Express 10x - x^2 in the form
a - (x + b)^2

1)  The total number of computers they would buy if they get 10 notebooks and 19 desktop computers is: 54 computers

2) The total number of computers they would buy if they get n notebooks and d desktop computers is: (350/n) + (375/n)

The parameters given are:

Cost of notebook Computers = $350

Cost of Desktop desktop = $375

Thus, if they  get 10 notebooks and 19 desktop computers, then:

Total number of computers is:

(350/10) + (375/19) = 35 + 19

= 54 computers

(375/19) was approximated to 19 because we must use a whole number and not a decimal.

If they buy n notebooks and d desktop computers, then total computers will be:

(350/n) + (375/n)

Read more about Algebraic Expressions at: https://brainly.com/question/4344214

#SPJ1

solution:

3x^2+9x-5

i hope this helps

:)

We can say with 95% confidence that the true mean number of hours that students at the college study is between 11.76 and 12.64 hours per week.

Based on a sampling from the population, a confidence interval is a range of values that is likely to include the real population parameter (such as the population mean). The confidence level, which is often stated as a percentage (e.g., 95%), expresses how confident we are in the interval.

The likelihood that a finding arose by accident or as a result of random variation in the data is referred to as statistical significance, on the other hand. In general, if a result is unlikely to have happened by chance, it is deemed statistically significant.

The 95% confidence interval is given as:

CI = X ± Zα/2 (σ/√n)

The critical value for 95% is 1.96.

Substituting the value:

CI = 12.2 ± 1.96 (1.6/√49)

CI = 12.2 ± 0.44

CI = (11.76, 12.64)

Hence, we can say with 95% confidence that the true mean number of hours that students at the college study is between 11.76 and 12.64 hours per week.

Learn more about confidence interval here:

https://brainly.com/question/29680703

#SPJ1

Answer:

There are 76 students:

g + b = 76

girls is 13 more than twice the boys:

g = 2b + 13

replace g with 2b + 13 in 1st equation

2b+13+b = 76

3b + 13 = 76

3b = 63

b = 21 boys

g = 76-21 = 55 girls

Step-by-step explanation:

This enabled the borrower to obtain 90 percent financing while avoiding the additional cost of pmi. these loans are more commonly referred to as  piggyback mortgage loans.

A loan is the lending of cash via one or more individuals, organizations, or different entities to other individuals, corporations, etc. The recipient incurs a debt and is normally susceptible to pay hobby on that debt till it is repaid as well as to repay the foremost amount borrowed.

A mortgage is a shape of debt incurred by using an character or different entity. The lender—commonly a business enterprise, economic organization, or authorities—advances a amount of money to the borrower. In return, the borrower agrees to a sure set of phrases together with any finance charges, hobby, repayment date, and different situations.

Learn more about loans here

https://brainly.com/question/19905911

#SPJ4

Answer:

y=-1/8x+11/16

Step-by-step explanation:

The slope-intercept form is y=mx+b. You have to move over 2x to the other side. After that you have to divide both sides by 16 to get to the y intercept form, so it would end up as y=-1/8x+11/16, where -1/8=m and 11/16=b

Answer:

18cm = 45km

Step-by-step explanation:

Divide 18 by 4 to get 4.5. Multiply 4.5 by 10 to get 45km.

Answer:

Step-by-step explanation:

what grade is this ...

this look hard

The formula to calculate the area of a trapezoid is as follow:

4 * (8 + 16) * 1/2

Answer:

trapezoid area :(a+b)/2 ×h

(16+ 8)/2 ×4

=48

Answer:

Step-by-step explanation:

well the x is 1/1 and the 2 is over 1 so divided and it is B is what i got

As you can see we have a trapezoid inside a rectangle. The blue section is equivalent to the area of the rectangle that it's not covered by the trapezoid. Then the area of this section is equal to the area of the rectangle less the area of the trapezoid. Then we just need to find the areas of both figures. Remember than the area of a rectangle is given by the product between its height and its base:

Trapezoids are figures with two parallel sides known as bases. The area of a trapezoid is given by product between the sum of its bases and its height divided by 2:

Then the area of the rectangle in the picture is given by:

So it's 80 cm².

The area of the trapezoid considering that its base has the same length as the rectangle is:

So its area is of 21 cm².

Finally the area of the blue section is given by:

Then the answer is 59cm².

Answer:

-31 c + 13

Step-by-step explanation:

-13c+8-18c+5

combine like terms

-18c and -13c combined is -31c

8 + 5 = 13

-31 c + 13

Answer

-31c+13 is your answer (see explanation below!)

Step-by-step explanation:

1) Add the numbers:

\(-13c + 8 - 18c + 5\\-13c + 13 -18c\\\)

2) Combine like terms:

\(-13c+13-18c\\-31c+13\\\)

\(A: -31c+13\)

Hope this helped you! Please mark me brainliest! Thanks! Have a great day! :)

The Taylor polynomial t1(x) for the function f(x) = ln(1+x) based at b = 0 is given by t1(x) = x.

The Taylor polynomial represents an approximation of a function around a specific point using a polynomial. The first-order Taylor polynomial, also known as the linear approximation, involves considering only the first derivative of the function. In this case, the function is ln(1+x), and the approximation is centered at b = 0.

To find the first-order Taylor polynomial, we start by evaluating the function and its derivative at the point of interest. The function ln(1+x) evaluated at x = 0 is ln(1+0) = ln(1) = 0. The first derivative of ln(1+x) is 1/(1+x), and evaluating it at x = 0 gives 1/(1+0) = 1.

Thus, the first-order Taylor polynomial t1(x) = x is obtained by taking the linear term of the Taylor series expansion. It provides a good approximation of the function ln(1+x) in the neighborhood of x = 0.

Learn more about Taylor polynomial here:

https://brainly.com/question/30481013

#SPJ11

The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

for such more question on interest

https://brainly.com/question/25845758

#SPJ11

a) An upper bound for error |f (0.5) − P2(0.5)| using the error formula is 0.0208

b) On the interval [0, 1], we have |R2(x)| <= (e/6) √10 x³

c) The maximum value of |f(x) - P2(x)| on the interval [0, 1] occurs at x = π/2, and is approximately 0.1586.

a. As per the given polynomial, to approximate f(0.5) using P2(x), we simply plug in x = 0.5 into P2(x):

P2(0.5) = 1 + 0.5 - (1/2)(0.5)^2 = 1.375

To find an upper bound for the error |f(0.5) - P2(0.5)|, we can use the error formula:

|f(0.5) - P2(0.5)| <= M|x-0|³ / 3!

where M is an upper bound for the third derivative of f(x) on the interval [0, 0.5].

Taking the third derivative of f(x), we get:

f'''(x) = ex (-3cos x + sin x)

To find an upper bound for f'''(x) on [0, 0.5], we can take its absolute value and plug in x = 0.5:

|f'''(0.5)| = e⁰°⁵(3/4) < 4

Therefore, we have:

|f(0.5) - P2(0.5)| <= (4/6)(0.5)³ = 0.0208

b. For n = 2, we have:

R2(x) = (1/3!)[f'''(c)]x³

To find an upper bound for |R2(x)| on the interval [0, 1], we need to find an upper bound for |f'''(c)|.

Taking the absolute value of the third derivative of f(x), we get:

|f'''(x)| = eˣ |3cos x - sin x|

Since the maximum value of |3cos x - sin x| is √10, which occurs at x = π/4, we have:

|f'''(x)| <= eˣ √10

Therefore, on the interval [0, 1], we have:

|R2(x)| <= (e/6) √10 x³

c. To approximate the maximum value of |f(x) - P2(x)| on the interval [0, 1], we need to find the maximum value of the function R2(x) on this interval.

To do this, we can take the derivative of R2(x) and set it equal to zero:

R2'(x) = 2eˣ (cos x - 2sin x) x² = 0

Solving for x, we get x = 0, π/6, or π/2.

We can now evaluate R2(x) at these critical points and at the endpoints of the interval:

R2(0) = 0

R2(π/6) = (e/6) √10 (π/6)³ ≈ 0.0107

R2(π/2) = (e/48) √10 π³ ≈ 0.1586

To know more about polynomial here

https://brainly.com/question/11536910

#SPJ4

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

For more questions on: integers

https://brainly.com/question/17695139

#SPJ8  

The correct answer is (e) Between 890,000 and 900,000 people.

To find out how many people from this city will have a monthly income between £2,000 and £2,300, we need to use the z-score formula:

z = (x - μ) / σ

where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

First, we'll find the z-score for £2,000:

z = (2000 - 2075) / 162 = -0.46

Next, we'll find the z-score for £2,300:

z = (2300 - 2075) / 162 = 1.39

Using a z-table, we can find the corresponding probabilities for these z-scores. The probability for a z-score of -0.46 is 0.3228, and the probability for a z-score of 1.39 is 0.9177.

To find the probability of having a monthly income between £2,000 and £2,300, we need to subtract the smaller probability from the larger probability:

0.9177 - 0.3228 = 0.5949

This means that approximately 59.49% of the population will have a monthly income between £2,000 and £2,300. To find out how many people this represents, we'll multiply the probability by the total population:

0.5949 * 1,500,000 = 892,350

Therefore, the answer is (e) Between 890,000 and 900,000 people.

To know more about normal distribution refer here:

https://brainly.com/question/29509087#

#SPJ11

Answer:

B.

Step-by-step explanation:

Answer:

B.) -9/7, -1, 1/4, √7, 4.8

Step-by-step explanation:

Turn all the values into decimals first to make things easier:

1/4 = 0.25

-1 = -1

√7 = 2.7

4.8 = 4.8

-9/7 = -1.3

So, from least to greatest on a number line it'd be:

-1.3, -1, 0.25, 2.7, 4.8 or -9/7, -1, 1/4, √7, 4.8

Answer:

m<PQT = 56

Step-by-step explanation:

Angles PQS and SQT are shown to be congruent in the figure, so their measures are equal.

m<PQS = m<SQT

3x + 13 = 6x - 2

Subtract 6x from both sides.

-3x + 13 = -2

Subtract 13 from both sides.

-3x = -15

Divide both sides by -3.

x = 5

m<PQT = m<PQS + m<SQT

m<PQT = 3x + 13 + 6x - 2

m<PQT = 3(5) + 13 + 6(5) - 2

m<PQT = 15 + 13 + 30 - 2

m<PQT = 28 + 28

m<PQT = 56

If Michael selects option one, his account balance after 4 weeks will be $410, and if he selects option two, his account balance after four weeks will be $160.

Micheal has two options to increase his account balance. The first option is to add $100 to his account each week, while the second option is to double the amount in his account at the end of each week. We need to find Michael's account balance after 4 weeks if he follows either of these two options.

Option 1: If Micheal selects option one, he will add $100 to his account each week, and after 4 weeks, his account balance will be:

10 + (100 * 4) = $410

Option 2: If Micheal selects option two, the amount in his account will double after each week. Therefore, his account balance will be:

Week 1: $10 * 2 = $20

Week 2: $20 * 2 = $40

Week 3: $40 * 2 = $80

Week 4: $80 * 2 = $160

Michael's account balance after four weeks will be $160 if he follows option 2.

For such more questions on  account

https://brainly.com/question/1859113

#SPJ8

Note: The complete question is - If Micheal has $10 in his account and has the option to add $100 to his account each week or to double the amount in his account at the end of each week, what would be his account balance after 4 weeks?

The approximate change formula for a function z=f(x, y) at the point (a, b) in terms of differentials is given by Δz ≈ ∂z/∂x |(a, b) dx + ∂z/∂y |(a, b) dy

Function is equal to,

z=f(x, y)

In terms of differential the approximate change formula at (a, b) is,

Δz ≈ ∂z/∂x |(a, b) dx + ∂z/∂y |(a ,b) dy

where,

Δz is the approximate change in z

∂z/∂x is the partial derivative of z with respect to x

∂z/∂y is the partial derivative of z with respect to y

dx is the small change in x

dy is the small change in y

The vertical bars indicate that the partial derivatives are evaluated at the point (a, b).

This formula represents the total differential of z at the point (a, b).

Which is the linear approximation of the change in z due to small changes in x and y.

It is based on the assumption,

That the change in z is approximately proportional to the changes in x and y and is valid for small changes in x and y.

Learn more about function here

brainly.com/question/31406491

#SPJ4

Answer:

3/1.5=h/5

Step-by-step explanation:

3/1.5=h/5. Solving for the height, you get that h is 5*2=10 m long.

A flower that can be split vertically through its axis into two equal halves but has unequal halves if split in any other way is said to be bilaterally symmetrical.


1. Bilateral symmetry is a characteristic of many organisms, including flowers.
2. It means that the organism can be divided into two equal halves along a vertical axis.
3. However, if the organism is divided in any other direction, the resulting halves will be unequal.

Therefore, a flower that can be split vertically through its axis into two equal halves but has unequal halves if split in any other way is said to be bilaterally symmetrical. This means that its symmetry is only evident when divided vertically.

To know more about bilaterally symmetrical visit:

https://brainly.com/question/1103437

#SPJ11

Answer:

748.23 in^2.

Step-by-step explanation:

Area = 1/2 * apothem * perimeter

        = 1/2 * 14.7 * 101.8

        =  748.23 in^2.

Answer:

748.23

Step-by-step explanation:

A divisibility rule is a simple method for determining whether or not an integer is divisible by a fixed divisor without having to divide it by looking at its digits.

The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three.

The total of all the digits in 1377 is 1+3+7+7 = 18. Because 18 is divisible by three, 1377 is likewise divisible by three. The quotient is 1377 3 = 459, and the remainder is 0.

The divisibility rule of 9 asserts that if a number's sum of digits is divisible by 9, the number is divisible by 9 as well.

The three-digit divisibility rule and the nine-digit divisibility rule are quite similar. As previously stated, the divisibility rule for the divisibility test of 3 asserts that if a number's sum of all digits is divisible by 3, the number is also divisible by 3. The divisibility rule of 9 is similar to the divisibility rule of 3, in that a number is said to be divisible by 9 if the sum of all of its digits is divisible by 9.

Take 52884 for example. 52884 is divisible by three since the total of all digits is 5+2+8+8+4 = 27. The quotient is 52884 ÷ 3 = 17628, and the remainder is 0. It's worth noting that the sum of the digits is 27 is 2 + 7 = 9, which is likewise divisible by three.

To learn more about this visit ,https://brainly.com/question/28306146

#SPJ9

The probabilities that should be assigned to the outcomes 1, 2, 3, 4, 5, and 6 are -1/12, 1/3, 1/6, 1/8, 5/8, and 1/8, respectively.

Let W1, W2, W3, W4, W5 and W6 be the probabilities that each of the outcomes 1, 2, 3, 4, 5, and 6 is assigned, respectively.

A die is weighted so that odd numbers are 3 times as likely to come up as even numbers. Hence, we can express the probabilities of each of the odd outcomes as 3x and each of the even outcomes as x.

Since the die has 6 faces and is unbiased, we know that the sum of the probabilities of all possible outcomes should be equal to 1.

Thus, we have:

W1 + W2 + W3 + W4 + W5 + W6 = 1

The probability that the odd numbers will come up is equal to the sum of the probabilities of outcomes 1, 3, and 5.

Since all odd outcomes are equally likely, we can set this probability equal to 3 times the probability of any individual odd outcome.

Thus, we have:

W1 + W3 + W5 = 3(W3)

Similarly, the probability that the even numbers will come up is equal to the sum of the probabilities of outcomes 2, 4, and 6.

Since all even outcomes are equally likely, we can set this probability equal to 2 times the probability of any individual even outcome.

Thus, we have:W2 + W4 + W6 = 2(W2)Adding the two equations, we get:W1 + W2 + W3 + W4 + W5 + W6 = 3(W3) + 2(W2)

Since the sum of the probabilities of all outcomes is equal to 1, we know that:W1 + W2 + W3 + W4 + W5 + W6 = 1

Substituting this into the previous equation, we get:

1 = 3(W3) + 2(W2)Solving for W2, we get:

W2 = (1 - 3(W3))/2

Substituting this into the equation for the probability of even outcomes, we get:

W4 + W6 = W2

Thus, we have:

W4 + W6 = (1 - 3(W3))/2

Since all even outcomes are equally likely, we know that:

W4 = W6

Thus, we have:

2W4 = (1 - 3(W3))/2

Solving for W4, we get:

W4 = (1 - 3(W3))/4

Substituting this back into the equation for W2, we get:

W2 = (1 + 3(W3))/4

Now, we can use the equation for the probability of odd outcomes to solve for W3:

W1 + W3 + W5 = 3(W3)

Substituting the expressions for W2 and W4 into this equation, we get:

W1 + (1 - 3(W3))/4 + 3(W3) = 9(W3)/4 + (1 - 3(W3))/4 + 3(W3)

Simplifying, we get:W1 + (1 - 3(W3))/4 = 1

Thus, we have:W1 = (3(W3) - 1)/4

Now we can express all the probabilities in terms of W3:

W1 = (3(W3) - 1)/4W2 = (1 + 3(W3))/4W3 = W3W4 = (1 - 3(W3))/4W5 = (3 - 3(W3))/4W6 = (1 - 3(W3))/4

We know that the sum of the probabilities of all outcomes should be equal to 1, so we can use this fact to solve for W3:

W1 + W2 + W3 + W4 + W5 + W6 = (3(W3) - 1)/4 + (1 + 3(W3))/4 + W3 + (1 - 3(W3))/4 + (3 - 3(W3))/4 + (1 - 3(W3))/4= 1

Multiplying through by 4, we get:

3(W3) - 1 + 1 + 3(W3) + 4(W3) - 3 + 1 - 3(W3) + 1 - 3(W3) = 4

Simplifying, we get:

6W3 = 2W3 = 1/3

Thus, we have:

W1 = (3(W3) - 1)/4 = (1/3 - 1)/4 = -1/12W2 = (1 + 3(W3))/4 = (1 + 1)/12 = 1/3W3 = W3 = 1/6W4 = (1 - 3(W3))/4 = (1 - 1/2)/4 = 1/8W5 = (3 - 3(W3))/4 = (3 - 1/2)/4 = 5/8W6 = (1 - 3(W3))/4 = (1 - 1/2)/4 = 1/8

Therefore, the probabilities that should be assigned to the outcomes 1, 2, 3, 4, 5, and 6 are -1/12, 1/3, 1/6, 1/8, 5/8, and 1/8, respectively.

To know more about probabilities visit:

https://brainly.com/question/13604758

#SPJ11

The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

To know more about Chi - squared distribution here

https://brainly.com/question/4543358

#SPJ4

Magnitude and direction of u + v + w is equals to 57.871 and 19°.

"Vectors are those quantity of which represents both direction as well magnitude."

According to the question,

As shown in diagram we have,

u + v + w

   = (wcos30°)\(\^{i}\) + (wsin30°)\(\^{j}\) +(vcos20°)\(\^{j}\) - (vsin40°)\(\^{i}\) -(ucos40°)\(\^{i}\) -(usin40°)\(\^{j}\)

  = ( wcos30° - vsin40° - ucos40°)\(\^{i}\) + (wsin30°+ vcos20° - usin40°)\(\^{j}\)

Substitute the value of ║w║ = 40 ,║v║=60,and ║u║= 90 we get,

u + v +w

= (  40cos30° - 60sin40° - 90cos40°)\(\^{i}\) + (40sin30°+ 60cos20° - 90sin40°)\(\^{j}\)

= (20√3 - 20.5212 - 68.9440)\(\^{i}\) + ( 20 +56.3816 - 57.8509)\(\^{j}\)

= ( -54.8242)\(\^{i}\) + (18.5307)\(\^{j}\)

Therefore,

Magnitude = √(-54.8242)² +(18.5307)²

                  =√3349.0798

                  = 57.8712

   tanθ = ( 0.3380)

⇒θ = tan⁻¹ (0.3380)

     = 18.67

    ≈ 19°

Hence, magnitude and direction of u + v + w is equals to 57.871 and 19°.

Learn more about vectors here

https://brainly.com/question/17108011

#SPJ2