The numbers 1, 2, 3, 4,5, 6, 7, 8, 9 are arranged in a list so that each number is either greater than all the numbers that come before it or is less than all the numbers that come before it. For example, 4, 5, 6, 3, 2, 7, 1, 8, 9 is one such list: Notice that (for instance) the 6 is greater than all the numbers that come before it, and the 2 is less than all the numbers that come before it. How many such lists of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are possible?

Answer:

an angle bisector

Step-by-step explanation:

This is showing the construction of the bisector of ∠LNM

The value of the rate of change of the function is 14a + 7h

The rate of change of function is also known as the slope expressed according to the equation shown below;

f'(x) = f(a+h)-f(a)/h

Given the function below expressed as:

f(x) =1 + 7x^2

Determine the function f(a)

To determine the function, simply replace x with 'a" to have:

f(a) =1 + 7a^2

Determine the function f(a+h)

f(a+h) = 1 + 7(a+h)^2

f(a + h) = 1 + 7(a^2+2ah+h^2)

f(a + h) = 1 + 7a^2 + 14ah + 7h^2

To determine the rate of change

f'(x) = f(a+h)-f(a)/h

f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) =  + 14ah + 7h^2/h

f'(x) = 14a + 7h

Hence the value of the rate of change of the function is 14a + 7h

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The correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

Given a function f(x)=[tex]a^{x+g} +k[/tex].

We are told to find the domain and range of the function.

The domain is basically the values which we enters in a function.

The range is basically the values which we are getting by entering some values in the function.

An exponential function is given in the function which has no restrictions hence the domain is  (-∞,∞).The range depends on the vertical shift given by k. Hence the range of function is (k,∞).

Hence the correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

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Considering the given linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

His payment for x copies bought is:

y = 120x + 2400.

Hence:

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Answer:

B

Step-by-step explanation:

The area of the triangle is half the base time the height.  The height is y sub 1.  The length is the distance between the x values.

To find the missing numbers in the sequence, we must identify the rule by which they change.

The sequence starts at 8 and then decreases by 1, therefore, the second term is 7. The third term increases by 4 units with respect to the second, going from 7 to 11, and the fourth decreases again by 1, now remaining at 10.

The fifth term increases again by 4 units, from 10 to 14. This already gives us a clear idea of the rule that the sequence follows.

                                                  ₊₄              ₊₄

                                            ⁻¹             ⁻¹               ⁻¹  

In this way, the sixth element must decrease by 1, that is 13 and the seventh must increase by 4, that is 17.

8, 7, 11, 10, 14, 13, 17,…

The next numbers that the numerical sequence are 13 and 17, to complete. ✅

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

From the question, we are to write a polynomial that has a GCF of 7m

That is,

We are to write a polynomial that has a greatest common factor of 7m

Writing the polynomial

14mn - 21m + 49m²n + 7mn²

The  polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms

We are to write a polynomial with a GCF of 2ab²

Writing the polynomial

6a²b² - 8ab³ + 4a³b² + 2a³b³

The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms

Hence,

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

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well, we know that 25 pecks is 1/4% or namely 0.25%, less than 1%, and let's say the amount of pecks per day will be "x", which is 100% of that.

[tex]\begin{array}{ccll} pecks&\%\\ \cline{1-2} 25 & \frac{1}{4}\\[1em] x& 100 \end{array} \implies \cfrac{25}{x}~~=~~\cfrac{ ~~ \frac{1}{4} ~~ }{100}\implies 2500=x\cfrac{1}{4} \\\\\\ 2500=\cfrac{x}{4}\implies 10000=x[/tex]

Pila can peck a tree approximately 10,000 times per day.

Given that Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4 % the average number of pecks that she can make each day.

We need to determine how many times per day can pila peck a tree.

Let's denote the average number of pecks Pila can make in a day as "x."

According to the information given, Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4% (0.25%) of the average number of pecks she can make each day.

We can set up the following equation to represent the relationship:

0.25% of x = 25

To solve for x, we first convert 0.25% to decimal form by dividing by 100:

0.25% = 0.25/100 = 0.0025

Now, we can rewrite the equation:

0.0025x = 25

To isolate x, we divide both sides of the equation by 0.0025:

x = 25 / 0.0025

Simplifying the right side gives us:

x = 10,000

Therefore, Pila can peck a tree approximately 10,000 times per day.

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Answer:

option B is the answer of given question

Answer:

D. 93.5

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

The lower arc is twice 52

c = 1/2( 104  +83)

c = 1/2 ( 187)

c =93.5

Answer: [tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Step-by-step explanation:

Given the requirement of function form

Point-slope form: y - y₁ = m (x - x₁)

Given information

Slope (m) = -6/5

Y-intercept (x₁, y₁) = 2 = (0, 2)

Substitute values into the required form

y - y₁ = m (x - x₁)

y - (2) = (-6/5) (x - 0)

[tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

From the given inverse function, we have

[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]

By definition of inverse function,

[tex]f\left(f^{-1}(x)\right) = x[/tex]

so that

[tex]f\left(2x-\dfrac12\right) = x[/tex]

[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]

[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]

[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]

[tex]\implies \boxed{a=\dfrac12}[/tex]

[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]

The behavior of the graph of I and what it means in context can be explained below:

Sound intensity, serves as the  power that is been carried by sound waves per unit area and this is usually in the direction perpendicular to that area.

we were given the  function [tex]I = \frac{P}{4pir^2}[/tex]

r  represent the Distance from the source of sound

P represent the Power of the sound

when there is increase in the  distance from the source the intensity moves to zero.

we can see that there is is an inverse proportion between the Intensity and the distance r  which implies that The intensity decreases  when the distance increases.

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At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].

So the population after [tex]t=4[/tex] years will be:

[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]

Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

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Answer:

[tex]h = \bf 28.3 \space\ m[/tex]

Step-by-step explanation:

• We are given:

○ Volume = 36 m³,

○ Circumference = 4 m

• Let's find the radius of the cylinder first:

[tex]\mathrm{Circumference} = 2 \pi r[/tex]

Solving for [tex]r[/tex] :

⇒ [tex]4 = 2 \pi r[/tex]

⇒ [tex]r = \frac{4}{2\pi}[/tex]

⇒ [tex]r = \bf \frac{2}{\pi}[/tex]

• Now we can calculate the height using the formula for volume of a cylinder:

[tex]\mathrm{Volume} = \boxed{\pi r^2 h}[/tex]

Solving for [tex]h[/tex] :

⇒ [tex]36 = \pi \cdot (\frac{2}{\pi}) ^2 \cdot h[/tex]

⇒ [tex]h = \frac{36 \pi^2}{4 \pi}[/tex]

⇒ [tex]h = 9 \pi[/tex]

⇒ [tex]h = \bf 28.3 \space\ m[/tex]

Answer:

9π m ≈ 28.27m

Step-by-step explanation:

The volume of a right cylinder is given by the formula

πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder

Circumference of base of cylinder is given by the formula 2πr

Given,

2πr = 4m

r = 2/π m

Volume given as 36 m³

So πr²h = 36
π (2/π)² h = 36

π x 4/π² h = 36

(4/π) h = 36

h = 36π/4 = 9π ≈ 28.27m

Katrina would pay less amount of interest on the nonsubsidized student loan

The total interest paid on the nonsubsidized loan is $3,860.80

What is monthly compounding?

Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.

In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.

In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:

FV=PV*(1+r/n)^(n*t)

FV=balance after 2 years=unknown

PV=loan amount

r=annual interest rate

n=number of times interest is compounded annually=12

t=number of years before repayments commence=2

Non-subsidized loan:

FV=$29,000*(1+2.5%/12)^(12*2)

FV=$30,485.28

Subsidized loan:

FV=$29,000*(1+4.5%/12)^(12*2)

FV=$31,725.71

Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly  payments would occur at the end of each month:

PV=PMT*(1-(1+r)^-N/r

PV=balance of loan after 2 years

PMT=monthly payment=unknown

r=monthly interest rate=annual interest rate/12

N=number of monthly payments in 6 years=12*6=72

Non-subsidized loan:

$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)

PMT=$456.40

total monthly payments=$456.40*72

total monthly payments=$32,860.80

Interest= total monthly payments-loan

interest=$32,860.80-$29,000

interest=$3,860.80

Subsidized loan:

$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)

PMT=$503.61

total monthly payments=$503.61 *72

total monthly payments=$36,259.92

Interest= total monthly payments-loan

interest=$36,259.92 -$29,000

interest=$7,259.92

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Answer:

3550

Step-by-step explanation:

C.P=Rs 1250

S.P=8(12)(50)

Rs4800

P=S.P-C. P

=Rs4800-Rs1250

= Rs3550

Answer:

vertex : (-5/2, -53/4)

solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)

Step-by-step explanation:

1.The vertex of the function is (-5/2, -53/4).

2.We have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.

1. Vertex:

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

x = -b / (2a)

y = f(x) = ax^2 + bx + c

Given: a = 1, b = 5, c = -7

x = -5 / (2 * 1) = -5 / 2

Now, substitute the value of x into the equation to find y:

y = (-5/2)^2 + 5 * (-5/2) - 7

y = 25/4 - 25/2 - 7

y = 25/4 - 50/4 - 7

y = (25 - 50 - 28) / 4

y = -53 / 4

So, the vertex of the function is (-5/2, -53/4).

2. Solutions (or roots or x-intercepts):

To find the solutions (x-intercepts) of the function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Given: a = 1, b = 5, c = -7

x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1

x = (-5 ± √(25 + 28)) / 2

x = (-5 ± √53) / 2

Now, we have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.

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Using the combination formula, it is found that 436,270,780 different selections are possible.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 7 numbers are taken from a set of 61, hence the number of different selections is given by:

C(61,7) = 61!/(7! x 54!) = 436,270,780

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By critically observing the number lines, the intersection of both (-∞, 6) and (-∞, 9) is (6, 9) because this is the point where they overlap. Also, the union of both (-∞, 6) and (-∞, 9) on a number line is (-∞, 9).

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Given the following intervals:

On a number line, the first interval would comprise the following numerical values -∞,..........-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.

On a number line, the second interval would comprise the following numerical values -∞,..........-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

By critically observing the number lines, we can logically deduce that intersection of both (-∞, 6) and (-∞, 9) is (6, 9) because this is the point where they overlap.

Also, the union of both (-∞, 6) and (-∞, 9) on a number line is (-∞, 9).

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Answer:

40 liters of 30% solution.

20 liters of 60% solution.

Step-by-step explanation:

Let x = amount of 30% solution.

Let y = amount of 60% solution.

Equation of amounts of solutions.

x + y = 60

Equation of amounts of alcohol in the solutions.

0.3x + 0.6y = 0.4 × 60

x = 60 - y

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

x + y = 60

x + 20 = 60

x = 40

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Let 30% solution = m

Let 60% solution = n

Now,

A scientist needs 60 liters of a 40% solution of alcohol.

He has a 30% solution and a 60% solution available.

This means,

m + n = 60 _____(1)

30% of m + 60% of n = 40% of 60

0.30m + 0.60n = 0.40 x 60

0.30m + 0.60n = 24 ____(2)

From (1) and (2) we get,

m + n = 60

m = 60 - n _____(3)

Putting (3) in (2) we get,

0.30m + 0.60n = 24

0.30(60 - n) + 0.60n = 24

18 - 0.30n + 0.60n = 24

18 + 0.30n = 24

0.30n = 24 - 18

0.30n = 6

n = 6/0.30

n = 20

Putting n = 20 in (3) we get,

m = 60 - 20

m = 40

Now,

The number of liters of the 30% solution is 40.

The number of liters of the 60% solution is 20.

Thus,

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

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Answer:

$20

Step-by-step explanation:

$5.00 = 10miles

$0.25(40) = 40 miles

Remaining miles: 100 - (10 + 40) = 50

0.10(50) = 50 miles

5.00 + 0.25(40) + 0.10(50)

5.00 + 10.00 + 5.00

$20.00 for 100 miles

Answer:

Step-by-step explanation:

85!/82! = 85*84*83 = 592620

n choose 0 is always equals 1

n P n also always equals 1

The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Answer:

The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.

'25' above sigma is the upper bound.

In general it means adding 42 from 1 to 25 times.

so 42(25).

Answer:

C. 42(25)

Step-by-step explanation:

Took the unit test review and this was the correct option choice.

Goodluck on your unit test, I am sure that you will do good :)

Answer:

60.

100 (total) - 40 (amount in the library Saturday morning) = 60.

Type: Percentages / Fractions

The total interest cost to Bette is  $145.89

What is exact interest basis?

Exact interest means that the interest is computed on 365-day per year basis rather than a 360-day per year basis, which is the case with financial institutions.

The first task in this case is to determine the number of days from May 19, when the amount was borrowed till October 8, when loan repayment was effected.

There are 142 days between the two dates, hence, we can compute exact interest on the loan as shown by the below formula:

exact interest=loan principal*number of days the borrowing last/365days *interest rate

loan principal=$3000

number of days the borrowing last=142

interest rate=12.5%(1/2%=0.5%)

Exact interest=$3000*142/365*12.5%

Exact interest=$145.89

The amount would have been different if ordinary interest where the number of days in a year is deemed to be 360, was used instead

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Answer:

a) A = 3, B = 8.

b) C = 2, D = 25

Step-by-step explanation:

See the image below.

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of [tex]a^{2}[/tex] + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

[tex]3x^{2}[/tex] - 2 = -5x
[tex]3x^{2}[/tex] + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.