Subtract. Simplify your answer and write it as a mixed number. 12 5/12 - 4 1/6

No, they cannot construct a cube from the square pieces of foam board.

A square has four equal sides. When we multiply the length and width of a square to determine its area, we are essentially squaring one of its sides because they are the same.

A=s²

If we already know the area, we can work backward and take the square root to find the side:

√169=√s²

13=s

13 inches is the side length.

The length, breadth, and height of a cube are all equal. These three measurements are multiplied to determine a cube's volume; since they are equal, this essentially equals cubing the side length:

V=s³

The volume is 1728, so we have the following:

1728=s³

We take the cubed root and move backwards:

∛1728=∛s³

12=s

So, In order to construct a cube with the given volume 12 should be length of the side but the length of the square is 13 so it is not possible.

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1) The probability that the sum of the spots on the up-faces is 7 : 1/6

2)the probability that the sum of the spots on the up-faces is 11 : 1/18

3) the probability that the sum of the spots on the up-faces is 7 or 11: 2/9

For the experiment of rolling two Casino dice,

Let event A: the sum of the spots on the up-faces is 7

We have 1+6, 2+5, 3+4, 4+3, 5+2, 6+1

There are 6 ways for this to happen. so,

P(A) = 6/36

P(A) = 1/6

event B: the sum of the spots on the up-faces is 11

We have 5 + 6, 6 + 5

There are 2 ways for this to happen, therefore,

P(B) = 2/36

P(B) = 1/18

We need to find the probability that the sum of the spots on the up-faces is 7 or 11

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

               = 6/36 + 2/36

               = 8/36

               = 2/9

Therefore, the probability that the sum of the spots on the up-faces is 7 : 1/6

the probability that the sum of the spots on the up-faces is 11 : 1/18

the probability that the sum of the spots on the up-faces is 7 or 11: 2/9

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The value of x  in this triangle is [tex]67.1^{o}[/tex]

The angle can be calculated as follows:

The first you should calculate the long of the side in front of the angle

as we know [tex]c^{2}= a^{2}+ b ^{2}[/tex]

so  [tex]a^{2}= c^{2}- b ^{2}[/tex]

     [tex]a =\sqrt{ 72^{2}- 28 ^{2}}[/tex] = 66.3

then we can calculate the angle of the triangle by calculate the sin of x

sin x = [tex]\frac{66.3}{72}[/tex]

sin x = 0.92

x =[tex]\sqrt{0.921}[/tex] = [tex]67.1^{o}[/tex]

hence, The value of x  in this triangle is [tex]67.1^{o}[/tex]

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Answer: A change from 20 to 22 represents a positive change (increase) of 10% Use the formula found below on this webpage to find the percent change by replacing the given values: Percent change = New - Old|Old| × 100% Percent change = 22 - 20 |20| × 100% = 2 20 × 100 = 10% (increase)

Answer: 10%

How: you know that 10 percent of 20 is 2 because you divide it by 10. by this you'll know that you are adding an extra 10 percent onto 20 to make it 22.

Answer:

emily and her friend each paid $4 for the parking fee.

Step-by-step explanation:

The parking fee is 48% increase in the cost of a ticket.

Answer:

48%

Step-by-step explanation:

Only set (B) represents the side lengths of a right triangle.

In right triangle,

[tex](Hypotenuse)^{2} = (Perpendicular)^{2}+(Base)^{2}[/tex]

(A) [tex]8^{2} = 16[/tex]

     [tex]12^{2} = 144[/tex]

     [tex]15^{2} = 225[/tex]

    225 ≠ 144 + 16

(B) [tex]10^{2} = 100[/tex]

     [tex]24^{2} = 576[/tex]

     [tex]26^{2} = 676[/tex]

    676 = 576 + 100

(C) [tex]12^{2} = 144[/tex]

     [tex]20^{2} = 400[/tex]

     [tex]25^{2} = 625[/tex]

    625 ≠ 400 + 144

(D) [tex]15^{2} = 225[/tex]

     [tex]18^{2} = 324[/tex]

     [tex]20^{2} = 400[/tex]

    400 ≠ 324 + 225

Only (B) satisfies the condition.

Correct question,

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

(A) 8, 12, 15  (B) 10, 24, 26  (C) 12, 20, 25  (D) 15, 18, 20.

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Answer:

[tex]\frac{3}{4} < \frac{33}{40}[/tex]

Explanation:

[tex]\frac{3}{4}[/tex] (< = >) [tex]\frac{33}{40}[/tex]

To figure this out, you want both fractions to have the same denominator. So, you would find the GCF (Greatest Common Factor).

The GCF for 4 and 40 would be 40 because 4 * 10 = 40 and 40 * 1 = 40.

To make the whole fraction have the denominator 40, you have to multiply the numerator and the denominator by 10.

[tex]\frac{3}{4} = \frac{30}{40}[/tex]

So,

[tex]\frac{30}{40} < \frac{33}{40}[/tex]

or

[tex]\frac{3}{4} < \frac{33}{40}[/tex]

The probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Given information:

A company is considering purchasing materials:

The probability of purchasing mineral rights

Form the first mountain P1 = 0.55

From the second mountain P2 = 0.4

As the decision is made independently

So, P(P2∩ notP1) = 0.55 * 0.6

P(P2∩ notP1) = 0.33

Similarly, the value of

P(P2∩ notP1) =0.4 * 0.45

P(P2∩ notP1) = 0.15

Hence ,

P = 0.33 + 0.18

P = 0.51

Hence , the probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

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Based on the given parameters, the amount owed is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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The proportion statement is 2/3. The missing angles are CK = 12, GN = 15 and GT = 9

Given that: Polygon ROCK ~  Polygon GNAT.

The symbol ~ means the polygons are similar to each other. That means the ratios of all their corresponding sides are the same. Thus:

CO/AN = 4/6 = 2/3 (This is the proportion statement)

We can also say CK/AT= 2/3 because the ratios of all their corresponding sides are the same

With this, we can determine  the missing sides:

CK/AT= 2/3     where AT = 18

CK/18= 2/3

CK = (18×2)/3 = 12

OR/GN = 2/3    where OR = 10

10/GN = 2/3

2GN = 10×3

2GN = 30

GN = 30/2 = 15

KR/GT = 2/3   where KR = 6

6/GT = 2/3

2GT = 6×3

2GT = 18

GT = 18/2 = 9

Therefore, the proportion statement is 2/3, and the missing angles are CK = 12, GN = 15 and GT = 9

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Answer:

x=14

y=2

Step-by-step explanation:

a: to do this we isolate x

x-2=6y

 +2.  +2

x=6y+2

b now substitute it into an equation

6y+2-2y=10

4y+2=10

    -2. -2

4y=8

/4. /4

y=2

now fill in y to find x

x-2(2)=10

x-4=10

 +4. +4

x=14

Hopes this helps please mark brainliest

The perpendicular height of the parallelogram is 13 cm.

A right triangle is a triangle that has an angle that measures 90 degrees. The three sides of a right -angled triangle are known as the length, base and the hypotenuse.

Area of a right-angled triangle = 1/2 x base x height

Area of a right-angled triangle = 1/2 x 13 x 6 = 39 cm²

A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

Area of the parallelogram = 4 x 39 = 156 cm²

Height = area / base

156 cm² / 12 = 13 cm

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The function whose graph is given below is y = tan (x).

Therefore, for x = 0, y = 0 for the given function

Now, at x = 0,

y = sec (0) = 1

y = tan (0) = 0

y = cosec (0) = Not defined

y = cot (0) = Not defined

Now, it is clear that, the function y = tan (x) represents the given graph.

The complete question is:

Choose the function whose graph is given below.

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The cost of one text message is $0.04

Algebra is a branch of mathematics that helps with the representation of problems or situations through the use of mathematical expressions. We use definite or fixed numbers in algebra, such as -1,11, and so on. In algebra, in addition to numbers, we use variables such as x, y, and z.  Elementary algebra covers the fundamental concepts of algebra. It is frequently contrasted with arithmetic: arithmetic deals with fixed numbers, whereas algebra incorporates variables.

Given that $6. 32 to send 158 text messages

We have to determine the cost of one text message

158 = 6.32

1 = ?

= 6.32/158

= 0.04

Therefore the cost of one text message is $0.04

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The annual premium of Susie's insurance company apply as a result of accident is $255 for an year. This is because the monthly insurance payment has been increased by $21.25.

What is Health insurance?

Health insurance or the medical insurance is an insurance which covers the whole or a part of the risk of a person which is incurring the medical expenses. Depending upon the health insurance plan, the risk is shared among many individuals.

Main body:

The increase in monthly insurance payment = $21.25

So, the annual increase in the premium amount paid by Susie will be:

Monthly increase in insurance payment × 12

(As there are 12 months in an year)

Annual increase in premium amount = $21.25 × 12

Annual increase in premium amount = $255

Therefore, the annual increase in the amount of premium paid by Susie for health insurance is $225.

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5+-13/2

x= -b ±√b²-4ac÷2a

x^{2}-5x+3=0

a=1

b=-5

c=3

x=-(-5±√(-5)²-4.1.3÷2.1

Evaluate the exponent

Multiply the numbers

Subtract the numbers

Multiply the numbers

x=5±√13÷2

To solve for the unknown variable, separate it into two equations: one with a plus and the other with a minus.

x=5+√13÷2

x=5-√13÷2

Rearrange and isolate the variable to find each solution

x=5+√13÷2

x=5-√13÷2

x=5±√13÷2

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The commission that Nadia made last week iis $975.

The commission made in 2011 is $50700.

From the information, Nadia earns 13% commission each week and last week, she sold $7,500 worth of stocks.

The amount of commission will be:

= Percentage × Worth of stock

= 13% × $7500

= $975

Note that 52 weeks = 1 year

The amount that she made in 2011 will be:

= $975 × 52

= $50700

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Answer:

1,750m

Step-by-step explanation:

3x9x10x5 = 1,750

120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

Let we have to mix existing mixture in x,y respectively in amount to make the new mix of 70% purity.

Given that the first type is 65% pure.

So the pure juice = 65x/100

Given the second type is 100% pure.

So amount of pure juice in it = 100y/100

So the amount of pure juice in new mix = 65x/100+100y/100 = (65x+100y)/100

So the total amount of new mix = x+y

According to question,

((65x+100y)/100)/(x+y) = 70/100

(13x+20y)/(20x+20y) = 7/10

(13x+20y)/(2x+2y) = 7

13x+20y = 14x+14y

14x-13x = 20y-14y

x = 6y

x:y = 6:1

So we have to mix the existing mixture in 6:1 ratio.

So to make 140 pints of new mix need,

first mix = 140*(6/(6+1)) = 140* (6/7) = 120

second mix = 140*(1/(6+1)) = 140*(1/7) = 20

Hence 120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

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The equation of slope intercept form is  y =−4x+24

An intercept is a y-axis point through which the slope of a line passes. It is the y-coordinate of a y-axis point at which a straight line or a curve intersects. This is represented by the straight-line equation y = mx+c, where m is the slope and c is the y-intercept.

Given m = -4 and point)-3, -12)

One way to write a line's equation is in slope-intercept form, which looks like this:

y = mx+b

m = slope

b = y-intercept (where the line crosses the y-axis)

The problem has already been given

m = −4

x=-3

y=-12

Normally, the equation of a line is left with x and y being variables, and m and b having values. Since we do not have a value for b, we will plug all those numbers in and solve.

When those are substituted, the equation should look like this.

-12=(4)(-3)+b

-12=12+b

24=b

So the line's equation would be:

y=−4x+24

And this is your equation graphed. Notice how the line crosses the y-axis at 24, and that the slope is −4, just like the equation says.

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Amelia and Ryan need 4 weeks to have the same amount of money.

A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.

Given, Amelia has $12 and saves $10 per week and Ryan has $24 and saves $7 per week.

Assuming they need x no. of weeks to have the same amount of money.

∴ 10x + 12 = 7x + 24.

3x = 12.

x = 4.

So, in 4 weeks they'll have the same amount of money.

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Answer:

-2

Step-by-step explanation:

Step by step explanation is in the picture

Answer:

simplify the equation

5x+3x

4+2

8x+6

The answer will be 8x+6

Answer:

The number 2, so answer choice A.

In order to make 441 liters of Petrolyn oil, we need 189 liters of synthetic oil.

Given, for every 3 liters of synthetic oil, we use 4 liters of natural oil.

⇒ For 1 liter of synthetic oil, we will be adding 4/3 liters of natural oil.

Let 'x' be the liters of oil needed to make 441 liters of Petrolyn oil

⇒ For 'x' liters of synthetic oil, we will need 4x/3 liters of natural oil

Total Volume = 441 liters

Volume of Synthetic oil + Volume of natural oil = 441

x + 4x/3 = 441

⇒ (3x + 4x)/3 = 441

⇒ 7x/3 = 441

⇒ x = (441×3)/7

⇒ x = 189 liters

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Answer:

True, True, False, True

Step-by-step explanation:

For line 2:

[tex]0 + 5(2) = 10[/tex]

[tex]0 + 10 = 10[/tex]

True

-2x - 2y = 4-------> -x - y = 2

x + 5y = 10-----> x + 5y = 10

--------------

4y = 12

y = 3, x = -5

(-5, 3) is a solution to the system----True

(4, 10) is a solution to the system----False

For Line 1:

[tex] - 2( - 10) - 2(8) = 4[/tex]

[tex]20 - 16 = 4[/tex]

True

The equation of the line that passes through the point (-12,15) with slope -1 in point slope form is y = -x + 3 .

In the question ,

it is given that

the required line passes through the point (-12 , 15) ,and the slope is -1 .

We know that the equation of the line passing through the points (x₁ , y₁) and slope " m " is given by

(y - y₁) = m(x - x₁)

So ,equation of line in "point slope form" is

(y - 15) = (-1)(x -(-12))

y - 15 = -1(x + 12)

y - 15 = -x - 12

y = -x - 12 + 15

y = -x + 3

Therefore , the equation of the line is y = -x + 3.

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Answer: f(0)=11/2

f(n) = f(n - 1) · (-2)

Step-by-step explanation:

f(0)=f(1)*(f(0+1)/f(1+1))

f(0)=f(1)*(f(1)/f(2))

f(0)=-11*(-11/22)

f(0)=-11*(-1/2) ==> -11/22 simplifies to -1/2

f(0)=-11*(-1)/2

f(0)=11/2

f(n) = f(n - 1) · f(2)/f(2-1)

f(n) = f(n - 1) · f(2)/f(1)

f(n) = f(n - 1) · 22/(-11)

f(n) = f(n - 1) · 2/(-1)

f(n) = f(n - 1) · (-2)

The probability of selecting a woman among students is 27/59.

According to the question,

We have the following information:

A class consists of 27 women and 32 men. And a student is randomly selected.

Now, we know that the following formula is used to find probability:

Probability of an event = Number of women in class/total number of students in the class

(More to know: probability of an event can be equal to 1 or less than 1.)

Total number of students in the class = 27+32

Total number of students = 59

Probability of selecting a woman = 27/59

Hence, the probability of selecting a woman among students is 27/59.

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