A cylindrical swimming pool is approximately 12 feet wide and 4 feet deep. About how many gallons of water can the swimming pool contain? Remember that 1 cubic foot is approximately 7.48 gallons.

We have been given that in ΔRST, s = 93 inches, ∠S=123° and ∠T=28°. We are asked to find the length of r to the nearest 10th of an inch.

We will use law of sines to solve for side r.

[tex]\frac{a}{\text{Sin}(a)}=\frac{b}{\text{Sin}(B)}=\frac{c}{\text{Sin}(C)}[/tex], where a, b and c are corresponding sides to angles A, B and C respectively.

Let us find measure of angle S using angle sum property of triangles.

[tex]\angle R+\angle S+\angle T=180^{\circ}[/tex]

[tex]\angle R+123^{\circ}+28^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}=180^{\circ}[/tex]

[tex]\angle R+151^{\circ}-151^{\circ}=180^{\circ}-151^{\circ}[/tex]

[tex]\angle R=29^{\circ}[/tex]

[tex]\frac{r}{\text{sin}(R)}=\frac{s}{\text{sin}(S)}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}=\frac{93}{\text{sin}(123^{\circ})}[/tex]

[tex]\frac{r}{\text{sin}(29^{\circ})}\cdot \text{sin}(29^{\circ})=\frac{93}{\text{sin}(123^{\circ})}\cdot \text{sin}(29^{\circ})[/tex]

[tex]r=\frac{93}{0.838670567945}\cdot (0.484809620246)[/tex]

[tex]r=110.889786233799179\cdot (0.484809620246)[/tex]

[tex]r=53.7604351[/tex]

Upon rounding to nearest tenth, we will get:

[tex]r\approx 53.8[/tex]

Therefore, the length of r is approximately 53.8 inches.

The complete question is;

Marquis wrote the linear regression equation y = 1.245x - 3.685 to predict the cost, y, of x songs purchased. Marquis spent $40 on songs. Which is the best estimate of the number of songs that Marquis purchased?

Answer:

The best estimate of the number of songs that Marquis purchased = 35 songs

Step-by-step explanation:

First of all, let's make x the subject of the linear regression equation.

 We are given that,

 y = 1.245x - 3.685

 So,

 1.245x = (y + 3.685)

 x = (y + 3,685) / (1,245)

We are told that Marquis spent $40 on songs.

Thus;

Substituting the value of $40 for y into the equation to get;

 x = (40 +3,685)/(1,245)

x = 35.09

x ≈ 35

Thus, the best estimate of the number of songs that Marquis purchased is 35

Answer:

the number of songs that Marquis purchased is 35

Answer:

Step-by-step explanation:

Total weight=The garbage truck weight + recyclables weight =3 tons + 2 tons = 5 tons

Answer: 5

Step-by-step explanation:

3+2=5

Answer:

21, 22 and 26

Step-by-step explanation:

To answer this question first we need to know which are the factors of 12:

[tex]12= 2^2(3)[/tex]

So, now, we need 3 numbers that are between 20 and 30 and that only have one common factor with 12, in other words, they need to have just a 2 or a 3 in their factorization.

Let's take number 21:

[tex]21= (7)(3)[/tex], we can see that 21 only has a 3 and a prime so therefore it has only one common factor with 12

Now, let's take the number 22,

[tex]22=11 (2)[/tex], thus since 22 has a 2 and a prime, it has only one common factor with 12.

Now, let's take the number 26

[tex]26= 13 (2)[/tex], thus, since 26 has a 2 and a prime, it has only one common factor with 12.

Thus, the three possible answers are 21, 22 and 26

Answer:

The measure of angle N to the nearest degree is 28 degrees

Step-by-step explanation:

To answer this question, we shall be needing a diagrammatic representation of the triangle. Please check attachment for this.

To calculate the angle N, we shall be making use of trigonometric identities. From the diagram we see that we have the hypotenuse ( the longest side and the side facing the angle 90) and also the opposite ( the side facing the angle N)

Thus, the correct trigonometric identity to use here is the Sine

Mathematically, the sine of an angle = length of the opposite/length of the hypotenuse

Our opposite here is 4.2 feet with our hypotenuse as 9 feet

Plugging these values, we have

Sin N = 4.2/9

Sin N = 0.46666667

N = arc sin (0.46666667)

N = 27.82 , to the nearest degree we have 28 degrees

Answer:

28°

Step-by-step explanation:

:)

Answer:

15

Step-by-step explanation:

Use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-4(3-5)+10-3(7+4)+30 ​= -4(-2)+10-3(11)+30

-4(-2)+10-3(11)+30 = 8+10-33+30

8+10-33+30 = 18-33+30

18-33+30 = -15+30

-15+30 = 15

Answer:

i tried so i hope this helps you

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

Learn more here: https://brainly.com/question/16459885

Answer:

1. C) quadratic

2. b) exponential

Step-by-step explanation:

Answer:

Str (Texture aspect ratio) Str is a measure of uniformity of the surface texture

Step-by-step explanation:

Answer:

(See explanation for further details)

Step-by-step explanation:

Similarities: Both expression have the same slope for the same values of x.

Difference: The second expression is a translated form of the first function in -3 units.

Answer: 5

Step-by-step explanation:

two negatives equal a positive, so if you are subtracting with two negatives it just like 7-2 if that makes sense :)

Answer:

5

Step-by-step explanation:

you have to multiply the 2 negative signs in between of 2 and 7 and then you will get a positive sign

since the 2 signs are different you will need to subtract.

so 7-2 equals 5 and you put the bigger number's sign which is positive

Answer & Step-by-step explanation:

If each fruit tree produces an average of 590 pounds of fruit, then that means we are going to multiply. For the apples, we are going to multiply 120 by 590. For the pears, we are going to multiply 90 by 590. After we multiply these numbers, we are going to add the products so we can find the total amount of pounds of fruit.

Apples:

120 × 590 = 70800

Pears:

90 × 590 = 53100

Now, we add 70800 to 53100.

70800 + 53100 = 123900

So, the orchard produces 123900 pounds of fruit in one year.

Answer:

210 adult tickets were sold

Step-by-step explanation:

let x be the number of adult tickets sold

let y be the number of children tickets sold

x+y=260 equation 1

9x+5y=2140 equation 2

multiply equation 1 by 5

multiply equation 2 by 1

5x+5y=1300

9x+5y=2140

subtract equation 1 from 2

4x=840

x=840/4 =210  tickets

substitute for x in equation 1

210+y=260

y=260-210=50

Answer:

Look at the attachment

Answer:

you have to add all the angles including 'x' which is equals to 180°.

The process is

99+49+x=180

148+x=180

x=180-148

x=32.

Answer:

Richard gets 15 more sweets than Natasha.

Step-by-step explanation:

Given that the ratio of Sarah's sweets is 5 and she has 75 sweets. So firstly, you have to find out how many sweets in a ratio of 1 :

Let ratio be units,

[tex]5 units = 75 sweets[/tex]

[tex]1 unit = 75 \div 5[/tex]

[tex]1 unit = 15 sweets[/tex]

Now we have to find how many sweets does Natasha and Richard has :

Richard (ratio of 3),

[tex]3 units = 15 \times 3[/tex]

[tex]3 units = 45 sweets[/tex]

Natasha (ratio of 2),

[tex]2 units = 15 \times 2[/tex]

[tex]2 units = 30 sweets[/tex]

In order to find how many sweets Richard has more than Natasha, you have to substract :

[tex]45 - 30 = 15 sweets[/tex]

Answer:

15

Step-by-step explanation:

the answer is 15

This question is incomplete and it lacks the attached diagram of the square based pyramid. Find attached to this answer, the square based pyramid.

Correct Question

A concrete planter is formed from a square-based pyramid that was inverted and placed inside a cube.

A. What is the slant height of the pyramid?

B. What is the surface area of the composite figure?

HINT: The surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

C. How many cubic yards of concrete are needed to make the planter?

Answer:

A. The slant height of the pyramid = 2.24 yards.

B. The surface area of the composite figure = 12.94 square yards.

C. The cubic yards of concrete are needed to make the planter = 2.67 cubic yards.

Step-by-step explanation:

A. What is the slant height of the pyramid?

To calculate the Slant height of a pyramid we make use of the Pythagoras Theorem which is given as:

a² + b² = c²

Where a = Height of the square pyramid represent by h

b = radius of the square pyramid represented by r

c = Slant height of the square pyramid represented by s

Therefore, we have

h² + r² = s²

Looking at the attached diagram, we are given the side length = 2 yards.

The radius of the square based pyramid = side length ÷ 2

= 2÷ 2 = 1 yard.

The height of a square based pyramid = 2 yards

Since , h² + r² = s²

The slant height of the square pyramid is calculated as :

√h² + r² = s

√(2² + 1²) = s

√5 = s

s = 2.24 yards

B. What is the surface area of the composite figure?

We were given hints in the question that the the surface area consists of lateral faces of the inside of the inverted pyramid and the remaining 5 faces of the cube.

Step 1

We find the Lateral area of the faces of the insides of the inverted pyramid

We have 4 faces, Hence,

The formula is given as

a × √( a² + 4h²

a = 2 yards

h = 2 yards

So, = 2 × √( 2² + 4 ×2²

The Lateral area of the faces = 8.94 square yards.

Step 2

Area of the 5 faces of the cube

= a²

Where a = side length = 2 yards

= 2²

= 4 square yards.

Step 3

Therefore, surface area of the composite figure = 8.94 square yards + 4 square yards

= 12.94 square yards.

C. How many cubic yards of concrete are needed to make the planter?

This is calculated by find the Volume of the Square based pyramid.

The formula is given as :

V = (1/3)a²h

Where a = side length = 2 yards

h = height of the square based pyramid = 2 yards

V = 1/3 × 2² × 2

V = 2.67 cubic yards

Answer:

(x - 4)² + (y - 5)² = 4

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (4, 5) and r = 2, thus

(x - 4)² + (y - 5)² = 2², that is

(x - 4)² + (y - 5)² = 4 ← second option on list

The required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

The standard equation of a circle is expressed as:

(x-a)^2  + (y-b)^2 = r^2

where:

(a, b) is the centre = (4, 5)

r is the radius = 3 units

Substitute to have;

(x-4)^2  + (y-5)^2 = 2^2

(x-4)^2  + (y-5)^2 = 4

Hence the required equation represents a circle with the same center as the circle shown but with a radius of 2 units is (x-4)^2  + (y-5)^2 = 4

Learn more on equation of circle here: https://brainly.com/question/14150470

Answer:

Step-by-step explanation:

im confuesd here

Answer:

Im 99 percent sure its b or c

Step-by-step explanation:

but wait for the other kid to answer

Answer:

(0,0)

Step-by-step explanation:

y= -3x

The y intercept is the y value when x =0

Let x =0

y = -3(0)

y = 0

(0,0)

Answer:

C.

Step-by-step explanation:

You can either graph this function to find the y-intercept or set x =0 and solve for y.

Answer:

-3/4

Step-by-step explanation:

Point A is at (-4,3) and Point B is at (4,-3)

The slope is at

m = (y2-y1)/(x2-x1)

   = (-3 -3)/(4 - -4)

   = (-3-3)/(4+4)

    = -6/8

     = -3/4

Answer:

the two opposite angles equal 45 and the other two who are twice the amount is 90

Step-by-step explanation:

sum of angles in a quadrilateral is 360. Lets name the two equal diagonal angles x that means the equation wil be

x+x+2x+2x=360

8x=360

x=45

so the equal diagonal ones will be 45 and the other two angles will be twice as much so 45x2=90

Answer:

920 ft^2

Step-by-step explanation:

area of triangles: base x height / 2 (2)

8 x 15 / 2

= 60 x 2

= 120

area of rectangular base: length x width

15 x 20 = 300

area of sloped rectangle: length x width

17 x 20 = 340

area of rectangle: length x width

8 x 20 = 160

Total: 120 + 300 + 340 + 160

=920 ft^2

Answer:

920 ft²

Step-by-step explanation:

2 triangles + 3 rectangles

2(½×15×8) + 20(17+8+15)

120 + 800

920

There are 52 cards in the deck.

Picking a spade would be 13/52 which reduces to 1/4

After the first card is picked there are 51 cards left, picking a club would be 13/51

Picking both would be 1/4 x 13/51 = 13/204

The answer is C.

Answer:

C. Exponential decay

Step-by-step explanation:

Answer:

x/2 = 12.5/5

5 · x = 12.5 · 2

5x = 25

5x / 5 = 25 / 5

x = 5

Step-by-step explanation: