classify 1/3 if it is rational, irrational, integer, whole, or natural​

Answer:

16

Step-by-step explanation:

I subtracted the number at the bottom and added the joints at the right and top

-Lemony Snicket

Using the z-distribution, it is found that 1068 students have to be polled to be 95% confident of the outcome within +/- 3% of the vote.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

We have no estimate for the true proportion, hence we use \(\pi = 0.5\), and solve for n when M = 0.03. Then:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{(0.5)(0.5)}{n}}\)

\(0.03\sqrt{n} = 1.96(0.5)\)

\(\sqrt{n} = \frac{1.96(0.5)}{0.03}\)

\((\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.03}\right)^2\)

n = 1067.11.

Rounding up, 1068 students have to be polled to be 95% confident of the outcome within +/- 3% of the vote.

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10.5 lawn tickets and 3.5 pavilion seats were sold, which equals the total cost of $462.

We can utilise substitution to solve this set of equations. Let x represent the number of lawn tickets and y represent the number of pavilion seats. We can create two equations to represent the total cost of the tickets.

26x + 54y = 462

x + y = 14

To find the value of y, we can change the value of x from the second equation into the first equation.

26(14 - y) + 54y = 462

364 - 26y + 54y = 462

-26y + 54y = 462 - 364

28y = 98

y = 3.5

The second equation can then be solved for x by reintroducing the value of y.

x + 3.5 = 14

x = 10.5

This means that 10.5 lawn tickets were sold, and 3.5 pavilion seats were sold. To check if this solution makes sense, we can substitute our answer into the first equation to calculate the total cost.

26(10.5) + 54(3.5) = 462

This equation does equal 462, so our solution is correct. This makes sense in the context because it is a valid combination of tickets that adds up to the total cost of $462.

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The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

Using the formula shown replace r with 11 and pi with 3:

Volume = 4/3 x 3 x 11^3

Volume = 5,324 in^3

To find the cost per ounce for the 40 oz jar, divide the price by the number of ounces: $5.25/40 oz = $0.13 per oz.

To find the cost per ounce for the 15 oz jar, divide the price by the number of ounces: $2.10/15 oz = $0.14 per oz.

Therefore, the 40 oz jar is the better deal because it has a lower cost per ounce.

Can you show more of the problem so we can see more of what the question is giving?

Answer:

40 books

Step-by-step explanation:

Divide 20 kg by 500 g, or, alternatively, divide 20 kg by 0.5 kg.

Either way, the result is 20/0.5, or 40.

40 books of the same mass would have the same mass as the bookcase.

Hope this helps :)

Answer:

40

Step-by-step explanation:

.5kg*40=20kg

40 books

The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

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Based on the given options, the statement that best describes the regression cannot be determined without additional information.

The options do not provide any details about the regression coefficients, R-squared value, or p-values, which are necessary to make a meaningful statement about the regression. It is not possible to determine the quality of the predictions or the significance of the regression based solely on the dependent variable and sample size.
Your answer: B) Statistically significant and quite small MPG prediction errors

This option best describes a regression with a strong relationship between the independent variable (e.g., car characteristics) and the dependent variable (highway miles per gallon). The statement suggests that the model is statistically significant, meaning it can reliably predict MPG, and the prediction errors are small, indicating good accuracy in the predictions.

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Answer:

220

Step-by-step explanation:

The new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

The circumference of a circular lawn is 110 feet.

2πr = 110

r = 55/π

Double the radius:

R = 2r= 110/π

New circumference = 2πR = 2π(110/π) = 220 feet

Thus, the new circumference of the circle will be 220 feet if the circumference of a circular lawn is 110 feet.

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Answer: x = 15 or x = -7

Step-by-step explanation:

Step 1: Divide both sides by 3.

Step 2: Solve Absolute Value.

|x−4|=11 We know either x − 4 = 11 or x − 4 = −11

x−4=11(Possibility 1)

x−4+4=11+4(Add 4 to both sides)

x=15

x−4=−11(Possibility 2)

x−4+4=−11+4(Add 4 to both sides)

x=−7

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

1 3/8

Step-by-step explanation:

2 1/2= 2 4/8

2 4/8+1 3/8=  7/8

5 1/4= 5 2/8

5 2/8-3 7/8= 1 3/8

The correct answer is d. $17,179.23. The amount of money that would have accumulated in interest by the time the mortgage is paid off is approximately $17,179.23 (the total savings minus the initial investment).

To calculate the accumulated interest, we need to find the difference in payments between the two interest rates and then calculate the interest earned on those savings.

First, let's calculate the monthly payment for the mortgage loan at the higher interest rate of 13%:

Loan amount: $130,000

Interest rate: 13% per year, compounded monthly

Loan term: 25 years (300 months)

Using the formula for calculating the monthly payment on a mortgage, we can find the monthly payment (P):

P = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-n))

Where Monthly interest rate = Annual interest rate / 12 = 13% / 12 = 0.01083, and n is the total number of months (300).

Calculating P, we find:

P = ($130,000 * 0.01083) / (1 - (1 + 0.01083)^(-300))

P ≈ $1,456.62 (rounded to the nearest cent)

Now, let's find the monthly payment at the lower interest rate, which we assume the person could have received:

Interest rate at lower rate = 13% - 6% = 7%

Using the same formula as above, but with the lower interest rate, we find:

P_lower = ($130,000 * 0.007) / (1 - (1 + 0.007)^(-300))

P_lower ≈ $1,163.95 (rounded to the nearest cent)

Now, let's calculate the difference in monthly payments between the two rates:

Monthly savings = P - P_lower

Monthly savings ≈ $292.67 (rounded to the nearest cent)

Since we are interested in the savings for the first five years (60 months) of the loan, we can calculate the total savings over that period:

Total savings = Monthly savings * Number of months (60)

Total savings ≈ $17,560.20 (rounded to the nearest cent)

If this total amount is then invested in an account paying simple interest at a rate of 2%, the interest earned can be calculated as:

Interest earned = Total savings * Annual interest rate

Interest earned ≈ $17,560.20 * 0.02

Interest earned ≈ $351.20 (rounded to the nearest cent)

Therefore, the amount of money that would have accumulated in interest by the time the mortgage is paid off is approximately $17,179.23 (the total savings minus the initial investment).

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Answer:

-35

Step-by-step explanation:

X's cancel out each other

-10+-25

a.

= (5x)² - 3 = 25x² - 3

- 5f(x) = 5(x² - 3) = 5x² - 15

b.

- f(x - 2) = (x - 2)² - 3 = x² - 4x + 1

- f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

a. To calculate f(5x), we substitute 5x into the function f(x) and simplify the expression.

  f(5x) = (5x)² - 3 = 25x² - 3

  To calculate 5f(x), we multiply the function f(x) by 5.

  5f(x) = 5(x² - 3) = 5x² - 15

b. To calculate f(x - 2), we substitute (x - 2) into the function f(x) and simplify the expression.

  f(x - 2) = (x - 2)² - 3 = x² - 4x + 4 - 3 = x² - 4x + 1

  To calculate f(x) - f(2), we evaluate f(x) and f(2) separately and then find their difference.

  f(x) = x² - 3

  f(2) = 2² - 3 = 4 - 3 = 1

  f(x) - f(2) = (x² - 3) - (2² - 3) = x² - 3 - 1 = x² - 4

For the difference quotient of f(x) = -7x² - 5x + 9, we can calculate it as follows:

Difference quotient = [f(x + h) - f(x)] / h

Expanding the function and substituting into the difference quotient formula, we have:

[f(x + h) - f(x)] / h = [-7(x + h)² - 5(x + h) + 9 - (-7x² - 5x + 9)] / h

Simplifying and expanding further:

= [-7(x² + 2hx + h²) - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-7x² - 14hx - 7h² - 5x - 5h + 9 + 7x² + 5x - 9] / h

= [-14hx - 7h² - 5h] / h

= -14x - 7h - 5

The difference quotient of f(x) = -7x² - 5x + 9 is -14x - 7h - 5.

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-25 + 15 = -10

1 - 13 = -12

-1 divided by 5 = -1/5

-5 multiplied by -1/5 = 1

The bold ones are the answers

Answer:

Step-by-step explanation:

1) n+15=10

     solution;

n+15= -10

so, n= -10 -15

      n= -25

2) n-13= -12

        solution;

remember the rule i told you in number 1 that's the same rule we will use here

n= -12+ 13

n=1

you see so easy... lets continue

3) n\5= -1\5

now in this one there is a new rule which is; when you see two fractions and there is an equal two in between them you cross multiply... okay lets solve

n\5= -1\5

-1*5=n*5

the reason why i exchanged was because the unknown should always be at the left hand side....okay

n*5=-1*5

5n/5= -5/5

5 will divide 5 which is remaining n

5 divide 5 which is -1

so n = -1

4) -5n =1

 this is not a fraction so we just take the -5 to 1 and no cross multiplication (they are whole numbers so they meet each other)okay...

so, n=1/-5

Answer:

1

EXPLAINATION:

y = mx +b

b = y intercept

Answer:

3.5f − 19

Explanation:

2.7f + 0.8f − 14 − 5

= 2.7f + 0.8f + −14 + −5

[ Combine Like Terms ]

= 2.7f + 0.8f + −14 + −5

= (2.7f + 0.8f) + (−14 + −5)

= 3.5f + −19

-PNW

2 cans of paint is needed to cover the toy chest of 1866 in²

Area is the amount of space occupied by a two dimensional object or figure. Area (A) of rectangle is:

A = length * breadth.

Area of A = 13 * 16 = 208 in²

Area of B = 13 * 25 = 325 in²

Area of C = 25 * 16 = 400 in²

Area of D = 13 * 25 = 325 in²

Area of E = 13 * 16 = 208 in²

Area of F = 25 * 16 = 400 in²

1) Combined Area = 208 + 208 = 416 in²

2) Combined Area = 325 + 325 = 650 in²

3) Combined Area = 400 + 400 = 800 in²

4) Combined Area = 416 + 650 + 800 = 1866 in²

5) Amount of paint = 1866 in² / 933 in² = 2

2 cans of paint is needed to cover the toy chest of 1866 in²

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The area and perimeter of the figure be 562.08 m² and 123.68 m.

The figure referred to is made out of a parallelogram and a crescent. The area of the parallelogram can be determined by utilizing the equation base x level, bringing about an area of 336 m².

The area of the crescent is determined utilizing the formula (π x r²)/2, calculating an area of 226.08 m². Thus, the complete area of the figure is 562.08 m².

The perimeter of the parallelogram is 86 m, while the border of the half circle is 37.68 m, giving an all-out perimeter of 123.68 m.

The area of the figure is 562.08 m², while the perimeter is 123.68 m.

This can be additionally separated into the area and perimeter of the parallelogram and half circle, which are 336 m² and 226.08 m² for the area, and 86 m and 37.68 m for the border, individually.

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Answer:

All of them are rational except for 0.0100100010001, root50, and pi

rational = no forever decimal these are the ones that arent rational

Hope this helps plz hit the crown :D

Answer:

I think it is 55 mph but I'm not 100% sure.

Step-by-step explanation:

Answer: 24+3r≥100

Step-by-step explanation:

If swimming 1/4 of a mile uses about the same number of calories as running 1 mile.

a.  The distance her sister have to swim to use the same number of calories Gilda used during the marathon is 6 1/2 mile.

b. The number of miles that he would have to run to use the same number of calories used during his swim is 20 miles.

a. Number of miles:

1/4 swim / 1 run = x swim / 26 run

Cross multiply

= 6 1/2 mile

b.  Number of miles:

1/4 swim / 1 run = 5 swim/x

Cross multiply

x = 20 miles

Therefore the number of mile is 6 1/2 miles and 20 miles.

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The complete question is:

Swimming 1/4 of a mile uses about the same number of calories as running 1 mile.

a. Gilda ran a 26 mile marathon. About how far would her sister have to swim

to use the same number of calories Gilda used during the marathon?

b. Juan swims 5 miles a day. About how many miles would he have to run to

use the same number of calories used during his swim?

Answer:

The Volume is equal to 2x^3-3x^2+2x-3

Step-by-step explanation:

Formula for the volume of a rectangular prism is V=WHL

We know that:

W=x-1

L=x+1

H=2x-3

So, V= (x-1)(x-1)(2x-3)

Simplify

(x^2+1)(2x-3)

2x^3-3x^2+2x-3

Answer:

Answer given in the photo