The equation T^2=A^3 shows the relationship between a planets orbital period, T, and the planets mean distance from the sun, A in astronomical units, AU. If planet y is twice the mean distance from the sun as planet x. by what fsctor is the orbital period increased?

Answer:  A.   x=3     y= -1         z=4

Step-by-step explanation:

I plugged it into my graphing calculator.

>2nd Matrix

>Edit >A

>choose 3x3

>Enter all coefficients as they look

>2nd Matrix

>Edit >B

>Choose 3x1

>Enter answers as they look

Go to main page

[tex][A]^{-1} [B]\\[/tex]

Answers end up being 3, -1,  4

Answer:

a. 73°

b. 98°

Step-by-step explanation:

In quadrilateral EFGH

∡E+∡G=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

11x+8+8x+1=180°

19x+9=180°

19x=180=9

19x=171

x=171/19

x=9°

similarly,

∡H+∡F=180° sum of opposite angle of quadrilateral inside the circle is 180°

substituting value

6y-4+5y-3=180°

11y-7=180°

11y=180°+7

11y=187°

y=187/11

y=17°

Now

a. m∡G=8x+1=8*9+1=73°

b. m∡H=6y-4=6*17-4=98°

Answer:

B Mean: 17.5  | W Mean: 20.5 | B Mode: 15 | W Mode: 20.5 | B Mode: 14 & 15 | W Mode: 20 & 21 | B Range: 17 | W Range: 3

Step-by-step explanation:

The surface area of the cylinder is: 156π.

Here, we have,

given that,

the cylinder has:

radius = 6 in

height = 10 in

now, surface area of the cylinder is:

SA = 2πrh + πr²

here, we have,

SA = 2π *6 * 10 + π6²

     = 120π + 36π

     = 156π

Hence, The surface area of the cylinder is: 156π.

learn more on surface area click :

brainly.com/question/23973712

#SPJ1

Answer:

15

Step-by-step explanation:

Container #1 is the only one large enough to hold the contents of a one liter bottle of soft drink.

Container #1: The volume formula for a cylinder is V = πr²h, where r is the radius and h is the height.

Radius (r) = 8 cm / 2 = 4 cm

Height (h) = 19 cm

So, V1 = π(4 cm)²(19 cm)

≈ 3032.07 cm³

Container #2:

Radius (r) = 5 cm

Height (h) = 12 cm

Using the formula:

V2 = π(5 cm)²(12 cm)

≈ 942.48 cm³

Container #3:

Diameter (d) = 12 cm

Radius (r) = 12 cm / 2 = 6 cm

Height (h) = 10 cm

V3 = π(6 cm)²(10 cm)

≈ 1130.97 cm³

Now, Comparing the volumes:

V1 ≈ 3032 cm³

V2 ≈ 942 cm³

V3 ≈ 1131 cm³

Learn more about Volume here:

https://brainly.com/question/28058531

#SPJ1

Answer:

5:52

Step-by-step explanation:

Answer: 5:52

Step-by-step explanation:

The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.

The null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The population variance is equal to 14.

Alternative Hypothesis (Ha): The population variance differs from 14.

To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.

For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.

In this case, n = 22, so the degrees of freedom is 21.

Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.

The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.

To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.

The chi-square test statistic is calculated as:

χ2 = (n - 1) ×(sample variance) / (population variance)

Plugging in the values, we have:

χ2 = (22 - 1) × 18 / 14

=27

To learn more on Null hypothesis click:

https://brainly.com/question/30821298

#SPJ1

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer:

Step-by-step explanation:

Answer:The max volume of Purple berry paint is 85

Step-by-step explanation:

Purple = Red + Blue

P = 5 : 2

Simplify 5 : 2 which is 2.5 : 1

P = 30L : 10L

P = (30 x 2.5 ) + (10 x 1)

P = 75 + 10

P = 85 L

Answer:

Answers following the rounding instructions:  see below for details

BC = 5.1

m∠B = 23°

m∠V = 116°

Step-by-step explanation:

Givens:

AC = 3

AB = 7

m∠A = 41°

Unknowns:

BC = ?

m∠B = ?

m∠C = ?

Find side BC using the law of cosines:  c² = a² + b² - 2ab cos(C)

a² = 3² + 7² - 2(3)(7)(cos41)

a = √9 + 49 - 42(cos41)

a = 5.128 ≈ 5.13

side BC = 5.13

Use the law of sines to find m∠B:  sin(A) / a = sin(B) / b = sin(C) / c

m∠B = sin⁻¹[sin41/5.13 x 3] = sin⁻¹(0.3837) = 22.56 ≈ 22.6°

Sum of interior angles of a triangle is 180, so now you can find m∠C:

m∠C = 180 - 22.6 - 41 = 116.44 ≈ 116.4°

Rounding side BC to nearest tenth: BC = 5.1

Rounding angles to nearest whole degree:

m∠B = 23°

m∠V = 116°

Answer:

  38.9 in²

Step-by-step explanation:

You want the area of the composite figure that is an 8-inch square with a semicircle removed.

The missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...

  A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²

The area of the square without the semicircle removed is ...

  A = s² = (8 in)² = 64 in²

After removing the semicircle from the square, the remaining area is ...

  A = square area - semicircle area

  A = 64 in² -25.1 in² = 38.9 in²

The area of the figure is about 38.9 square inches.

<95141404393>

Answer:

626.71 cm^2

Step-by-step explanation:

Area of figure = area of half circle + Area of half circle + area of a rectangle

here, diameter=15 cm

radius = 15/2=7.5 cm

length=30cm

breadth=15cm

Now

Area of figure = 1/2*π*radius^2+ 1/2*π*radius^2+length*breadth

=1/2* 1/2*π*7.5^2+1/2* 1/2*π*7.5^2+30*15

=626.71 cm^2

Answer: $1.50 for every 1 pound

Step-by-step explanation:

If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.

The outcomes that are in the sample space are red, blue, green, red, blue, and blue.

From the question, we have the following parameters that can be used in our computation:

Spinner = 6 sections

This means that

The spinner has 6 sections and as such, the sample size of the spinner is 6

The sample space are the colors in the spinner

So, we have

Space = red, blue, green, red, blue, and blue.

Hence, the outcomes that are in the sample space are red, blue, green, red, blue, and blue.

Read more about sample space at

https://brainly.com/question/2117233

#SPJ1

The calculated inches from end to end on the bed is 72 inches

From the question, we have the following parameters that can be used in our computation:

Length = 6 feet long

By conversion of units, we have

1 feet = 12 inches

using the above as a guide, we have the following:

Length = 6 * 12 inches long

Evaluate the products

Length = 72 inches long

Hence, the inches from end to end on the bed is 72

Read more about metric units at

https://brainly.com/question/229459

#SPJ1

[tex]\tan(y )=\cfrac{\stackrel{opposite}{6}}{\underset{adjacent}{4}} \implies \tan( y )= \cfrac{3}{2} \implies \tan^{-1}(~~\tan( y )~~) =\tan^{-1}\left( \cfrac{3}{2} \right) \\\\\\ y =\tan^{-1}\left( \cfrac{3}{2} \right)\implies y \approx 56.31^o \\\\[-0.35em] ~\dotfill\\\\ \tan(x )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{6}} \implies \tan( x )= \cfrac{2}{3} \implies \tan^{-1}(~~\tan( x )~~) =\tan^{-1}\left( \cfrac{2}{3} \right) \\\\\\ x =\tan^{-1}\left( \cfrac{2}{3} \right)\implies x \approx 33.69^o[/tex]

Make sure your calculator is in Degree mode.

Answer:

The area of the rectangle is 168 ft².

Step-by-step explanation:

Formula: A = lw

where l and w are the length and width of the rectangle respectively.

We're given with the length and the width as

a = 12 ft

b = 14 ft

Let's solve for the area using the formula above.

A = lw

A =  12ft(14ft)

A = 168 ft²

Answer:

[tex]\huge\boxed{\sf h \approx 6.4\ cm}[/tex]

Step-by-step explanation:

Volume = v = 1280 cm³

Radius = r = 8 cm

π = 3.14

Height = h = ?

V = πr²h

Put the given data in the above formula.

Finding height of cylinder.

1280 = (3.14)(8)²(h)

1280 = (3.14)(64)(h)

1280 = 200.96 (h)

1280 / 200.86 = h

[tex]\rule[225]{225}{2}[/tex]

Answer:

please see answers below

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

volume of hemisphere = (2/3)X π X r ³

12) volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (5)³

= (250/3)π

= 261.80 km³ to nearest hundredth

13) 18 foot is the diameter. radius = 1/2 X diameter = 9.

volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (9) ³

=  1526.81 ft³ to nearest hundredth

Answer:

Step-by-step explanation:

To calculate Su-Lo's score on the test, we can multiply her percentage by the total marks for the test.

Su-Lo scored 45% out of 80, so her score can be calculated as follows:

Score = Percentage × Total marks

Score = 45% × 80

To find the score, we need to convert the percentage to a decimal by dividing it by 100:

Score = (45/100) × 80

Score = 0.45 × 80

Score = 36

Therefore, Su-Lo scored 36 marks on the test.

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.

Using the Pythagorean theorem:

s^2 = (b/2)^2 + h^2

We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.

Plugging in the values:

89.3^2 = (23.8/2)^2 + h^2

Simplifying:

h^2 = 89.3^2 - (23.8/2)^2

h^2 = 7950.49 - 141.64

h^2 = 7808.85

Taking the square root of both sides:

h = √7808.85

h ≈ 88.37

Therefore, the height of the square pyramid is approximately 88.37 inches.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Answer:

[tex]\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}[/tex]

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

[tex]\boxed{f(x) = A \sin (B(x + C)) + D}[/tex]

where:

Given values:

Calculate the value of B:

[tex]\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16[/tex]

Substitute the values of A, B C and D into the standard formula:

[tex]f(x) = 5 \sin (16(x + 0)) + 7[/tex]

[tex]f(x) = 5 \sin (16x) + 7[/tex]

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

[tex]\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}[/tex]

The factored expression of n² - 11n + 10 is (n - 10)(n - 1)

From the question, we have the following parameters that can be used in our computation:

n² - 11n + 10

To determine the pair of factors to factor the expression, we find two expressions

using the above as a guide, we have the following:

The expressions are -10n and -n

So, we have

n² - 11n + 10 = n² - 10n - n + 10

When factored, we have

n² - 11n + 10 = (n - 10)(n - 1)

Hence, the factored expression of n² - 11n + 10 is (n - 10)(n - 1)

Read more about expressions at

brainly.com/question/15775046

#SPJ1

The Volume of Trapezoidal prism is 420 cm².

From the given figure we can write the dimension of the prism as

a = 5, b=15, c= 15, d= 15

h= 7 and l = 6 cm

Now, Volume of Trapezoidal prism

= 1/2 (a+b) x h x l

= 1/2 (5+15) x 7 x 6

= 1/2 x 20 x 42

= 10 x 42

= 420 cm²

Thus, the Volume of Trapezoidal prism is 420 cm².

Learn more about Volume here:

https://brainly.com/question/28058531

#SPJ1

Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

The expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

The amounts of packets of crisps purchased are given as follows:

The expression for the total number of packets of crisps that Jane buys is given by the addition of these two amounts.

Hence the expression for the total number of packets of crisps that Jane buys is given as follows:

p + c.

More can be learned about expressions at https://brainly.com/question/13729904

#SPJ1