1
Sam can run 8 miles in 2 hours. At this rate, how far will he be in 9 hours.

Answer:

300 : 180 = 5 : 3

8

In this pattern, we have 4 12 then 20.

We can see that the difference 4 and 12 is 8.

Since the difference between 12 and 20 is also 8, the common difference of the sequence is 8.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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\(x=-2\hspace{5em}y=2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^2 - y^3}{x^3 + y^2}\implies \cfrac{(-2)^2 - (2)^3}{(-2)^3 + (2)^2}\implies \cfrac{(-2)(-2)~~ - ~~(2)(2)(2)}{(-2)(-2)(-2)~~ + ~~(2)(2)} \\\\\\ \cfrac{(+4)~~ - ~~(+8)}{(-8)~~ + ~~(+4)}\implies \cfrac{4-8}{-8 + 4}\implies \cfrac{-4}{-4}\implies \text{\LARGE 1}\)

for the sake of clarity, is better to parenthesize all, since plugging in the value for the variable, only includes the variable, no any exponents or signs in front.

that said, let's recall that minus * minus = plus, and that plus * plus = plus, however minus * plus = minus.

so you can think of it this way, if you have a negative value multiplied an "even times", it'll positivize, if you multiply it an "odd times", it'll go back to negative, so is not like it remains negative, it changed a few times and in the end negativized back.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms

The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.

Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.

Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.

According to the question,

Option A and option E are correct about the machine learning algorithms

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The length of rectangle is 20cm and width is 12cm.

Let the length is x cm and width is y cm.

then perimeter 2(x+y) =64 cm

=> x+y = 64/2 = 32

=> x + y = 32 .............(1)

and according to question twice the width is 4cm more than length so,

2y = x + 4

=> 2y -x = 4 .............(2)

now we add these two equation to find the value of x and y.

3y = 36

=> y = 12

now put the value of y on any equation to find value of x ,

x +12 = 32

=> x = 32 -12 = 20

so, the length of rectangle is 20cm and width is 12cm.

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Answer:

7/25

Step-by-step explanation:

0.28 = 28/100 = 7/25

Answer:

56.57 yards (rounded to the nearest hundredths)

Step-by-step explanation:

Well follow Pythagorean theorem

20^2+b^2=60^2

400+b^2=3600

B^2= 3200

√3200=56.57 (rounded)

Answer:

37 years old

Step-by-step explanation:

If Dee is 7 years older than Sydney we can write an equation using the variables D to represent D and S to represent Sydney.

D + S = 81

Since Dee is 7 years older than Sydney we can say

D = S + 7.

To get S to stand alone replace the D with its equivalent equation.

(S+7) + S = 81.

Solve by subtracting 7 on both sides.

S + S = 74.

Combine like terms to get:

2S = 74.

Now divide by 2 to get S to stand alone.

S = 37

Therefore Sydney is 37 years old.

Joan catches up to Jeff at 8:49.8 am (or approximately 8:50 am).

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It represents a value or a set of values when the variables are replaced by specific numerical values.

Let's call the distance Jeff travels before Joan catches up to him "d". We know that Jeff travels this distance in half an hour less time than Joan, so we can use the following equation:

d = 5(t + 0.5) (Jeff's distance equation)

d = 8t (Joan's distance equation)

where t is the time in hours after 7:30 am that Joan catches up to Jeff.

Setting the two equations equal to each other, we get:

5(t + 0.5) = 8t

Simplifying this equation, we get:

5t + 2.5 = 8t

Subtracting 5t from both sides, we get:

2.5 = 3t

Dividing both sides by 3, we get:

t = 0.83 hours

This is the time in hours after 8:00 am that Joan catches up to Jeff. To convert this to minutes, we multiply by 60:

t = 0.83 × 60 = 49.8 minutes

Therefore, Joan catches up to Jeff at 8:49.8 am (or approximately 8:50 am).

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Answer:

C.

Step-by-step explanation:

because f(x) is directly proportional to the numerator which greater than the denominator ( 5>1 ).

While in other cases, f(x) is inversely proportional to the greatest value which is the denominator

Answer:

$1,065,597.22

Step-by-step explanation:

Simple interest = Principal * Rate * Time/100

10,510 = P * 12 * 30/365*100

10,510*365*100 = 360P

383,615,000 = 360P

Note that the time was converted to years by dividing by 365

P = 383,615,000/360

P = $1,065,597.22

Hence the principal is $1,065,597.22

The principal amount is $1065597.222 and this can be determined by using the formula of simple interest and the given data.

Given :

The following steps can be used in order to determine the principal amount:

Step 1 - The simple interest formula can be used in order to determine the principal amount.

Step 2 - The formula of simple interest is given below:

\(\rm I = P\times R \times T\)

where P is the principal amount, I is the simple interest, R is the interest rate and T is the time period.

Step 3 - Now, substitute the values of the known terms in the above formula.

\(\rm 10510 = P\times 0.12 \times \dfrac{30}{365}\)

Step 4 - Simplify the above expression.

P = $1065597.222

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Answer:

D, E and F

calculating the volume of regular bodies like prims works by multiplication alone.

you need some addition for surface area and for more complicated bodies that when the volume can't be calculated in one step

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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this is the answer I believe

Answer:

1, -1 , -3 ,3

Step-by-step explanation:

A function is a relationship between inputs where each input is related to exactly one output.

The values of f(x) for x = 1, 0, -1, 2 are 1, -1, -3,  and 3.

x        f(x)

1         1

0        -1

-1       -3

2        3

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 2x - 1

For x = 1

f(1) = 2 - 1 = 1

For x = 0

f(0) = 0 - 1 = -1

For x = -1

f(-1) = -2 - 1 = -3

For x = 2

f(2) = 4 - 1 = 3

Thus,

The values of f(x) for x = 1, 0, -1, 2 are 1, -1, -3,  and 3.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

C. 35

55 degrees + 35 degrees= 90 degrees

Answer: 987654301

Step-by-step explanation:

The factors of 6 are 2 and 3:

2*3 = 6.

So we want a big number that is no divisible by 2 or 3.

Then:

The number can not end in 0, 2, 4, 6 or 8.

The addition of the digits can not add to a multiple of 3.

If we want to construct the largest number possible, we should try to use the largest number at the beginning, so we have:

9876543210

but we can not end in 0, so we can write this as:

9876543201

but 9 + 8 +7 + 6 +5 + 3 + 2 + 1 = 45, it is a multiple of 3, so we should discard one of these numbers, lets discard the 1, as it is the smaller one.

we can write:

987654203 but if instead we remove the 2, we can leave the 3 in the place and get:

987654301 that is bigger, it ends with an odd number so it is not a multiple of 2, and the addition of all the digits adds up to 44, so this is not a multiple of 3.

Then this is the answer,

Answer:

the answer of the question is 7

Let us start this problem by analyzing the area we want to calculate

.

To calculate the surface area we will divide the are in two parts:

The area of the base:

The area of the base can be calculated as the difference between the areas of the to disks , as follows:

Where we use twice the formula for the area of a circle pi*radius^2, for the outer disk the radius is 12 and for the inner disk the radius is 4.

The lateral area of the two cones, the outer and the inner

Now we will calculate the lateral area of a cone (that is we will not include the base) this area is illustrated by the following draw:

The lateral area of a cone can be calculated using the next formula

Where h is the height of the cone, and r is the radius of the base, for the bigger cone we know from the figure that the height is 6 ft and the radius is 12 ft, for the smaller cone we also know from the figuere that the height is 3 ft and the radius is 4 ft. Therefore we can calculate:

and

Finally, putting all the areas together we find that:

Let the daily rate of each associate, A = $700

And the daily rate of each partner, P = $1700

Let the total number of individuals involved in the case = NT

Total number of partners = NP

Total number of associates = NA

NP + NA = NT -------- (i)

From the question; NP - NA = 4 -------- (ii)

From (i), NA = NT - NP

Substitute in (ii) as: NP - (NT - NP) = 4

Therefore, 2NP - NT = 4.

And NP = 2 + (NT/2) --------- (iii)

Substitute for NP in (i) above: NT = NA + 2 + (NT/2)

Therefore, NT - (NT/2) - 2 = NA.

NA = (NT/2) - 2 ---------- (iv)

Finally, the total daily rate was $21200. This is a composite of the daily rate and numbers of both associates and partners.

Therefore, (A * NA) + (P * NP) = $21200 ---------- (v)

To find the individual number of associates and partners involved in this case, first substitute the values of NP and NA from (iii) and (iv) respectively into (v) such that the only variable in (v) is NT.

Solve for NT and then use the value to find NP and NA.

NT = 16

NP = 10

NA = 6

Notice that 10 - 6 = 4. Q.E.D

Hope this helps.

Answer:

p=a+4

Step-by-step explain:

Let a=the number of associates designated

let p=the number of partners designated

Write System of Equations:

700a+1700p=21200

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer: S=11

Step-by-step explanation:

to find the area of a square is height times length. The square root of a number is a number that when multiplied by itself equals the original number. 121 is a perfect square because x times x =121 is rational. 11x11=121. Hence, 11 is how long each side of the garden is.

hope this helps!

Answer:

5/18

Step-by-step explanation:

Parentheses next to each other mean to multiply. So, this problem means you need to multiply -4/9 and -5/8. To multiply fractions, you just have to multiply across. To make it easier to understand what I mean...

-4 x -5  = 20 (when you multiply two negatives, it makes a positive)

9 x 8   = 72

20/72 simplifies to 5/18.

Hope this helps!! Have a wonderful day C:

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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