dollars per pint
pints per dollar.
▼
Find the unit rates. If necessary, round your answers to the nearest hundredth.
$6.79 for 16 pints

The dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

We can think of this as a right triangle, where the hypotenuse measures 30 inches, and the angles of the triangle are 30°, 60° and 90°.

If we step on the 30° angle, the length will be the opposite cathetus, then we can use the trigonometric relation:

sin(θ) = (opposite cathetus)/(hypotenuse).

Replacing what we know:

sin(30°) = length/30 in

length = sin(30°)*30in = (1/2)*30 in = 15in

And the adjacent cathetus will be the width, then we can use:

cos(θ) = (adjacent cathetus)/(hypotenuse).

Replacing what we know:

cos(30°) = width/(30 in)

width = cos(30°)*30in = (√3/2)*30in = (√3)*15in

Then the dimensions of the TV are 15 inches by  (√3)*15 inches, so the correct option is D.

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Answer:

Answer is (-3, 2)

Answer:

Answer:

Angles are 45, 45 and 90 degrees because

AB and BC are congruent so that means the angles eating the sides are also congruent.

So to find the congruent angles:

180-90=90/2=45 degrees

To find AC:

a²+b²=c²

x²+x²=h²

√18=√c²

3√2=c

(I don't know why it says 3√3, but I think the q is wrong)

Hope it helps!

Answer:

45 degrees

Step-by-step explanation:

This is a special right triangle with these lengths. Which leads us to find the angles of 45, 45, 90 and B is 90 so A and C are 45 degrees.

The ratio is given by 98:0.34.

The ratio of (1/5 of 245ml) to (0.2 of 0.84ml).

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

we have  (1/5 of 245ml) to (0.2 of 0.84ml).

⇒ [tex]\frac{1}{5} 245 :0.2*0.84[/tex]

⇒[tex]98:0.34[/tex]

Thus, the required ratio is 98:0.34.

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The value of the expression 8 / m - 11 / 3m is  13 / 3m

8 / m - 11 / 3m

Therefore,

8 / m - 11 / 3m

The factor of the denominator is 3m

Therefore,

8 / m - 11 / 3m = 3(8) - 11/ 3m

3(8) - 11/ 3m = 24 - 11 / 3m

24 - 11 / 3m = 13 / 3m

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Answer:

2200 + 0.5x >= 2500

Step-by-step explanation:

x is the amount of sales

Only Set B  is a partition of set N of natural numbers .

Numbers starting from 1 to infinity comes under Natural Numbers.

It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers

A  ) {{n | n > 5}, {n | n < 5}]

It is not a set of natural numbers as it does not include 5.

B  )  [{n | n ≥ 6}, {1, 3,5} , {2, 4}]

{1,3,5} {2,4}and {n|n≥6} include all the natural numbers

Therefore , it forms a partition of N.

C ) {{n | n^2 > 11}, {n | n^2 < 11}

Every natural number n must satisfy either n^2 > 11 or n^2 < 11

This cannot be possible , therefore it is not the partition of Natural Numbers.

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Part 1: Finding slope

The slope is [tex]\frac{-3-15}{5-(-10)}=\frac{-18}{15}=\boxed{-\frac{6}{5}}[/tex]

Part 2: Finding the equation

Using the point (-10, 15) to substitute into point-slope form,

[tex]y-15=-\frac{6}{5}(x+10)\\\\y-15=-\frac{6}{5}x-12\\\\\boxed{y=-\frac{6}{5}x+3}[/tex]

Answer:

Using the given points we find that the slope is -1.2 and using the slope-point form we find that the equation of line is y+1.2x = 3.

Step-by-step explanation:

In the question, two points are given, (5,-3) and (-10,15). Using them we can find the slope using the formula, (y2 - y1) / (x2 - x1). So, the slope is

(-3-15) / (5+10) = -18 / 15 = -1.2

Now, we have to find the equation of line. We have two points and a slope. Using any one point and the slope, we can find the equation of line using slope-point form of line. Let us take (5,-3).

(y+3) / (x-5) = -1.2

y+3 = -1.2(x-5)

y+3 = -1.2x + 6

y+1.2x = 3

So, the slope of line is -1.2 and the equation of line is y+1.2x = 3.

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Answer:

shown below

Step-by-step explanation:

3a = 2b - 6

a = (2b - 6) / 3 or 2b / 3 - 2

Answer:

a = (2b-6)/3

Step-by-step explanation:

3a = 2b + -6

lets make a the subject of the formula

divide both sides of the equation by 3

3a/3 = a = (2b-6)/3

a = (2b-6)/3

Answer:

x=0

Step-by-step explanation:

when the reflection falls on the y-axis the answer is x=0

Answer:

1/5764801

Step-by-step explanation:

7^-1 × 7^-7

= 1/7(7^-7)

= 1/7(1/823543)

= 1/5764801

Answer:

Triangular prisms

Remember the formula for calculating volume is: Volume = Area by height. V = A X h.

For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.

So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h

Step-by-step explanation:

Answer:  The price per ton of topsoil is $179

and price per ton of mulch is $248.

Step-by-step explanation:

Let price of 1 ton of topsoil be x

and price 1 ton of mulch be y

According to question

4x + 3y = $1460   -(i)

and 5x + 2y = $1391    -(ii)

Now solving these linear equations

By multiply (i) equation with 5 and divide it by 4

we get 5x + [tex]\frac{15}{4}[/tex]y = $1825  -(iii)

Subtract equation (ii) from equation (iii)

5x +[tex]\frac{15}{4}[/tex] y - 5x - 2y = $1825-$1391

[tex]\frac{7}{4}[/tex]y=$434

y = $434х[tex]\frac{4}{7}[/tex] = $248

put value of y in equation (i)

4x + 3($248) = $1460

4x - $744 =$1460

4x = $716

x = $179

The price per ton of topsoil is $179

the price per ton of mulch is $248.

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Answer:

a=9

b=9

c=18

Step-by-step explanation:

c(a+b)+a+b=36

2a+2b=36

a+b=18

c=18

Answer:

I exactly don't know the answer

Answer:

- 112 + 100 n

Step-by-step explanation:

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

~~~~~~~

[tex]a_{1}[/tex] = - 12

d = 100

[tex]a_{n}[/tex] = - 12 + 100( n - 1 )

[tex]a_{n}[/tex] = - 12 + 100n - 100

[tex]a_{n}[/tex] = - 112 + 100 n

The total amount Maria ended up paying for the equipment will be $14,861.76. And The interest of Maria on the loan will be 8.48%.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

To purchase 13700 worth of restaurant equipment for her business.

Maria made a down payment of 1500 and took out a business loan for the rest, after 3 years of paying monthly payments of 371.16 she finally paid off the loan.

The total amount Maria ended up paying for the equipment will be

Total amount = 371.16 × 3 × 12 + 1500

Total amount = $14,861.76

The interest of Maria on the loan will be

Interset = [(14861.76 – 13700) / 13700] x 100

Interset = 8.48%

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Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes, the values are mathematically given as

Generally, the equation for Material-handling cost for one lens mathematically given as

MH1=Total projected costs for material handling /{Total number of direct labor hours x Direct labor hours per unit)

MH1={$50,000/10.000)x 200

MH1=$1,000

2)

Material-handling cost for one mirror

MH2=Total budgeted material handling cost/ Total number of direct labor hours x direct labor hours per unit

MH2={$50,000/10.000)x 200

MH2=$1,000

3) Material-handling cost per lens

[tex]MH3=\frac{Total projected costs for material handling}{\frac{Number of material moves per lens + Number of material moves per mirror}{(Total number of lenses)}}* Material moves per lens[/tex]

[tex]MH3=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH3=$1500

4)

[tex]MH4=\frac{Total projected costs for material handling}{\frac{Number of material moves per mirror + Number of material moves per lens}{(Total number of mirror)}}* Material moves per mirror[/tex]

[tex]MH4=\frac{50,000}{\frac{5+15}{25}}*5[/tex]

MH4=$1500

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Answer:

x = [tex]\frac{172-2y}{6}[/tex]

Step-by-step explanation:

6x + 2y + 8 = 180 ( subtract 8 from both sides )

6x + 2y = 172 ( subtract 2y from both sides )

6x = 172 - 2y ( divide both sides by 6 )

x = [tex]\frac{172-2y}{6}[/tex]

Step-by-step explanation:

2.

the volume of the box is

length × width × height = 13×13×13 = 13³ = 2197 cm³

the ratio of the density indignation tells us that every cm³ of soil weighs 1.33 g (or every unit of 1.33g soil fits into 1 cm³).

we have 2197 cm³.

their weight is

2197 × 1.33 = 2,922.01 g

so, the filled box clearly exceeds the max. weight of the window ledge, and it is NOT safe to put it there.

b

yes, it would be a little bit less dense.

because every bit of weight you put on top of something increases the pressure on and therefore the density of that something.

The graph is shown in the attached image.

Answer:D

Step-by-step explanation:

Answer:

833.25 or 877.59

Step-by-step explanation:

I solved this in two different ways because I wasn't sure on how the question was meant to be read.

Attempt 1:

(833.3/1)-(1+0.00833)^-360

(1+0.00833)^-360 = 0.0505

so:

833.3 - 0.0505 = 833.25

Attempt 2:

833.3/(1-(1+0.00833)^-360)

1- 0.0505 = 0.9495

833.3/0.9495 = 877.59

Answer:

43

Step-by-step explanation:

because if you add it up thats how you get that

Answer:

B, A, C

Step-by-step explanation:

add the like terms together (ending in x2 with x2, ending in x with x etc )

Answer:

B A C

Step-by-step explanation:

combining like terms

To find the point of intersection for two lines, we can use substitution to solve for the coordinates.

We're given:

With these two equations, we can:

Isolate x in the second equation:

[tex]x+2y=7\\x =7-2y[/tex]

Substitute the second equation into the first:

[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]

Solve for y:

[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]

Solve for x:

[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]

The point of intersection of the lines is (3,2).

Answer:

∠PQT = 97°

∠SQR = 83°

Step-by-step explanation:

Supplementary angles sum to 180°

⇒ ∠PQT + ∠SQR = 180°

Given:

Therefore:

⇒ (3x + 43) + (6x - 25) = 180

⇒ 3x + 6x + 43 - 25 = 180

⇒ 9x + 18 = 180

⇒ 9x = 162

⇒ x = 18

Substitute the found value of x into the expression for each angle:

⇒ ∠PQT = (3x + 43)°

⇒ ∠PQT = (3(18) + 43)°

⇒ ∠PQT = 97°

⇒ ∠SQR = (6x - 25)°

⇒ ∠SQR = (6(18) - 25)°

⇒ ∠SQR = 83°

Check

⇒ ∠PQT + ∠SQR = 97° + 83° = 180°

Five number summary and IQR of both the data sets are different.

For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5

For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5

No, the box plots are not symmetric.

Part A:

The given data sets are

School A : 9,14,15,17,17,7,15,6,6

School B : 12,8,13,11,19,15,16,5,8

Arrange the data in ascending order.

School A : 6,6,7,9,14,15,15,17,17

School B : 5,8,8,11,12,13,15,16,19

Divide each data set into four equal parts.

School A : (6,6),(7,9),14,(15,15),(17,17)

School B : (5,8),(8,11),12,(13,15),(16,19)

For school A:

Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17

The interquartile range of the data is

For school B:

Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19

[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =16-6.2\\ =9.5[/tex]

The interquartile range of the data is

[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =15.5-8\\ =7.5[/tex]

Part B:

The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data sets are different.

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