Sasha is making a quilt. Her pattern requires that 1/4 of the pieces of cloth be green. She has 188 pieces of green cloth. If she uses all of her green cloth, how many pieces does she need for her quilt?

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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let's bear in mind that complex roots never come alone, their conjugate sister is always with her, so if we have the complex root of "i" or namely "0 + i", her conjugate is also coming along, or "0 - i", so we really have four roots, so

\(\begin{cases} x = 0+i &\implies x -i=0\\ x = 0-i &\implies x +i=0\\ x = \sqrt{2} &\implies x -\sqrt{2}=0\\ x = 3 &\implies x -3=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{we are assuming that}}{a=1} \\\\\\ 1( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y\implies ( x -i )( x +i )( x -\sqrt{2} )( x -3 ) = y \\\\[-0.35em] ~\dotfill\)

\(\stackrel{ \textit{difference of squares} }{( x -i )( x +i )}\implies x^2 - i^2\implies x^2-(-1)\implies x^2+1 \\\\[-0.35em] ~\dotfill\\\\ (x^2+1)( x -\sqrt{2} )( x -3 )\implies (x^2+1)(x^2-3x-x\sqrt{2}+3\sqrt{2}) \\\\\\ (x^2+1)[x^2-x(3+\sqrt{2})+3\sqrt{2}] \\\\\\ x^4-x^3(3+\sqrt{2})+3x^2\sqrt{2}+x^2-x(3+\sqrt{2})+3\sqrt{2} \\\\\\ \boxed{x^4-x^3(3+\sqrt{2})+x^2(3\sqrt{2}+1)-x(3+\sqrt{2})+3\sqrt{2}~~ = ~~y}\)

Answer:

x= 21/4

Step-by-step explanation:

1- Convert the expressions

5 ( x - 3 3/4 ) = 7 1/2

2- Remove the parentheses

5 ( x - 15/4 ) = 15/2

3- Move the constant to the right

5x - 75/4 = 15/2

4- Calculate the sum

5x = 15/2 + 75/4

5- Divide both sides

5x = 15/2 + 75/4

Answer:

-13 17/24

Step-by-step explanation:

-12 41/24 is equivalent to -(-12 41/24), or - (12 + 24/24 + 17/24)

Combining 12 and 24/24, we get 13, and thus have:  -(13 17/24), or

-13 17/24

Answer:

-11 17/24

Step-by-step explanation:

-12 41/24 is equivalent to -(-12 41/24), or - (12 + 24/24 + 17/24)

Combining -12 and 24/24, we get -11, and thus have:  -(11 17/24), or

-11 17/24

Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

The probability density function for U is: f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

The joint distribution for the length of life of two different types of components operating in a system is given by f(y_1, y_2) = {(1/8)y_1 e^-(y_1 + y_2)/2, y_1 > 0, y_2 > 0, 0, elsewhere. We are asked to find the probability density function for U = Y_2/Y_1.

To find the probability density function for U, we first need to find the joint distribution of U and Y_1. We can do this by using the change of variables formula:

f_U,Y_1(u, y_1) = f_Y_1,Y_2(y_1, uy_1) * |J|

where J is the Jacobian determinant of the transformation.

The Jacobian determinant is given by:

J = |∂(y_1, uy_1)/∂(u, y_1)| = |y_1|

So, the joint distribution of U and Y_1 is:

f_U,Y_1(u, y_1) = (1/8)y_1 e^-(y_1 + uy_1)/2 * |y_1| = (1/8)y_1^2 e^-(1+u)y_1/2

Next, we need to find the marginal distribution of U by integrating out Y_1:

f_U(u) = ∫f_U,Y_1(u, y_1) dy_1 = (1/8)∫y_1^2 e^-(1+u)y_1/2 dy_1

This integral can be solved using integration by parts. The final result is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2

So, the probability density function for U is:

f_U(u) = (4/(1+u)^3) * e^-(1+u)/2, u > 0

This is the final answer.

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Answer:

\(f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}\)

Step-by-step explanation:

We have to find the formula for f(x)

Let x be the number

According to question

Now,

\(\sqrt{x}+x+3\)

Now,

After squaring  we get

\((\sqrt{x}+x+3})^2\)

Add x+2 to above result then, we get

\((\sqrt{x}+x+3})^2+2+x\)

Then,

\(\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}\)

Therefore, the formula for f(x) is given by

\(f(x)=\frac{(\sqrt{x}+x+3)^2+2+x}{x^2+2}\)

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

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The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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4 feet = 1.2192 meters

Formula: multiply the value in feet by the conversion factor '0.3048'.

So, 4 feet = 4 × 0.3048 = 1.2192 meters

The number of meters in 4 feet nearest to the hundred will be 1.22 meters.

Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.

The conversion from foot to the meter is given as,

1 foot = 0.3048 meters

The number of meters in 4 feet is calculated as,

4 feet = 4 x 0.3048 meters

4 feet = 1.2192 meters

4 feet = 1.22 meters

The number of meters in 4 feet nearest to the hundred will be 1.22 meters.

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The 8-count pack of AA batteries has a lower unit prices of $0.78 per battery.

Option B is correct.

Division in mathematics is the process of breaking a number up into equal parts, and finding out how many equal parts can be made. For example, dividing 15 by 3 means splitting 15 into 3 equal groups of 5.

According to the question

Unit price of 8 AA batteries

= 6.24 ÷ 8

= 0.78

Unit price of 20 AA batteries

= 15.8 ÷ 20

= 0.79

Since, 0.78 < 0.79

Therefore, the unit price of 8 AA batteries is low.

Option B is correct.

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Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

Answer:

c.

Step-by-step explanation:

we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.

59 is much closer to 60 than to 50.

42 is much closer to 40 than to 50.

of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.

and the sum of the differences of the factors should be as close to 0 as possible.

so, 60×40 is the closest and therefore best estimation.

the sum of the factor differences is (+1 - 2) = -1.

compare to the real result :

59×42 = 2,478

answer a and b are by the way not correct :

50×40 = 2000 (and not 2500)

60×50 = 3000 (and not 3500)

FYI - in this case 50×50 = 2500 would be the closest estimation.

and the sum of the factor differences would be (-9 + 8) = -1.

normally, this wide "jumping" (-9 to +8) would make it only second choice.

Answer:

$8200

Step-by-step explanation:

rounded to the nearest dollar

The required interest earned is $8200.

Given that,
Suppose Shelly invests $2650 semiannually into an annuity for six years. At the end of this time, she has $40,000.
To determine how much of this balance is from interest.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Total balance earned = $40,000
Total investment in 6 year = 6*2*2650
                                            = 31,800
Interest earned = 40,000 - 31800
                          = $8200

Thus, the required interest earned is $8200.

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Answer:

The probability for A  is 1-0.1 is 90%

P(A)=90%

P(NOT B)=30%

P(A AND B)=0.9+0.7/2=1.6/2=80%

p(a and b) may be a little off.

Answers:

=======================================================

Work Shown:

P(A) = 1 - P(not A)

P(A) = 1 - 0.1

P(A) = 0.9

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

P(not B) = 1 - P(B)

P(not B) = 1 -0.7

P(not B) = 0.3

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

P(A and B) = P(A)*P(B) only when A and B are independent

P(A and B) = 0.9*0.7

P(A and B) = 0.63

Answer:

Probably the first one Bc the rest are technically somewhat correct and I’d think just 3 would be the least accurate

Step-by-step explanation:

Answer:

00.35 prett simple this fraction

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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Given:

4 5 6 7

Given that you picked a card at random, without replacement, you then pick a second card at random.

Let's find the probability of picking an even number and then picking an even number.

Number of possible events = 4

Number of even numbers = 4, 6, ==> 2 even numbers.

Hence, to find the probability, we have:

Therefore, the probability of picking an even number and then picking an even number is 1/6.

ANSWER:

Answer:

8%

Step-by-step explanation:

Solving our equation

r = 2800 / ( 7000 × 5 ) = 0.08

r = 0.08

converting r decimal to a percentage

R = 0.08 * 100 = 8%/year

The interest rate required to

accumulate simple interest of $ 2,800.00

from a principal of $ 7,000.00

over 5 years is 8% per year.

Answer:

=166.66% markup

Step-by-step explanation:

1800/300 = $6 a shirt

If they're being sold for $10

10/6 =5/3

=1.666

x100

=166.66% markup

Answer:

c) Statement i) is correct

Step-by-step explanation:

Experiment designed to compare relief from hay fever symptoms, by a low or high dose of a drug or placebo, with different hay fever patient volunteers given 3 different treatments (with sufficient gap) :

If the properly randomised experiment design reveals statistical difference between treatments - It states that study concludes, treatments have significantly different impacts on hay fever symptoms, & so treatment is the cause of the difference in hay fever symptoms. (i)

However, it doesn't necessarily state that these study results can be generalized to the population of all hay fever sufferers. (ii)

Answer:

False

Step-by-step explanation:

Answer:

hey i new to this app and i think the answer is c

Answer:

-7/54

Step-by-step explanation:

decimal form= 0.129

Answer:

I think it's -7/54 which in decimal form is -0.1296

Answer:

thursday

Step-by-step explanation:

there are 7 days in a week, and the multiple of 7 closest to 100 is 14, so after 98 days, it will be a monday. 3 days after monday is thursday, which is your answer. I hope this helps!

Answer:

2,584

Step-by-step explanation:

You just add or subtract the numbers if hes going up or down.