A circular plate has circumference of 30.1 inches. What is the area of this​ plate? Use 3.14 for pi

The probability that their first child will have kidney disease is 1/8.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here, we have

Both parents must be heterozygous to have a 1/4 chance of having an

affected child. Parent 2 is heterozygous (her father was homozygous recessive, but she has unaffected).

For the child to have the disease, both Parent 1 and Parent 2 would need to be heterozygous

There is a 50% chance of this for Parent 1 and a 100% chance of this for Parent 2 and then, there is a 25% chance that their first child will be affected:

50%× 100% × 25% = 12.5%

1/2 × 1/4 = 1/8

Hence, the probability that their first child will have kidney disease is 1/8.

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Ms. Sanders bought 6 packages of cheese sticks and 3 packages of waffles.

Let c = cheese sticks and w = waffles.

We have

c + w = 9

4c + 7w = 45

Solving using substitution,

w = 9 - c

4c + 7(9 - c) = 45

4c + 63 - 7c = 45

-3c = -18

c = 6

6 + w = 9

w = 3

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The polynomial 2x^3 - 4x^2 + 3x - 7 has the remainder is -1, and the quotient is 2x^2 + 3.

To find the quotient and remainder of a polynomial, follow these steps:

Arrange the polynomials in descending order of degrees.

Divide the term with the highest degree of the dividend polynomial by the term with the highest degree of the divisor polynomial. This will be the first term of the quotient.

Multiply the divisor polynomial by the first term of the quotient and subtract the result from the dividend polynomial.

Bring down the next term from the dividend polynomial.

Repeat steps 2 to 4 until all the terms of the dividend polynomial are exhausted or the degree of the remaining polynomial is lower than the degree of the divisor polynomial.

The resulting polynomial after the division process is complete is the remainder.

The terms obtained during the division process form the quotient polynomial.

For example, let's divide the polynomial 2x^3 - 4x^2 + 3x - 7 by the polynomial x - 2.

The term with the highest degree in the dividend polynomial is 2x^3, and the term with the highest degree in the divisor polynomial is x.

Dividing 2x^3 by x gives 2x^2, which is the first term of the quotient.

Multiply (x - 2) by 2x^2, giving 2x^3 - 4x^2.

Subtracting 2x^3 - 4x^2 from the dividend polynomial gives 3x - 7.

Bring down the next term, which is 3x.

Dividing 3x by x gives 3, which is the next term of the quotient.

Multiply (x - 2) by 3, giving 3x - 6.

Subtracting 3x - 6 from the remaining polynomial gives -7 + 6 = -1.

Since the degree of -1 is lower than the degree of x - 2, the division process is complete.

The remainder is -1, and the quotient is 2x^2 + 3.

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The particular solution to the given initial value problem is given by y(x) = -65/22\(e^{4x}\) + 137/18\(e^{2x}\) + 34/99\(e^{-7x}\)

The initial value problem is y''' - 8y'' + 23y' - 28y = 0, y(0) = 5, y'(0) = 1.

Let y' = r, y'' = r², y''' = r³.

The characteristic equation of the given differential equation is r³ - 8r² + 23r - 28 = 0.

Factoring the characteristic equation yields (r - 4)(r - 2)(r + 7) = 0.

Equating the all factor equal to zero.

This yields the three roots r₁ = 4, r₂ = 2, and r₃ = -7.

The general solution to the given differential equation is then given by y(x) = c₁\(e^{4x}\) + c₂\(e^{2x}\) + c₃\(e^{-7x}\)..............(1)

At y(0) = 5, put x = 0 in equation 1

y(0) = c₁\(e^{4\cdot 0}\) + c₂\(e^{2\cdot 0}\) + c₃\(e^{-7\cdot 0}\)

c₁\(e^{0}\) + c₂\(e^{0}\) + c₃\(e^{0}\) = 5

c₁ + c₂ + c₃ = 5..............(A)

Now differentiate the equation 1

y'(x) = 4c₁\(e^{4x}\) + 2c₂\(e^{2x}\) - 7c₃\(e^{-7x}\)..............(2)

At y'(0) = 1, put x = 0 in equation 2

y'(0) = 4c₁\(e^{4\cdot 0}\) + 2c₂\(e^{2\cdot 0}\) - 7c₃\(e^{-7\cdot 0}\)

4c₁\(e^{0}\) + 2c₂\(e^{0}\) - 7c₃\(e^{0}\) = 1

4c₁ + 2c₂ - 7c₃ = 1..............(B)

Now differentiate the equation 2

y''(x) = 16c₁\(e^{4x}\) + 4c₂\(e^{2x}\) + 49c₃\(e^{-7x}\)..............(3)

At y''(0) = 0, put x = 0 in equation 2

y''(0) = 16c₁\(e^{4\cdot 0}\) + 4c₂\(e^{2\cdot 0}\) + 49c₃\(e^{-7\cdot 0}\)

16c₁\(e^{0}\) + 4c₂\(e^{0}\) + 49c₃\(e^{0}\) = 0

16c₁ + 4c₂ + 49c₃ = 0..............(C)

Using the initial conditions, we get the following system of equations:

c₁ + c₂ + c₃ = 5

4c₁ + 2c₂ - 7c₃ = 1

16c₁ + 4c₂ + 49c₃ = 0

Solving this system of equations yields c₁ = -65/22, c₂ = 137/18, and c₃ = 34/99.

Therefore, the particular solution to the given initial value problem is given by

y(x) = -65/22\(e^{4x}\) + 137/18\(e^{2x}\) + 34/99\(e^{-7x}\)

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The complete question is:

Solve the given initial value problem y'''-8y''+23y'-28y = 0; y(0)=5, y'(0)=1, y''(0)=0.

Answer:

5/20

Step-by-step explanation:

5 over 20

it is just literally a five upward and a 20 downward

\(\frac{5}{20}\)

Answer:

4/19

Step-by-step explanation:

Its because yall did it wrong.

To convert 21.73 m to customary units, we need to use the conversion factors as follows:

meter = 39.37 inches1

inch = 2.54

cm1 foot

= 12 inches

We have:

21.7.

3 m

= 21.73 x 39.37 inches (since 1 mete

r = 39.37 inches)

= 856.301 inches

= 71 feet 4.3 inches (since 1 foot = 12 inches)

The smallest tick mark on

1" = 1' 0"

architect’s scale is 1/16 inch.

This means that there are 16 tick marks in an inch. A fractional ruler was used for scale measurements of a line on the 1/4" = 1'-0" scale. The two ends of the line correspond to 6 2.7/4" and 9 6/8". To get the length of the line in inches, we need to convert the two ends to inches, then subtract them to get the length as follows:

\(6 2.7/4" \\= 6 x 12 + 2.7\\ = 74.7"  (since 1 foot\\ = 12 inches)\\9 6/8" = 9 x 12 + 6 \\= 114" (since 1 foo\\t = 12 inches)\)

Length of the line = 114 - 74.7 = 39.3 inches (rounded off to one decimal place)

Multiplying 3/5 by

\(17/13\\ gives:\\3/5 x 17/13\\= (3 x 17)/(5 x 13)\\= 51/65\)

This is already in its lowest form.

Therefore, the answer is:51/65 (an improper fraction)

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To make the expression x * equivalent to the C expression (x << 3) + (x << 1), the blank should be filled with 10.

In the given C expression, (x << 3) represents left-shifting the value of x by 3 bits, and (x << 1) represents left-shifting the value of x by 1 bit. To achieve an equivalent expression using multiplication, we need to determine the multiplication factor that corresponds to the left shifts.

The left shift by 3 bits is equivalent to multiplying by 2 raised to the power of 3, which is 8. Similarly, the left shift by 1 bit is equivalent to multiplying by 2 raised to the power of 1, which is 2.

Therefore, to make the expression x * equivalent to (x << 3) + (x << 1), the blank should be filled with 10, as x multiplied by 10 gives the same result as the given C expression.

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Answer:

This expression can be written as 53-2m

Step-by-step explanation:

Sometimes it can help to reword the sentence...

2 times Mai's score is being subtracted from 53.

Use 'M' for Mai's score:

53-2m

Answer:

B

Step-by-step explanation:

that is a linear equation, therefore it makes a line, eliminating choices C and D.

Lines can literally Any x or y. So it would be B, a set of all the solutions to the equations.

Let S be the subspace of P3 consisting of all polynomials p(x) such that p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) The two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b) The two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c) The vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

We have the information from the question:

Let S be the subspace of \(P_3\) consisting of all polynomials p(x).

We have:

p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) S is all polynomials of the form p(x) = \(ax^2 + bx\) where a, b are

real numbers.

p(0) = \(a(0)^2 + b(0)\) = 0 for all a, b.

I propose that {x, \(x^{2}\)} forms a basis for S.

We must show that:

The vectors x and \(x^{2}\) are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1(x^2) + \alpha _2(x) = 0(x^2) + 0(x)\)

Only has the solution :

\(\alpha _1=\alpha _2=0\)

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span S we must show that any element

in S which I will represent by p(x) = ax^2 + bx can be written as:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

where, \(\alpha _1,\alpha _2\) are scalar  vectors.

Upon grouping the terms we find that:

\(\alpha _1=a\\\\\alpha _2=b\)

With this solution we have:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

which means the two vectors span S.

Thus, the two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b)T is all polynomials of the form :

\(q(x) = a(x - 1)(bx + c) =abx^2 + acx - abx - ca = ab(x^2) + (ac - ab)x - ac\)where a, b, c are real numbers.

This is because q(1) = a(1 − 1)(b + c) = 0 for all a, b, c.

Let s = ab and t = ac.

Now we have that T is all polynomials of the form

\(q(x) = sx^2 + (t - s)x - t\)

\({(x - 1),(x - 1)^2}\)forms a basis for S.

In order to confirm this we must show that the vectors x − 1 and \((x - 1)^2\)are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1((x -1)^2) + \alpha _2(x - 1) = 0(x - 1)(0(x) + 0)\)

only has the solution α1 = α2 = 0

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span T we must show that any element

in T which I will represent by \(q(x) = sx^2 + (t - s)x - t\) can be written as:

\(\alpha _1((x - 1)^2) + \alpha _2(x - 1) = sx^2 + (t - s)x - t\)

Where, \(\alpha _1,\alpha _2\) are scalars.

Upon grouping the terms we find that:

\(\alpha _1=s\\\\\alpha _2=s+t\)

With this solution we have:

\(sx^2 + (t - s)x - t = sx^2 + (t - s)x - t\)

which means the two vectors span T

Thus, the two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c)  S∩T is all polynomials of the form \(c(x) = a(x-1)(bx) = abx^2-abx\)

where a, b are real numbers.

This is because \(c(0) = a(0 - 1)^2\)

(b(0)) = 0 and

c(1) =\(a(1 - 1)^2\)

(b(1)) = 0 for all a, b.

Let ab = t

This means S∩T is all polynomials of the form \(c(x) = tx^2-tx = tx(x-1).\)

I propose that {x(x − 1)} forms a basis for S ∩ T.

Now, we must show that the vector x(x − 1) is linearly independent and spans S ∩ T.

To show it is linearly independent we must show that:

\(\alpha _1\)(x(x − 1)) = 0(x(x − 1))

only has the solution \(\alpha _1\) = 0.

Upon grouping the terms we find:

\(\alpha _1\) = 0

Thus the two vectors are clearly linearly independent.

Now to show that the vector spans S ∩ T we must show that any element

in S ∩ T which I will represent by c(x) = tx(x − 1) can be written as:

\(\alpha _1\)(x(x − 1)) = tx(x − 1).

where \(\alpha _1\) is a scalar.

Upon grouping the terms we find that:

\(\alpha _1\) = t

With this solution we have:

tx(x − 1) = tx(x − 1)

which means the vector spans S ∩ T.

Thus, the vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

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Answer:

13

Step-by-step explanation:

the next number is the sum of the two predictions.

0+1 = 1+1 = 2+1 = 3+2 = 5

Then the sequence will continue in the same way:

3+5 = 8

5+8 = 13

Given :

You rent an apartment that costs $1700 per month during the first year, but the rent is set to go up 9% per year.

To Find :

The rent of the apartment during the 12th year of living in the apartment.

Solution :

Let, A is the final price after 12 year and P is the principal amount.

We know, by formula of compounding :

\(A = P( 1 + \dfrac{r}{100})^t\\\\A = 1700( 1 + \dfrac{9}{100} )^{12}\\\\A = \$4781.53\)

Therefore, the rent of the apartment during the 12th year of living in the apartment is $4781.53 .

Answer:

16 : 5

Step-by-step explanation:

Number of jays: 16

Number of hawks: 5

Ratio of jays to hawks -> 16 : 5

Answer:

180 ft cubed.

Step-by-step explanation:

The formula for volume is V = lwh

6 is the height, 10 is the length, and 3 is the width.

So then you would multiply 6, 10 and 3, which equals 180.

The book is opened to pages 11 and 12.

How to get the product of the page

x * (x + 1) = 132

Expanding the equation, we get:

x² + x = 132

To solve for x, we need to rewrite the equation as a quadratic equation:

x²+ x - 132 = 0

Now, we can factor the quadratic equation:

(x - 11)(x + 12) = 0

This equation has two solutions for x:

x = 11

x = -12

Since page numbers cannot be negative, we discard the second solution. Thus, the left-hand page number is 11, and the right-hand page number is 11 + 1 = 12.

So, the book is opened to pages 11 and 12.

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Answer:

8

Step-by-step explanation:

solve the 2 cube first = 8

then solve the .2 with 8 = 16

then minus 24

24-8.2

24-16

8

Answer:

13. It is a paralellogram, because its opposite sides are equal & parallel

14. It is a paralellogram , because it's two diagonals bisect each other .

15. Is a paralellogram, cause its opposite angles are equal

Step-by-step explanation:

The total surface area of the new box is given by the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7).

To calculate the new total surface area of the box after increasing the height by 3.5 centimeters, we need to consider the dimensions of the box and how each side is affected by the increase.

Let's assume the original box has dimensions:

Length (L)

Width (W)

Height (H)

The total surface area of the original box is given by:

SA_original = 2(LW + LH + WH)

After increasing the height by 3.5 centimeters, the new height becomes H + 3.5. The other dimensions, length and width, remain the same.

The new total surface area of the box can be calculated as follows:

SA_new = 2(LW + (L(H + 3.5)) + (W(H + 3.5)))

Simplifying the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7)

Therefore, the total surface area of the new box is given by the equation:

SA_new = 2(LW + LH + 3.5L + WH + 3.5W + 7)

To find the closest value to the total surface area of the new box, you would need to know the specific values of L, W, and H for the original box. With those values, you can substitute them into the equation to calculate the exact surface area.

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Answer:

My sister learn to play piano for 5 years

Step-by-step explanation:

Is that correct?

If so can I please get a brainless i only need one more please

Answer:

I think;

My sister has been learning piano for 5 years.

I hope I helped you^_^

To find the production level that maximizes profit for the company manufacturing x pocket calculators per week

Given cost and demand equations: C(x) = 8,000 + 5x and P = 14 - x/4000, where 0≤ x ≤25,000.

Step 1: Determine the revenue function (R(x)). Revenue is the product of the price (P) and the quantity (x) sold.
R(x) = P * x = (14 - x/4000) * x

Step 2: Simplify the revenue function.
R(x) = 14x - (x^2)/4000

Step 3: Determine the profit function (π(x)). Profit is the difference between revenue and cost.
π(x) = R(x) - C(x) = (14x - (x^2)/4000) - (8,000 + 5x)

Step 4: Simplify the profit function.
π(x) = 9x - (x^2)/4000 - 8,000

Step 5: Find the critical points of the profit function by taking the derivative with respect to x and setting it to 0.
dπ(x)/dx = 9 - (x/2000) = 0

Step 6: Solve for x.
x = 18,000

Step 7: Check if the critical point is a maximum by taking the second derivative of the profit function.
d²π(x)/dx² = -1/2000 < 0, so the critical point is a maximum.

Thus, the production level that maximizes profit is x = 18,000 pocket calculators per week.

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The greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6.

This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6. This means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

To calculate the GCF, the prime factors of each number must be determined. The prime factors of 24 are 2 and 3 (2 x 2 x 2 x 3). The prime factors of 48 are 2 and 3 (2 x 2 x 2 x 2 x 3). The prime factors of 18 are 2 and 3 (2 x 3 x 3).

To determine the GCF, the highest power of each prime factor must be determined. In this case, the highest power of each prime factor is 3 (2 x 2 x 2 x 3). Therefore, the GCF of 24, 48, and 18 is 6. This means that the greatest number of baskets that can be made with the given items is 6.

In conclusion, the greatest number of baskets that can be made with 24 movies, 48 packages of popcorn, and 18 boxes of candy is 6. This is determined by finding the greatest common factor (GCF) of each item. The GCF of 24, 48, and 18 is 6, which means that 6 is the greatest number of baskets that can be made if each basket has an equal number of each of the three items.

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Direct variation equations have the following form:

Where "k" is the Constant of variation.

In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:

You know that:

When:

So you need to make the conversion from feet to miles. Since:

You get:

Then, you can find the value of "k" as following:

Answer:

B

Step-by-step explanation:

Not counting human error he should get exactly eight questions right using scicence, but since it is random there is margin of error that may disfigure the outcome.

The current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.Vending machines are used to offer goods like snacks and beverages to consumers for sale without the need for a salesperson.  

These machines often necessitate cash or debit card payments to operate. Vending machines have become a preferred method of retailing due to their cost-effectiveness and ease of use. The current value of the vending machine can be determined using the present value formula.

The present value is the sum of the future payments, discounted back to their current value. In this case, we must discount the future payments to their present value using the given interest rate. The formula is as follows:PV = Pmt x ((1-(1/(1+r)n))/r).

Where, PV = Present Value Pmt = Payment per period n = Number of periods r = Interest rate per periodIn this scenario, Pmt = $750n = 30 periods (since the payments are made every six months for 15 years, which is 30 periods)r = 5% per period.

Present Value = $750 x ((1-(1/(1+0.05)^30))/0.05) Present Value = $150,411.90.

Therefore, the current value of the vending machine that is expected to pay out $750 every six months for 15 years at a 5% interest rate per annum, and the first payment is made four years after from today is $150,411.90.

In conclusion, the current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.

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Answer:

15

Step-by-step explanation:

Answer:

\( {.2}^{4} = .0016\)

Answer:

Step-by-step explanation:

0.2^4 is

0.2 x 0.2 x 0.2 x 0.2  =

0.04 x 0.04 =

0.0016

As we need to select counterexamples, we have to select all the options that make the statement x+2>7 a FALSE statement.

Then, we can rearrange:

We have to select all the options where x is NOT greater than 5: -2, 0, 3, 4.

The options -2, 0, 3, 4 have to be selected.