a belt is drawn tightly around three circles of radius 10 cm each, as shown. the length of the belt, in cm, can be written in the form a + b\pi for rational numbers a and b. what is the value of a + b?

It looks like you are trying to find the values of a, b, c, d, e, and f in the matrix [-3x+3y] given the matrices X and Y.

To find the values of a, b, c, d, e, and f, you will need to perform matrix multiplication. Here is how you would do this:

[-3x+3y] = [-3X+3Y]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [-3*[-7 7]+3*[5 1]]

= [[-21 21] [9 -3]]

Therefore, the matrix [-3x+3y] is equal to [[-21 21] [9 -3]].

Among the four options provided, the Marshall plan is the example of the option c, i.e Foreign aid.

The Marshall Plan, also known as the European Recovery Program (ERP), was a U.S. government initiative to rebuild the economies of Western Europe after World War II.

The Marshall plan was announced by U.S. Secretary of State George Marshall in 1947 and provided economic aid to European countries to help them recover from the devastation of the war and to prevent the spread of communism.

The Marshall Plan, also known as the European Recovery Program (ERP), was a foreign aid initiative provided by the United States government to aid in the reconstruction of the economies of European nations that were severely impacted by the effects of World War II. The main objective of this program was to provide financial support to these countries in order to rebuild their infrastructure, industries, and economies, with the aim of preventing the spread of communism and fostering economic recovery and stability throughout Europe.

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Answer:

the LCM of 105, 126, and 147 is 18420.

Since the fruit boxes need to be equally packed and no fruit is left, the largest possible number of fruit boxes needed is 18420/105 = 176 fruit boxes.

Step-by-step explanation:

To find the largest number of fruit boxes needed, we need to find the least common multiple (LCM) of 105, 126, and 147.

[The least common multiple is the smallest number that is a multiple of all the given numbers. One way to find the LCM of three numbers is to first find the LCM of two of the numbers, and then find the LCM of the result with the third number.]

To find the LCM of 105 and 126, we can list the multiples of each number and look for the smallest number that is a multiple of both:

Multiples of 105: 105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, ...

Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, 1386, 1512, ...

The smallest multiple that both 105 and 126 share is 1260. Therefore, the LCM of 105 and 126 is 1260.

Now we can find the LCM of 1260 and 147 by finding the smallest multiple of 1260 that is also a multiple of 147:

Multiples of 1260: 1260, 2520, 3780, 5040, 6300, 7560, 8820, 10080, 11340, 12600, 13860, 15120, ...

Multiples of 147: 147, 294, 441, 588, 735, 882, 1029, 1176, 1323, 1470, 1617, 1764, ...

The smallest multiple that both 1260 and 147 share is 18420. Therefore, the LCM of 105, 126, and 147 is 18420.

Since the fruit boxes need to be equally packed and no fruit is left, the largest possible number of fruit boxes needed is 18420/105 = 176 fruit boxes.

The volume comparison of the given data is written below:

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, A cone, cylinder, and Sphere all have the same radius with the height of the cone and cylinder being twice the radius.

The volume of the cone =  [tex]\frac{1}{3}[/tex] πr²h

Since, h = 2r

The volume of the cone =  [tex]\frac{1}{3}[/tex] πr² * 2r = 2/3 πr³

The volume of the Cylinder = πr²h

Since, h = 2r

The volume of the Cylinder = πr² * 2r = 2πr³

The volume of the sphere = 4 πr³

Thus, the volume of 3 cones = 2πr³

that is also equal to The volume of one Cylinder.

Thus, the volume of 2 cones = 4/3πr³

that is also equal to The 1/3 volume of the Cylinder.

Thus, the volume of 1 sphere = 4πr³

that is also equal to The volume of 2 cylinders.

Thus, the volume of 1 cone = 2/3πr³

that is also equal to The 1/6 volume of the cone.

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Answer:

9 bags

Step-by-step explanation:

2 1/4 ÷ 1/4

9/4 ÷ 1/4

9/4 x 4/1 = 9

The double integral for this problem has the result given as follows:

[tex]\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx = 20\ln{(5)} - 16[/tex]

Considering the variable y as the inner variable, the double integral is defined as follows:

[tex]\int_{0}^4 \int_0^1 \frac{4x}{1 + xy} dy dx[/tex]

We start calculating the inner integral, as follows:

[tex]I = \int_0^1 \frac{4x}{1 + xy} dy[/tex]

Using substitution, we have that:

u = 1 + xy

du = x dy.

dy = du/x

Hence:

[tex]I = \int \frac{4x}{u} \times \frac{du}{x}[/tex]

[tex]I = 4\int \frac{1}{u} du[/tex]

I = 4 ln(u).

Returning to x and y, we have that:

I = 4 ln(1 + xy), from y = 0 to y = 1.

Applying the Fundamental Theorem of Calculus for the definite integral, we have that:

I = 4 ln(1 + x) - 4 ln(1 + 0)

I = 4ln(1 + x).

Then the outer integral is given as follows:

[tex]O = \int_{0}^4 4 \ln{(1 + x)} dx[/tex]

Hence:

O = 4[ln(1 + x) + xln(1 + x) - 1 - x], from x = 0 to x = 4.

Applying the Fundamental Theorem again, now for the variable x, we have that:

O = 4[ln(5) + 4ln(5) - 1 - 4] - 4[ln(1) + 0ln(1) - 1 - 0]

O = 4[5ln(5) - 5] + 4

O = 20ln(5) - 20 + 4

O = 20ln(5) - 16.

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Answer:

0.225

Step-by-step explanation:

hour= 60 min

18miles/h

18miles/60 = 0.3 per minute

minute = 60 sec

0.3/60 = 0.005 per second

0.005s x 45 sec = 0.225

The answer is B because that is what paraphrasing is

Answer:

Step-by-step explanation:

balls

The length of arc FE, considering the dilation is given as follows:

4.42.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For the dilation, due to the multiplication of the side lengths by the scale factor, the side lengths are modified, meaning that the original triangle and the dilated triangle are not congruent.

The angle measures, conversely, remain constant, meaning that the original triangle and the dilated triangle are similar.

As the two circles in this problem are similar, we have that the central angle has the same measure.

The scale factor of the dilation is given as follows:

k = 2.5/5 = 0.5.

Then the length of arc EF is given as follows:

EF = 0.5 x 8.84 = 4.42.

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Answer:

what

Step-by-step explanation:

The work done by a force [tex]$\overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$[/tex], to displace a body from position A to position B is 5j

Now basically here we, are talking about the work done by a body in the form of displacement.

This displacement is done due to the force that acted upon the body.

To calculate the work done we use the formula as,

W = F.ds

where F is the force acted on the body and the 'ds' is the displacement vector or the factor,

thus we calculate 'ds' as

AB vector = r2 - r1

AB = (2i + 2j +3k ) - ( i+3j+k)

so we get as,

AB = i -j +2k

now substituting in the formula we get as

W = (i + 2j + 3k ) .(i - j +2k)

W = 1 -2 +6

W = 5 joules

Work done = 5 J

The complete question is,

The work done by a force [tex]$\overrightarrow{\mathrm{F}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}) \mathrm{N}$[/tex], to displace a body from position A to position B is : [The position vector of A is [tex]$\overrightarrow{r_1}=(\hat{i}+3 \hat{\jmath}+\hat{k}) \mathrm{m}$[/tex] and the position vector of B is [tex]$\left.\overrightarrow{r_2}=(2 \hat{i}+2 \hat{j}+3 \hat{\mathbf{k}}) \mathrm{m}\right]$[/tex]

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Answer:

3. 8÷ x² is the correct answer.

Answer:

[tex] \frac{1}{x {}^{2} y {}^{4} }[/tex]

Step-by-step explanation:

[tex] \frac{x {}^{ - 2} }{y {}^{4} } = x {}^{ - 2} \times \frac{1}{y {}^{4} } [/tex]

[tex]x {}^{ - 2} = \frac{1}{x {}^{2} } [/tex]

[tex]therefore \: \frac{x {}^{ - 2} }{y {}^{4} } = \frac{1}{x {}^{2} } \times \frac{1}{y {}^{4} } \\ = \frac{1}{x {}^{2}y {}^{4} }[/tex]

There are 16 pieces of 1/2 of a whole

Numeric simplification is the process of reducing a number or expression to its simplest form.

If 8 is divided into pieces that are each 1/2 of a whole, there would be 16 pieces.

Mathematically, this can be written as:

8 / (1/2) = 18 × (2/1) = 16

Therefore, the pieces that are each 1/2 of a whole would result in 16 pieces.

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Answer:

5/2

Step-by-step explanation:

Perpendicular lines are opposite reciprocals:

For example, -2 and 1/2 are opposite reciprocals:

Negate 1/2 to get -1/2. Then take the reciprocal of -1/2 to get -2.

In order to find the slope of an equation, isolate y:

4x + 10y = -140  ==> solve for y

10y = -4x - 140  ==> subtract 4x on both sides

y = (-4x - 140)/10  ==> divide both sides by 10 to isolate y

y = -4x/10 - 140/10  ==> divide each term by 10

y = -2x/5 - 14  ==> simplify

^^ In this equation, the slope is -2/5 since y increases by -2/5 every time x increases by 1.

Now take the opposite reciprocal of -2/5:

First, take the reciprocal of -2/5 by switching the numerator and denominator: -2/5  ==> -5/2

Now negate the result: -5/2 ==> -(-5/2) = 5/2

Hence, 5/2 is the slope of the line perpendicular to 4x + 10y = -140

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Answer:

x ≥ 30

Step-by-step explanation:

The teacher wants to make at least 24 tutus. If each tutu requires 1.25 yards of tulle, then she will need to buy at least (1.25 × 24) yards of tulle. 1.25 yards × 24 is 30 yards.

The teacher will need at least 30 yards of tulle. In inequality form, this is x ≥ 30.

The price of each advanced tickets sold  is; $35

The price of each same day tickets sold is; $25

Let x be the cost of each advanced tickets sold

Let y be the cost of each same day tickets sold

We are told that for one performance, 25 advance tickets and 20 same-day tickets were sold. Thus;

x + y = 60  ------(1)

The total amount paid for the tickets was $1325 and as such, we have;

20x + 25y = 1325   ------(2)

Make x the subject in eq 1 to get;

x = 60 - y

Put (45 - y) for x in eq 2 to get;

20(60 - y) + 25y = 1325

1200 - 20y + 25y = 1325

5y = 125

y = 125/5

y = $25

Thus;

x = 60 - 25

x = $35

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Answer:

Sorry I dont have enough time

I hope it helps u..

Alright Ima go teacher mode for a moment,

1.

1/3+1/5= 8/15 explanation-

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD this is basically multiplying each fraction by 1.Complete the multiplication and the equation becomes. The two fractions now have like denominators so you can add the numerators.

This fraction cant be reduced Therefore - 1/3+1/5=8/15

Alright thats the only one I will explain i'll just put the answers for the rest lol

2. 1/8+2/6= 11/24

3. 8/9+11/12= 1 29/36

4. 1/7+5/8=43/56

5. 1/4+2/4=3/4

6. 1/2+3/9=5/6

7.1/10+1/4=7/20

8.3/11+11/12= 1 25/132

9. I cant see number 9 so just tell me the bottom numbers so I can help ya out :>

10. 1/8+3/5=29/40

Hope I helped good luck on your test :> <3 Ciao mate!!!

Answer:

Step-by-step explanation:

The volume of the cone is 37.68 centimetres cube.

Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.

What is a simplification of an algebraic expression?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easily with calculations and solving.

Zach simplifies the expression correctly because 2e + 2e + 2e = 6e with 2 left over.

The expression given "2+2+2+e+e+" is a mix of numerical constants and a variable, e. The correct simplification of this expression would be to combine like terms.

Like terms are terms that have the same variable raised to the same exponent.

In this case, 2's can be combined to give 6 and e's can be combined to give 2e. Adding 2 with 6 or 2e won't be correct as 6 and 2e are not like terms.

Hence, Zach's response correctly shows combining the like terms, 2e's, and giving the remaining 2 as it is.

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The given expression (25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)] is equivalent to 217.5.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is the expression as follows -

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]

The given expression is -

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]

Solving further, we get -

(25)2 x 100 ÷ 23 + [24 ÷ 8]

25(2) x 100 ÷ 23

25(2) x 4.35

50 x 4.35

217.5

Therefore, the given expression equivalent to 217.5.

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{

Complete question expression is -

(25)2 × 100 ÷ 23 + [24 ÷ (13 – 5)]

}

Answer:

The ratios are equivalent.

Step-by-step explanation:

If you multiply the ratio 20:14 by 4, it will give you 80:56.

or

If you simplify 80:56 by 4, it will give you 20:14

Answer:

the correct answer is 27.5 feet

Step-by-step explanation:

The scale of a blueprint is a ratio that represents the relationship between the size of an object on the blueprint and the size of the actual object. In this case, the scale is 1:55, which means that for every 1 unit of length on the blueprint, the actual object is 55 units long.

If a wall on the blueprint is 6 inches long, then the actual wall is 55 times longer, or 6 inches * 55 = 330 inches. Since there are 12 inches in a foot, the actual wall is 330 inches / 12 inches/foot = 27.5 feet long. Therefore, the correct answer is 27.5 feet

The value of x is 4/3 for equation 1+3x=5.

Two or more expressions with an Equal sign is called as Equation.

The given equation is 1+3x=5

One plus three times of x equal to five

We need to solve for x

1+3x=5

Subtract 1 from both sides

3x=5-1

3x=4

Three times of x equal to four

Divide both sides by 3

x=4/3

Hence, the value of x is 4/3 for equation 1+3x=5.

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The solution for the system of linear equations is (4,12)

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: Jessie purchased eight 8 books and 4 DVDs

Kayla purchased five books and six DVDs.

let the price of a book be x and price of a DVD be y.

Then we have as per question as

8x+4y=80

5x+6y=92

Thus solving for the two equations by the method of elimination we get

40x+20y=400

40x+48y=736

-___________

      -28y=-336

           y=12

∴ x=80-4×12 / 8

     =32/8

     =4

Hence, The solution for the system of linear equations is (4,12)

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The unit rate of the cost per pound is $1.5
False: Two pounds of Apple do not cost more that $3.50

8 pounds of Apple costs $12

The unit rate is

8= 12

1= x

cross multiply both sides

8x= 12

x= 12/8

x= 1.5

Hence the unit rate of the cost per pound is $1.5

Two pounds is 1.5 + 1.5

= 3

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