Isaac is on the 4th floor of a building. If he rides an elevator up 7 floors, what floor will he be on?

What integer represents the floor Isaac is starting on?
What integer represents how many floors the elevator will rise?
What floor will the elevator stop at?

Third graphrepresents the function [tex]f\left( x \right) = \left\lfloor x \right\rfloor-2[/tex] over the interval [tex]\left[ { - 3,3} \right].[/tex]

Further explanation:

Given:

The function is [tex]f\left( x \right) = \left\lfloor x \right\rfloor- 2.[/tex]

The function is defined in the interval [tex]\left[ {-3,3}\right].[/tex]

Explanation:

The greatest integer function is represented [tex]y = \left\lfloor x \right\rfloor.[/tex]

The greatest integer can also be known as floor function. The function is integral part of real numbers.

The values of greatest function [tex]f\left( x \right)= \left\lfloorx \right\rfloor- 2[/tex] in interval [tex]\left[{ - 3,3}\right][/tex] can be obtained as follows,

Substitute [tex]-3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)= \left\lfloor x \right\rfloor- 2.[/tex]

[tex]\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}[/tex]

Substitute [tex]3[/tex] for [tex]x[/tex] in the function [tex]f\left( x \right)=\left\lfloor x \right\rfloor- 2.[/tex]

[tex]\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}[/tex]

The minimum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.[/tex]

The maximum value of the function in [tex]\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.[/tex]

Third graphrepresents the function [tex]f\left( x \right)=\left\lfloor x\right\rfloor- 2[/tex] over the interval [tex]\left[{ - 3,3}\right].[/tex]

Kindly refer to the image attached.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

A square is cut from a circle with a 14-foot diameter. Remaining circle area ≈ 53.86 sq ft here nearest round off option is c. 50 square feet.

To find the area of the remaining portion of the circle after a square with a side of 10 feet is cut out,

Find the area of the square:

Area of square

= side × side

= 10 feet × 10 feet

= 100 square feet

Find the radius of the circle:

The diameter is approximately 14 feet, so the radius is half of that:

Radius = 14 feet / 2 = 7 feet

Find the area of the entire circle:

Area of circle = π × radius²

Area of circle

= π × (7 feet)²

≈ 153.86 square feet (using π ≈ 3.14)

Subtract the area of the square from the area of the circle to find the remaining portion:

Remaining area = Area of circle - Area of square

Remaining area

≈ 153.86 square feet - 100 square feet

≈ 53.86 square feet

Therefore, the approximate area of the remaining portion of the circle is approximately 53.86 square feet nearest option is c. 50 square feet.

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The above question is incomplete , the complete question is:

A square is cut out of a circle whose diameter is approximately 14 feet. What is the approximate area of the remaining portion of the circle in square feet?

Attached figure

Answer:

the answer is A on edge :)

Step-by-step explanation:

The graph that is a perfect fit for the given data in a quadratic regression problem is when r is; A: 1

Quadratic regression is defined as a statistical technique that is used to find the equation of the parabola that best fits a set of data.

Now, this type of regression is an extension of simple linear regression that is used to find the equation of the straight line that best fits a set of data.

Thus, in this type of regression, we say a graph is a perfect fit when r = 1.

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Final answer:

The current in a circuit with a supplied voltage of 1.5 volts and a resistance of 3 ohms is calculated using Ohm's Law (I = V/R), resulting in a current of 0.5 amperes.

Explanation:

Using Ohm's Law to Calculate Current

To determine the current in a circuit with a supplied voltage of 1.5 volts and a resistor value of 3 ohms, we can use Ohm's Law, which is stated as I = V/R, where I is the current, V is the voltage, and R is the resistance. Plugging in the values, we have I = 1.5 volts / 3 ohms. Therefore, I = 0.5 amperes or 500 milliamperes. This is the current flowing through the circuit.

Ohm's Law is a fundamental principle in physics used for analyzing simple circuits where the relationship between voltage, current, and resistance is linear. Remember that this law holds true for ohmic materials where the resistance remains constant over a range of voltages and temperatures.

Mary has 3 marbles.

To find out how many marbles Mary has, we can use the information that Joan has 45 marbles and Joan has 15 times as many marbles as Mary. So, we can set up an equation:

45 = 15m

To solve for m, we divide both sides of the equation by 15:

m = 45/15

Simplifying the expression, we get:

m = 3

Therefore, Mary has 3 marbles.

your Answer issss:

√3/2

Answer: The correct option is third, i.e., [tex]y\geq \frac{3}{2} x+\frac{1}{5}[/tex].

Explanation:

From the figure it is noticed that the line passing through the points (0,0.2) and (3,2.2).

The equation of line passing through two points is,

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

[tex]y-0.2=\frac{2.2-0.2}{3-0}(x-0)[/tex]

[tex]y-\frac{1}{5} =\frac{2}{3} x[/tex]

[tex]y =\frac{2}{3} x+\frac{1}{5}[/tex]

The equation of the line is [tex]y =\frac{2}{3} x+\frac{1}{5}[/tex].

From the figure it is noticed that as the value of x increases the value of y is less.

he point (1,0) lies on the shaded reason it means this point must satisfy the equation.

[tex](0)=\frac{2}{3} (1)+\frac{1}{5}[/tex]

[tex](0)=\frac{2}{3} +\frac{1}{5}[/tex]

[tex](0)=\frac{10+3}{15}[/tex]

[tex](0)=\frac{13}{15}[/tex]

It is true of the sign is less than or equal to instead of equal.

[tex]y \leq \frac{2}{3} x+\frac{1}{5}[/tex]

Therefore, option third is correct.

The remainder obtained when we carry out the operation (-6x³ + 3x² - 4) ÷ (2x - 3) is -17.5 (2nd option)

The following data were obtained from the question:

Using the remainder theorem, we can obtain the remainder as illustrated below:

Let

f(x) = -6x³ + 3x² - 4

2x - 3 = 0

From 2x - 3 = 0, make x the subject as shown below:

2x - 3 = 0

x = 3/2

Substitute the value of x into f(x). We have:

f(x) = -6x³ + 3x² - 4

f(3/2) = -6(3/2)³ + 3(3/2)² - 4

= -6(27/8) + 3(9/4) - 4

= -20.25 + 6.75 - 4

= -17.5

Thus, we can conclude that the remainder obtained when (-6x³ + 3x² - 4) is divided by (2x - 3) is -17.5 (2nd option)

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Answer: The answer is 5, 10, 20, 40 and 80.

Step-by-step explanation:  We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be  5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]

Therefore, we have

[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]

Therefore, the recursive formula is

[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]

And explicit formula is

[tex]a_n=a_1r^{n-1}.[/tex]

Answer:

Let the first five terms of a sequence be, 4,8,12,20,24

Ok, let me explain the meaning of term explicit and Recursive formula.

Explicit formula ,is the general formula to find any  term of the sequence.

And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.

So,the explicit formula for the sequence is,

y = 4 n, where , n is any natural number.

And the recursive formula is .

y = 4 (n-1), with the help of (n-1)th term we can find nth term.

First term =4=4 × 1

Second term =8 =4 × 2

Third term =12=4×3

Fourth term =16 =4 × 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.

As, you said you don't want simpler sequence

Consider the first five terms of the sequence, 0, 3,8,15, 24.

Explicit formula =n² + 2 n

Recursive formula=(n-1)²+2(n-1)

If,you will look at the sequence, it is neither Arithmetic nor geometric .

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

So, Explicit formula= n²+ 2 n, where n is a whole number.

The difference in payments from year 5 to year 6 is approximately $369.32 for the 5/1 ARM mortgage.

To calculate the payment difference from year 5 to year 6 for a 5/1 ARM (Adjustable Rate Mortgage) with a 3/12 cap structure, we need to understand how the ARM works and how the caps affect the adjustment.

1. Initial Mortgage Parameters :

  - Loan Amount: $265,000

  - Interest Rate: 5.25%

  - Term: 20 years

2. Adjustment Frequency : The 5/1 ARM adjusts after the initial 5-year fixed period, then annually.

3. Cap Structure :

  - Initial Adjustment Cap: 3%

  - Subsequent Adjustment Cap: Each year after the initial adjustment, the rate can adjust up to 3% from the previous rate.

4. Calculation Steps :

  a. Calculate the initial monthly payment using the loan amount, interest rate, and term.

  b. Determine the new interest rate for year 6 based on the cap structure.

  c. Calculate the monthly payment for year 6 with the new interest rate.

  d. Find the difference between the payments from year 5 to year 6.

Let's start the calculations:

a. Calculate the initial monthly payment  using the loan amount, interest rate, and term. We'll use the formula for a fixed-rate mortgage:

[tex]\[ P = \frac{P_r \cdot A}{1 - (1 + r)^{-n}} \][/tex]

Where:

- [tex]\( P \)[/tex] = Monthly Payment

- [tex]\( P_r \)[/tex] = Periodic Interest Rate (annual rate divided by 12)

- [tex]\( A \)[/tex] = Loan Amount

- [tex]\( r \)[/tex] = Periodic Interest Rate

- [tex]\( n \)[/tex] = Total number of payments (loan term in years multiplied by 12)

For the initial fixed period of 5 years:

[tex]\[ P_r = \frac{5.25\%}{12} = 0.004375 \][/tex]

[tex]\[ n = 20 \times 12 = 240 \][/tex]

Plugging these values into the formula:

[tex]\[ P = \frac{0.004375 \cdot 265000}{1 - (1 + 0.004375)^{-240}} \][/tex]

[tex]\[ P \approx 1645.80 \][/tex]

So, the initial monthly payment is approximately $1,645.80.

b. Determine the new interest rate for year 6 :

  - The initial rate can adjust up to 3% in year 6.

  - So, the new interest rate could be up to \( 5.25\% + 3\% = 8.25\% \).

c. Calculate the monthly payment for year 6 :

  - Use the formula for the monthly payment again with the new interest rate:

[tex]\[ P_r = \frac{8.25\%}{12} = 0.006875 \][/tex]

Plugging into the formula:

[tex]\[ P = \frac{0.006875 \cdot 265000}{1 - (1 + 0.006875)^{-240}} \][/tex]

[tex]\[ P \approx 1985.09 \][/tex]

So, the monthly payment for year 6 is approximately $1,985.09.

d. Find the difference in payments from year 5 to year 6:

[tex]\[ Difference = Payment_{Year6} - Payment_{Year5} \][/tex]

[tex]\[ Difference = 1985.09 - 1645.80 \][/tex]

[tex]\[ Difference \approx 339.29 \][/tex]

So, the difference in payments from year 5 to year 6 is approximately $339.29.

Therefore, the closest answer is C. $369.32 .

The equation of the ellipse is required.

The required equation is [tex]\dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]

It can be see that the major axis is parallel to the y axis.

The major axis points are

[tex](h,k+a)=(0,1)[/tex]

[tex](h,k-a)=(0,-9)[/tex]

[tex]k+a=1[/tex]

[tex]k-a=-9[/tex]

Subtracting the equations

[tex]2a=10\\\Rightarrow a=5[/tex]

The foci are

[tex](h,k+c)=(0,-1)[/tex]

[tex](h,k-c)=(0,-7)[/tex]

[tex]k+c=-1[/tex]

[tex]k-c=-7[/tex]

Subtracting the equations

[tex]2c=6\\\Rightarrow c=3[/tex]

[tex]k+c=-1\\\Rightarrow k=-1-c\\\Rightarrow k=-1-3\\\Rightarrow k=-4[/tex]

Foci is given by

[tex]c^2=a^2-b^2\\\Rightarrow b=\sqrt{a^2-c^2}\\\Rightarrow b=\sqrt{5^2-3^2}=4[/tex]

The equation is

[tex]\dfrac{(x-h)^2}{b^2}+\dfrac{(x-k)^2}{a^2}=1\\\Rightarrow \dfrac{(x-0)^2}{4^2}+\dfrac{(y+4)^2}{5^2}=1\\\Rightarrow \dfrac{x^2}{16}+\dfrac{(y+4)^2}{25}=1[/tex]

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if youre doing the vocab thing -- Distance

Answer:

[tex]10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]

Step-by-step explanation:

Exponentiation is the operation used to write the product of two or more equal factors. This expression can written as follows:

[tex]a^n\\\\Where:\\\\a=Base\\n=Exponent[/tex]

That is, [tex]a^n[/tex] is the product of multiplying n bases:

[tex]a^n=a\times...\times...\times a[/tex]

In this sense:

[tex]10^7=10\times 10\times 10\times 10\times 10\times 10 \times 10[/tex]

No, thanks to you, I got the question wrong it was hours.

Answer:

28

Step-by-step explanation:

Square: 4 * 4 = 16

Small Triangle: 1 * 4 = 4  / 2 = 2

Large Triangle: 5 * 4 = 20  / 2 = 10

16 + 2 + 10 = 28

Answer:

The ratio of the lengths of PR and QS is 1 : 1

Step-by-step explanation:

If your question is based on this exercise:

PQ Is parallel to RS.  PR and QS are perpendicular to PQ  and RS

Here is why

Answer:

The actual answer is D

The point (a, b) lies in the second quadrant. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

If a < 0 and b > 0.

Then the point (a, b) is in Quadrant will be given as,

Thus, the point (a, b) lies in the second quadrant.

Then the correct option is B.

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