

Common difference=d=5

Second term=4+5=9

Third term=9+5=14

Using Tn=a+d(n-1)

T12=4+5(12-1)

T12=4+5x11

T12=4+55

T12=59

Twelveth term=59

Answer:

D. 221.7 cm

Step-by-step explanation:

Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]

'r' - radius

We are given the radius of 4.2 centimetres.

[tex]SA=4\pi 4.2^2\\4 * \pi * 4.2^2\\\rightarrow 4.2^2 =17.64\\\text {Using 3.14 for pi: }\\4 * 3.14 *17.64\\12.56*17.64\\\boxed {221.5584}[/tex]

221.5584 ≈ 221.6

The closest answer is Option D, therefore it should be the correct answer.

Answer:

64

Step-by-step explanation:

Answer:

f/g(x) 1/x x=0

Step-by-step explanation:

f/g 1/x+2

x+2=0

-2      -2

x=-2

Answer:

D

If you put the equation into a calculator, it will show a graph of it.

Answer:

(0,1)

Step-by-step explanation:

i got it right

Answer:

not a solution

Step-by-step explanation:

p > -5

Let p = -11

-11 > -5

This is a false statement

It is not a solution

Answer:

5

Step-by-step explanation:

3+5+7+8+9+4+2+1+3+8=50

50/10=5

Answer:

Measure of first angle: 42 degrees,

Measure of second angle: 138 degrees

Step-by-step explanation:

Let us say x ⇒ measure of the smaller angle, y ⇒ measure of the larger angle

1. Now given that the measure of the larger angle is 12° more than 3 times the smaller angle: y = 12 + 3x

2. If these angles are supplementary, we could formulate another equation were the two angles add to 180°: x + y = 180

3. In this situation it is convenient to apply substitution as to solve for x, y:

1. x + ( 12 + 3x ) = 180

2. x + 12 + 3x = 180

3. 4x + 12 + 180

4. 4x = 168

5. x = 42 degrees

4. Now substitute this value of x into the first equation y = 12 + 3x, and to solve for y as well:

1. y = 12 + 3 ( 42 )

2. y = 12 + 126

3. y = 138 degrees

Here we need to find two angles given that the angles are supplementary and one is 12° larger than the other.

the two angles are 84° and 96°.

We should start by defining what supplementary angles are.

Two angles a and b are supplementary if:

a + b = 180°.

Now, we also know that one of the angles is 12° larger than the other, so we can write:

a = b + 12°

Now that we have that equation, we can replace it in the first one, so we get:

a + b = 180°

(b + 12°) + b = 180°

Now we can solve this for b.

2*b + 12° = 180°

2*b = 180° - 12°  = 168°

b = 168°/2 = 84°

To find the value of a, we can use the equation:

a = b + 12°

a = 84° + 12° = 96°.

Then the two angles are:

84° and 96°.

If you want to learn more, you can read:

https://brainly.com/question/18164299

Answer:

Graph B

Step-by-step explanation:

Answer:

An equilateral triangle has 3 lines of symmetry

Hope this helps

Step-by-step explanation:

Answer:

The unknown angle = 126°

Step-by-step explanation:

From angles in a triangle.

The total sum of angles in a triangle = 180°

Let the unknown angle be x

27 + 27 + x = 180

X = 180-27-27

X= 180-54

X = 126°

Answer: 81°

Step-by-step explanation:

m<p is a secant exterior angle which equals arcAB-arcDC divided by 2.

plug the numbers in and arcAB-27 / 2 =54 Arc AB is 27+54=81 degrees

Answer:

5 minutes

Step-by-step explanation:

200+15=215

214/43=5

It moved up a total of 200 + 15 = 215 meters at 43 meters per minute

t = 215 m / (43 m/min) = 5 minutes

Answer: 5 minutes

Answer:

the value of x is in the solution set of 4x-12<16=8x

Step-by-step explanation:

multiply the 4x take away from 12= 8x

Answer:

The number of boys are 64.

Step-by-step explanation:

We have,

The ratio of the boy to girl is 8:9.

Total number of girls are 72.

Let total boys are 8x and total girls are 9x.

According to the question,

[tex]9x=72\\\\x=8[/tex]

Since, number of boys are 8x. So,

[tex]B=8x=8\times 8=64[/tex]

So, the number of boys are 64.

Answer:

The perimeter of the field is 21 yards

Step-by-step explanation:

See attachment 1 for the coordinates plane.

The question is best solved using an attachment.

To calculate the perimeter of the fence, we simply add the sides of the rectangle.

Attachment 2 is a labelled diagram of attachment 1.

From 2, we have that

Perimeter = A + B + C + D + E + F

Where A to F represent the length of each sides of the fence

From coordinates geometry,

A = 5

B = 4

C = 6½

D = 1½

E = 1½

F = 2½

So,

Perimeter = 5 + 4 + 6½ + 1½ + 1½ + 2½

Perimeter = 21

Hence, the perimeter of the field is 21 yards

Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:

30

Step-by-step explanation:

2*15

= 30

Answer:

D understand the problem.

Step-by-step explanation:

Answer:

gathering of resources is the main first thing .....

Step-by-step explanation:

(11.99+23.98+9.95)= 45.92

she has to pay = 45.92 - 20/100 (45.92)

= 45.92 - 9.18 = 36.74

so option

about 37 is right

Answer:

a = 27

b = 81

Step-by-step explanation:

3^{3} = 27

3^{4} = 81

Answer:

The area 2730 possible arrangements of first, second, and third place.

Step-by-step explanation:

The order in which the students finish is important. For example A, B and C is a different finishing order(outcome) than B, A and C. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

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

In this question:

3 from a set of 15. So

[tex]P_{(15,3)} = \frac{15!}{(15-3)!} = 2730[/tex]

The area 2730 possible arrangements of first, second, and third place.

Answer:

5m x 5m, 6m x 4m and 7m x 4m

Step-by-step explanation:

in interval of 0.02 and for the same value of m.

Answer:

0.7463 gm/cm^3

Step-by-step explanation:

Density of any substance is mass of that substance per unit of volume.

it can be represented by given below expression

Density = mass/ volume

Given

mass = 500gm

volume = 670 cubic centimetres

Therefore, density = 500/670 gm/cubic centimetres

density = 0.7463 gm/cm^3

Thus , density of statue is 0.7463 gm/cm^3.

Answer: Equilateral, isosceles and scalene.

Step-by-step explanation:

Answer:

[tex]144 $ Square feet[/tex]

Step-by-step explanation:

The given triangular prism comprises of two equal right triangles and three rectangles.

The Surface Area of the Prism

=Area of Two Triangles + Area of Three Rectangles

[tex]=2(0.5X6X8)+(6X4)+(10X4)+(8X4)\\=48+24+40+32\\=144 $ Square feet[/tex]

Answer: 144

Step-by-step explanation:32+24+4-+48=144

Answer:

  y = 12

Step-by-step explanation:

Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)

We'll assume we are only interested in the case where the difference is in the order listed.

  [tex]\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{$y\ne -4$}\\\\\boxed{y=12}[/tex]

There is one solution.

_____

Comment on the solution

If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.

Answer:

764

Step-by-step explanation: