(1 point) If f(x) = x2 + 2, find and simplify the following:(a) f(t + 2)(b) f(t^3+ 2) =(d) 3f(t)(e) (f(t))^2 + 2 =

Answer: 108\(\pi\) + 72 \(mi^{2}\) or 411.29 \(mi^{2}\)

Step-by-step explanation:

In this situation, we need to seperate the polygon into two pieces, the part of a circle and the right angle triangle.

The area of the part of the circle is

\(\frac{3}{4}\) × \(\pi\)\(r^{2}\) as it is \(\frac{3}{4}\) of a circle. Insert r as 12(because the radius is 12), we get 108\(\pi\)

For the right angle triangle, we use the equation \(\frac{1}{2} bh\) , which in this case b and h are 12 so the area of the right angled triangle is \(\frac{1}{2}\) × 12 × 12 = 72

So the combined area is 108\(\pi\) + 72 or around 411.29 \(mi^{2}\)

Answer:

on a half circle of radius 12 Area = (12²*ft)/2

on a right angle triangle Area = (12*12)/2 = 72

on 1/4 radius 12mi Area = (12²*ft)/4

Area = (144ft)/2 + 72 + (144ft)/4

Area = 72ft+36ft+72 = 108ft+72(mi²)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

p ÷ 5 - 2, If p = 15

15/5 - 2

(15/5=3)

3 - 2 = 1

1 is the answer

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of the usage of the formula for work done.

The project is performing well at the end of WEEK 7.

1. The planned value (PV) at the end of WEEK 7 is $30,000.
2. The earned value (EV) at the end of WEEK 7 is $30,000.
3. The actual cost (AC) at the end of WEEK 7 is $30,000.
4. The cost variance (CV) at the end of WEEK 7 is $0.
5. The schedule variance (SV) at the end of WEEK 7 is $0.
6. The cost performance index (CPI) at the end of WEEK 7 is 1.0 (CV/AC).
7. The schedule performance index (SPI) at the end of WEEK 7 is 1.0 (EV/PV).
8. At the end of WEEK 7, this project is performing according to the plan. The CPI and SPI are both equal to 1.0, indicating that the project is on track in terms of cost and schedule. The cost variance (CV) and schedule variance (SV) being zero further support this conclusion, as it means that the project is meeting its planned budget and schedule.

To know more about project, visit:

https://brainly.com/question/28476409

#SPJ11

The completed table with regards to terms of an expression are presented as follows;

     Condition      \({}\)              (6·x + 3) + (5·x - 4)            (-4·y - 16) - 8·y + 10 + 2·y

         Exactly 3 terms          N/A     \({}\)                              N/A

         Exactly 5 terms          N/A         \({}\)                          N/A

Includes a zero pair             No \({}\)                                   No

Uses distributive property   No                                    No

Includes a negative factor   No                                    

Has no like terms                False                                False

Condition       \(8 - \dfrac{1}{2} \cdot \left(4 \cdot x - \dfrac{1}{2} + 12\cdot x -\dfrac{1}{4} \right)\)  0.25·(8·m - 12) - 0.5·(-4·m + 2)

Exactly 3 terms       No                         \({}\)                    No

Exactly 5 terms       Yes                          \({}\)   \({}\)              No

Includes a zero pair No    \({}\)                         \({}\)              Yes

Uses the distributive property Yes            \({}\)             Yes

Includes a negative factor      Yes           \({}\)                Yes

Has no like terms                    No          \({}\)                  No

A mathematical expression is a collection of variables and numbers along with mathematical operators which are all properly arranged.

The details of the conditions in the question are as follows;

Terms of an expression

A term is a subunit of an algebraic expression which are joined together by operators such as addition or subtraction

Zero pair

A zero pair are two numbers that when added together have a zero result

Distributive property

The distributive property of multiplication states that the multiplication of a number or variable by an addend is equivalent to the sum of the multiplication of the number or variable and each member of the addend

Negative factor

A negative factor is a factor that has a negative sign prefix

Like terms

Like terms are terms consisting of identical variables with the same  powers of the variable

Learn more about expressions here:

https://brainly.com/question/1859113

#SPJ1                      

The goat race is 324.25 meters longer than the ant race .

The goat race is 325 meters long. The ant race is 75 centimetres long.

The goat race is in meters while the ant race is in centimetres.

Let's convert the ant race to meters.

Hence,

1 cm  = 0.01 m

75 = ?

cross multiply

Ant race = 0.75 meters

Therefore, let's find the difference between the goat race and the ant race.

325 - 0.75 = 324.25 meters.

learn more on distance here: https://brainly.com/question/14384892

#SPJ1

Answer: Step 1: To compare the distances, they must both be in meters or both be in centimeters. Change 75 centimeters to meters.

So=75 cm ÷ 100 = 0.75 m

Step-by-step explanation:

Step 2: Determine how much longer the goat race is than the ant race in meters.  

o get the correct answer, subtract the length of the ant race in meters from the length of the goat race.

Remember to line up the decimal points and add zeros as plac

eholders. The difference of 325 and 0.75 is 324.25.

The goat race is 324.25 meters longer than the ant race.

Apriori algorithm refers to an algorithm that is used in mining frequent products sets and relevant association rules. Generally the apriori algorithm operates on a database containing a huge number of transactions.

The Apriori algorithm uses frequent itemsets to generate association rules and it is designed to work on the databases that contain transactions.

Aprori algorithm uses frequent itemsets to generate association rules. It is based on the concept that a subset of a frequent itemset must also be a frequent itemset.

The given three components comprise the apriori algorithm.

1. Support

2. Confidence

3. Lift

The apriori algorithm makes the given assumptions:

1. All subsets of a frequent itemset must be frequent.

2. The subsets of an infrequent item set must be infrequent.

3. Fix a threshold support level.

Apriori algorithm is an expensive method to find support since the calculation has to pass through the whole database.

Given question is incomplete.

To know more about algorithm here

https://brainly.com/question/7139379

#SPJ4

Answer:

Step-by-step explanation:

The mixture that contains the greatest amount of acetic acid is the mixture C.

A mixture is a substance that contains tow ore more constitutes in various quantities which may or may not be able to be separated.

To determine the mixture with a greater amount of acetic acid, all the mixtures are converted to decimal forms such as the following:

Mixture A = 0.036 acetic acid ( already in a decimal form)

Mixture B = 4.2% = 4.2/100 = 0.042

Mixture C = 1/22 = 0.046

Therefore,the mixture that has the highest amount of acetic acid = mixture C.

Learn more about percentage here:

https://brainly.com/question/24304697

#SPJ1

The formula for the area of a circular petri dish can be represented as A = πr², where "A" represents the area and "r" represents the radius.

To find the approximate increase in the area when the radius increases from r₁ mm to r₂ mm, we can calculate the difference between the areas by subtracting the initial area (A₁ = πr₁²) from the final area (A₂ = πr₂²). This can be expressed as ΔA = A₂ - A₁ = πr₂² - πr₁².

In the second paragraph, let's explain the formula and how to calculate the approximate increase in the area of the bacterial colony on the petri dish. The area of a circular shape is given by the formula A = πr², where "A" represents the area and "r" represents the radius. By substituting the initial radius, r₁, into the formula, we can find the initial area, A₁ = πr₁².

Similarly, by substituting the final radius, r₂, into the formula, we can find the final area, A₂ = πr₂². To calculate the approximate increase in area, we subtract the initial area from the final area: ΔA = A₂ - A₁ = πr₂² - πr₁². This formula allows us to find the difference in the areas of the bacterial colony on the petri dish when the radius increases from r₁ to r₂.

Learn more about Area:

brainly.com/question/1631786

#SPJ11

Total number of boys in class are 172

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

We have total  number of students in class = 410

We assume that the number of boys in class = X

Number of girls in class is  66 more then boys we assume total number of girls = X+66

If we add number of girls and boys then we found total strength of classX+X+66=4102X+66=4102x=344X=172

Number of boys = 172

Number of girls =238

To learn more about linear equation visit: brainly.com/question/11897796

SPJ4

\(\boxed{\sf (-3, -1)}\boxed\)

Answer:

Reflect over the horizontal axis, and then translate the graph up 3 units.

Step-by-step explanation:

Answer:

(B) Reflect over the horizontal axis, and then translate the graph up 3 units.

Step-by-step explanation:

Edge 2021

The probability of selection of diagonal which is not shortest nor longest is 13/17.

We know very well that Icosagon has 20 sides.

If any diagonal is possible, it can be possible by connecting two points, so to choose r objects from n objects can be done by ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\)

So, number of ways to choose diagonal = \(^2^0C_{2}\)

After that we need to subtract 20 ways as single point can lead to diagonal making.

So, total number of ways to choose 20 diagonals =  170

Now, talking about the shorter diagonal

so, shorter diagonal =Diagonal connecting(A₁A₃, A₂A₄,.....) =20 diagonals.

Now, talking about longer diagonal=Diagonal connecting(A₁A₈,A₂A₉.........) = 20 diagonals

So, we have total chances of ⁿ \(C_{r}\) = \(\frac{n!}{r! (n-r)!}\) and possible number of chances of selection of shorter and longer diagonal

So, according to the formula,

Probability= Favorable outcome /Total outcome

Probability = [(Total ways to select diagonals - (Ways to select shorter diagonal) - Ways to select longer diagonal)]/(Total number of ways)

Probability = (170-20-20)/170

Probability = 130/170

Probability = 13/17

Hence, the probability of selecting a  diagonal such that it is not shortest nor longest is 13/17.

Learn more about Probability:

https://brainly.com/question/30186543

#SPJ4

Answer:

poopy

Step-by-step explanation:

Tee Hee

Answer:

a, 30 minutes

Step-by-step explanation:

108 divided by 20 is 54

162 divided by 54 is 30

Answer:A= $75,075

Step-by-step explanation:

P = $73,125

R = 8%

T = 4/12

A =?

S.I = P*R*T

S.I = 73,125*4/12*8/100

S.I = 1,950

A = S.I + P

A = 1,950 + 73,125

A= $75,075

The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

To know more about the region refer here:

https://brainly.com/question/30059816#

#SPJ11

The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

Know more about maximum value here:

https://brainly.com/question/30236354

#SPJ11

The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

To know more about equation of the curve refer here:

https://brainly.com/question/31467851#

#SPJ11

The linear function that models the problem of T-shirt printing company sales is

y = 2.50x + 3.50

The number of T-shirts to be sold to have equal income and expense is 300 T-shirts

A linear function consists of functions where the variables has exponents of 1. The relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function below

c = y intercept is the cost of the Printing Machine = $3000.00

m = cost of blank T-shirts = $5

assuming number of T shirts is x

y = expenses = 5x + 3000

income = 15x

For income to be equal to expenses

5x + 3000 = 15x

3000 = 15x - 5x

3000 = 10x

x = 300

300 T-shirts should be sold to have equal income and expense

Learn more on  linear models at :

https://brainly.com/question/29650903

#SPJ1

The probability that four of the first five patients will be helped by the medicine is 0.39. The probability that a particular medicine will help a person is an important aspect of medicine.

The probability that a certain medicine will help a person is 0.75. A doctor will be seeing 15 patients today.

To find out the probability of the following:

a) P(The medicine will help all 15 patients)When each patient is independent of the other, then the probability of the medicine helping all 15 patients can be calculated by multiplying 0.75 by itself 15 times.

Therefore:

= P(The medicine will help all 15 patients)

= 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75 × 0.75

= 0.0047.

Therefore, the probability that the medicine will help all 15 patients is 0.0047.

b) P(The medicine helps 9 or more patients)

To determine this, we have to calculate the probability of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

We can calculate these probabilities using the binomial probability formula. The probability of the medicine helping at least 9 patients is the sum of the probabilities of the medicine helping 9 patients, 10 patients, 11 patients, 12 patients, 13 patients, 14 patients and 15 patients.

Therefore:

P(The medicine helps 9 or more patients) = P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15)

= 0.196 + 0.326 + 0.305 + 0.176 + 0.066 + 0.018 + 0.003

= 0.99

Therefore, the probability that the medicine helps 9 or more patients is 0.99.

c) P(The medicine helps exactly 10 patients)Using the binomial probability formula, we can find that the probability that the medicine will help exactly 10 patients is:

P(X = 10) = nCx * p^x * q^(n - x), where n = 15, x = 10, p = 0.75 and q = 0.25

Therefore:

P(X = 10) = 15C10 * (0.75)^10 * (0.25)^5

= 0.20

Therefore, the probability that the medicine helps exactly 10 patients is 0.20.

d) P(Four of the first five patients will be helped by the medicine)

Using the binomial probability formula, we can find that the probability that 4 of the first 5 patients will be helped by the medicine is:

P(X = 4) = nCx * p^x * q^(n - x)y, where n = 5, x = 4, p = 0.75 and q = 0.25

Therefore:

P(X = 4) = 5C4 * (0.75)^4 * (0.25)^1

= 0.39

Therefore, the probability that four of the first five patients will be helped by the medicine is 0.39.

The probability that a particular medicine will help a person is an important aspect of medicine. The likelihood of the medicine helping all 15 patients is very low, and the likelihood of the medicine helping 9 or more patients is very high. The likelihood of the medicine helping exactly 10 patients is relatively low, and the likelihood of four of the first five patients being helped by the medicine is relatively high.

To know more about the binomial probability formula, visit:

brainly.com/question/30764478

#SPJ11

If the desired margin of error E is halved, the required sample size n(E) increases by a factor of 2, not 4 or 1/2.

To determine the required sample size n(E) for the production personnel to be approximately 95% confident that their estimate of the average number of defective batteries per box is within E units of the true mean, we can use the formula for sample size estimation with a known population standard deviation.

The formula is given by:

n(E) = (Z × σ / E)²

Where:

n(E) is the required sample size

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to a Z-score of approximately 1.96)

σ is the known population standard deviation

E is the desired margin of error

Given that the population standard deviation (σ) is 0.9 defective batteries per box, and the desired confidence level is 95%, we can substitute these values into the formula.

n(E) = (1.96 × 0.9 / E)²

Now, we can analyze the relationship between n(E) and E.

If E is halved (E/2), let's denote the new sample size as n(E/2).

n(E/2) = (1.96 × 0.9 / (E/2))²

= (1.96 × 0.9 × 2 / E)²

= (3.52 × 0.9 / E)²

= (3.168 / E)²

= (3.168² / E²)

= 10.028224 / E²

Comparing n(E/2) with n(E), we can see that n(E/2) is not equal to n(E).

Therefore, the statement "If E is halved, n(E) increases by a factor of 4" is incorrect.

Similarly, the statement "If E is halved, n(E) goes down by a factor of 2" is also incorrect.

Learn more about the margin of error at

https://brainly.com/question/29419047

#SPJ4

Answer:

I think it is B sorry if I got it wrong

Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

The probability that none of the 4 light bulbs work is 2.56%.

As per the given information, the probability that an individual light bulb works is 0.6.

Therefore, the probability that it does not work (i.e., fails) is:

1 - 0.6 = 0.4

Since each light bulb works independently of the other light bulbs, the probability that none of the 4 light bulbs work is the product of the individual probabilities that each light bulb fails.

Calculated as,

P(none work) = P(first fails) × P(second fails) × P(third fails) × P(fourth fails)

P(none work) = 0.4 × 0.4 × 0.4 × 0.4

P(none work) = 0.0256

Therefore, the probability that none of the 4 light bulbs work is 0.0256 or approximately 2.56%.

For similar questions on limit,

brainly.com/question/282767

#SPJ4

Solving single variable equations involves isolating the unknown variable on one side of the equals sign.

When solving a single variable equation, the goal is to isolate the variable on one side of the equation. This is typically done by performing inverse operations to eliminate any constants or coefficients attached to the variable.

The steps involve simplifying both sides of the equation, combining like terms, and applying inverse operations such as addition, subtraction, multiplication, or division to move the variable to one side. The process continues until the variable is isolated, and the solution is obtained.

It's important to perform the same operation on both sides of the equation to maintain equality. By following these steps, the unknown variable can be determined, solving the single variable equation.

For more questions like Equation click the link below:

https://brainly.com/question/29657983

#SPJ11

The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.

Let's calculate the matrix product C = AB step by step:

Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.

In this case, both matrices satisfy this condition, so the product C = AB is defined.

Calculating AB:

AB = [23 + 912 26 + 94 21 + 95]

[103 + 612 106 + 64 101 + 65]

Simplifying the calculations:

AB = [6 + 108 12 + 36 2 + 45]

[30 + 72 60 + 24 10 + 30]

AB = [114 48 47]

[102 84 40]

Therefore, the product C = AB is:

C = [114 48 47]

[102 84 40]

In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:

C = [114 48 47]

[102 84 40]

To learn more about matrix visit:

brainly.com/question/29239316

#SPJ11

The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

To learn more about the explicit formula from the given link

https://brainly.com/question/9859279

#SPJ1