Consider the function f(x)=x3+3x2â51x+91. What is the remainder if f(x) is divided by (x+9)? Do not include (x+9) in your answer.

Answer:

The number of  people that received copies of the letter at the twentieth stage is 9.537 × 10¹³ .

Step-by-step explanation:

Using the discrete model,

a_k = r a_(k-1) for all integers k ≥ 1 and a₀ = a

then,

aₙ = a rⁿ for all integers n ≥ 0

Let a_k be equal to the number of people who receive a copy of the chain letter at a stage k.

Initially, one person has the chain letter (which the person will send to five other people at stage 1). Thus,

a = a₀ = 1

The people who received he chain letter at stage (k - 1),  will send a letter to five people at stage k and thus per person at stage (k - 1), five people will receive the letter. Therefore,

a_k = 5 a_(k - 1)

Thus,

aₙ = a rⁿ = 1 · 5ⁿ = 5ⁿ

The number of  people that received copies of the letter at the twentieth stage is

a₂₀ = (5)²⁰ = 9.537 × 10¹³ copies

Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:

Interest = Principal (loan amount) x Rate x Time

Where:

Principal (loan amount) = $7,900

Rate = 4.29% (0.0429 as a decimal)

Time = 4.5 years

Now, plug these values into the formula:

Interest = $7,900 x 0.0429 x 4.5

Interest = $7,900 x 0.19205

Interest ≈ $1,518.45

So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

Learn more about simple interest click;

https://brainly.com/question/30964667

#SPJ12

Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.

Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.

To calculate the interest that will accrue during the 4.5 years, we can use the formula:

Interest Accrued = Principal x Interest Rate x Time

Substituting the values, we get:

Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75

Therefore, the interest that will accrue during the non-payment time is $1,146.75.

https://brainly.com/question/34076874

#SPJ3

The expression which  gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD.  option C is correct.

The area of rectangle is obtained by multiplying the length and width.

The length of the rectangle is C+D

The width of the rectangle is A+B.

Now the complete area of rectangle :

Area = (A+B)(C+D)

Now to find area of rectangle which is red we have to subtract the red rectangle which are in blue:

The area of left side rectangle which is blue:

Area =C(A+B)

The area of rectangle below red rectangle:

Area =BD

So the area of red rectangle : (A+B)(C+D)-C(A+B)-BD.

Hence, option C is correct, the expression which  gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD.

To learn more on Area click:

https://brainly.com/question/20693059

#SPJ3

Answer:

√1 1

√4 2

√9 3

√16 4

√25 5

√36 6

√49 7

√64 8

√81 9

√100 10

√121 11

√144 12

√169 13

Step-by-step explanation:

1. = 49

2. = 169

3. = 81

4. = 100

5. = 441

6. = 36

I just finished the assignment, trust me.

Sarah has received £ 294

Solution:

Given that £980 is divided between Caroline, Sarah & Gavyn

Let "c" be the amount received by caroline

Let "s" be the amount received by sarah

Let "g" be the amount received by gavyn

Caroline gets twice as much as Sarah

amount received by caroline = twice as much as Sarah

amount received by caroline = 2(amount received by sarah)

c = 2s ---- eqn 1

Sarah gets three times as much as Gavyn

amount received by sarah = three times as much as Gavyn

amount received by sarah = 3(amount received by gavyn)

s = 3g ------- eqn 2

Given that total amount is 980

c + s + g = 980 --- eqn 3

Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"

From eqn 2,

[tex]g = \frac{s}{3}[/tex]  --- eqn 4

Substitute eqn 1 and eqn 4 in eqn 3

[tex]2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294[/tex]

Thus sarah has received £ 294

Final answer:

To solve for the amount Sarah receives, set up ratios based on the information provided and solve the resulting equation. The total amount divided among them is £980, which when divided by the total parts (10) gives Gavyn's share as £98. Sarah's share is three times Gavyn's share, resulting in £294.

Explanation:

The problem described is a classic division in ratio mathematics question where £980 is being divided among Caroline, Sarah, and Gavyn following certain rules.

According to the problem, Caroline receives twice the amount that Sarah receives and Sarah receives triple the amount that Gavyn receives.

We can set up the following ratios: C = 2S and S = 3G, where C stands for Caroline's amount, S for Sarah's, and G for Gavyn's. If we denote Gavyn's amount as G, then Sarah's amount is 3G and Caroline's is 2 × 3G which is 6G.

To find the value of G, we can write the equation G + 3G + 6G = £980 or 10G = £980. Solving for G gives us G = £98.

Therefore, Sarah, receiving three times as much as Gavyn, gets 3 × £98 = £294.

Answer:

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

Step-by-step explanation:

Given that the diameter of a sphere is 14cm.

That is d=14

First find the radius of the sphere with diameter

[tex]r=\frac{d}{2}[/tex]

[tex]r=\frac{14}{2}[/tex]

Therefore r=7cm

Now to find the volume of the sphere:

[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]

[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex]  (here[tex]\pi=\frac{22}{7}[/tex] and r=7)

[tex]V=\frac{4}{3}(22)(7)^2[/tex]

[tex]V=\frac{4}{3}(22)(49)[/tex]

[tex]V=\frac{4}{3}(1078)[/tex]

[tex]V=\frac{4312}{3}[/tex]

[tex]V=1437.33cm^3[/tex]

Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

[tex]A_2[/tex] = 18°

[tex]A_3[/tex] = 4(18°) = 72°

Given:

Angles:

[tex]A_1[/tex] = 90°

[tex]A_2[/tex] = x

[tex]A_3[/tex] = 4x

Solution Pathway:

Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:

Now let's solve for x.

Now that we know x is 18°, lets plug this value into the two unknown acute angles.

Answer:

72 degrees and 18 degrees.

Step-by-step explanation:

If the 2 angles are x and y, we have the system:

x + y = 90           (as it is a right triangle)

x = 4y                  (given).

Substitute x =- 4y in the first equation:

4y + y = 90

5y = 90

y = 18.

So  x + 18 = 90

x = 90 - 18

x = 72.

Answer:

$307.60

Step-by-step explanation:

multiple $76.90 by the 4 nights he stayed. $76.90×4

Answer:

76.00

Step-by-step explanation:

Answer:

5.30 PM

Step-by-step explanation:

time taken=(1/2)×(1/35)×245=7/2 hrs=3hrs 30 min.

so time =2+3.30=5.30 PM

Answer: 5:30pm

Step-by-step explanation:

Distance of family destination from the starting point = 245miles

Average speed = 35miles/1/2hour

Therefore 245 miles = 245/35 x 30mins.

7 x 30 = 210minutes.

Converted to hour by dividing by 60

210/60 = 3hours 30minutes.

Current local time at the point of commencement

Therefore, the arrival time at their destination = 14hours + 3hours 30mins.

= 17hours 30minutes. Convert to local time

17hours 30minutes = 12hours

= 5:30 pm in the evening

They have succeeded in spending 3hours 30minutes on the road. The final answer = 5:30pm.

Answer: 68

Step-by-step explanation:

range=47 lowest score = 21 let highest score =x

Range=highest score - lowest score

47 = x - 21

x = 47 + 21

x = 68

Therefore the highest score is 68

The highest score is 68.

Range = Highest Score - Lowest Score

In this case,

the lowest score is 21 and

the range is 47.

So, we can rearrange the formula to solve for the highest score:

Highest Score = Range + Lowest Score

Substituting in the given values:

Highest Score = 47 + 21

Thus, the highest score will be 68.

Answer:

The Area of the actual garden is 294 square feet.

Step-by-step explanation:

The scale model of a rectangular garden is 1.5 ft by 4 ft.

Length of scale model=1.5 ft

Breath of scale model=4 ft

The scale model is enlarged by a scale factor of 7 to create the actual garden.

It means that the dimension of the garden are multiplied with the scale factor to find the actual dimension.

Hence,

Length of actual garden=[tex]1.5\times 7= 10.5\ ft[/tex]

Breath of actual garden=[tex]4\times 7 = 28\ ft[/tex]

Now Area of garden can be calculated by multiplying length and breadth.

Framing the equation we get;

Area of actual garden=[tex]10.5\ ft \times 28\ ft = 294\ ft^2[/tex]

Hence, area of the actual garden is 294 square feet.

Answer:294 took test

Answer:

Step-by-step explanation:

Looking at both triangles, angle P in triangle PQR = 38 degrees. Angle N in triangle LMN = 38 degrees. Both angles are equal.

Side PQ in triangle PQR = 16

Side MN in triangle LMN = 8

Therefore,

PQ/MN = 16/8 = 2

Side PR in triangle PQR = 14

Side LN in triangle LMN = 7

Therefore,

PR/LN = 14/7 = 2

Therefore, triangle PQR is similar to

triangle LMN because

1) the length of PQ is proportional to the length of MN.

2) the length of PR is proportional to the length of LN

3) angle P = angle N

4) Therefore, QR is also proportional to ML

Therefore,

PQ/MN = PR/LN = QR/ML = 2

Answer: Sequence B is more probable than A.

Step-by-step explanation:

This two sequences are not equally probable. Sequence B is more probable than A due to the equal chances of getting head (H) and a tail (T). The probability of getting a head is equal to the probability of getting a tail which is 4/8 i.e 0.5

The sequence A is less probable because the head(H) occur more than tail (T). The probability of head occurring is almost a sure event i.e 1 which is not feasible.

Answer:

8 years

Step-by-step explanation:

Compound interest formula

[tex]A(t)= A_0(1+\frac{r}{n})^{nt}[/tex]

A(t) is the final amount 55000

A_0= 40000, r= 4% = 0.04, for quarterly n=4

[tex]55000=40000(1+\frac{0.04}{4})^{4t}[/tex]

divide both sides by 40000

[tex]1375=(1+\frac{0.04}{4})^{4t}[/tex]

[tex]1375=(1.01)^{4t}[/tex]

Take ln on both sides

[tex]ln(1375)=4tln(1.01)[/tex]

divide both sides by ln(1.01)

[tex]\frac{ln 1375}{ln 1.01}=4t[/tex]

Divide both sides by 4

t=8.00108

So it takes 8 years

The couple will need to invest their $40,000 at an interest rate of 4% compounded quarterly for about 7 years in order to reach their target of $55,000.

The subject of this question is compound interest. Compound interest is the interest computed on the initial principal as well as the accumulated interest from previous periods. Since the couple's money is being compounded quarterly, we will need to use this information in our calculations.

First, we must understand the compound interest formula which is:

A = P (1 + r/n)^(nt)

where,

Answer:

  y^2/25 -x^2/4 = 1

Step-by-step explanation:

The equation can be written as ...

  y^2/a^2 -x^2/b^2 = 1

where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.

Step-by-step explanation:

Let the small mass be m and position on x axis be y.

A 20 kg sphere is at the origin.

Distance to 20 kg mass = y

A 10 kg sphere is at x = 20 cm

Distance to 10 kg sphere = 20 - y

We have forces between them are equal

We have gravitational force   

                    [tex]F=\frac{GMm}{r^2}[/tex]              

          Where G =  6.67 x 10⁻¹¹ N m²/kg²

                      M = Mass of body 1

                      M = Mass of body 2

                      r = Distance between them

Here we have

            [tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]

So the small mass should be placed at x = 11.72 cm or x = 68.28 cm

The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.

Recall the force of universal gravitational attraction :

Sphere 1 :

Sphere 2 :

Gravitational force ; sphere 1 :

Gravitational force ; sphere 2 :

Equate (1) and (2)

[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]

[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]

20(400 - 40d + d²) = 10d²

8000 - 800d + 20d² = 10d²

10d² - 800d + 8000 = 0

Divide through by 10

d² - 80d + 800 = 0

Using a quadratic equation solver :

d = 68.28 cm or d = 11.72 cm

The possible positions are 68.28 cm and 11.72 cm

Learn more :https://brainly.com/question/8882508

Final answer:

The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.

Explanation:

Let's create a table to represent the given information:

Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70

To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.

Now, let's analyze the changes in cost for each additional pound of dried cherries:

Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:

y = (10.60/2)x

Area of path and garden = 11 x 11 = 121 square feet.

Area of garden only = 7 x 7 = 49 square feet.

Area of just the path = 121 - 49 = 72 square feet.

Answer:

[tex]\frac{15}{32}[/tex]

Step-by-step explanation:

Given that a coin is flipped 5 times. Let us assume it is a fair coin with probability for head or tail equally likely and hence 0.50

Sample space would have [tex]2^5 = 32[/tex] possibilities

For two heads never occurring in a row favourable outcomes are

HTTTT,HTTHT,HTTTH,  HTHTH,  HTHTT, THTHT, THTTT, THTTH, TTHTH, TTHTT, TTTHT, TTTTH, TTTTT, TTTTH

Hence probability =

Favorable outcomes/Total outcomes=

[tex]\frac{15}{32}[/tex]

Answer:

4

Step-by-step explanation:

To restore her server after a failure on Wednesday morning, Nancy would need to restore the full backup from Sunday, and then restore the differential backup from Tuesday.

In Nancy's case, she would need two backups to fully restore her server. These would be the full backup from Sunday and the differential backup from Tuesday. Here's why:

Because Nancy performs full backups every Sunday, the full backup will have all the data up until Sunday at 1 A.M. The differential backup from Tuesday will contain all the changes that occurred on Monday and Tuesday until 1 A.M.

https://brainly.com/question/32115051

#SPJ12

Answer:

The correct answer is C. 129.

Step-by-step explanation:

Let's recall that the Inscribed Quadrilateral Theorem states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.

In the case of the inscribed quadrilateral ABCD in the graph attached, we have that:

m∠C= 51°, therefore its supplementary angle, ∠A, should be the difference between 180° and m∠C.

m∠C= 180° - m∠A

Replacing with the real values:

51 = 180 - m∠A

m∠A = 129°

The correct answer is C. 129.

Answer:

36°

Step-by-step explanation:

Like your other question, the angles of the triangle must add up to 180. The tangent line is perpendicular to the center, so the angle must be 90°.

90° + 54° + 36° = 180°

Answer:

C) AC=DC

Step-by-step explanation:

In the figure of question attached below:

In Δ ACB and  Δ DCE, AB and DE are hypotenuse respectively.

According to HL theorem:

"If hypotenuse and one leg of right angle triangle is congruent to Hypotenuse and one leg of other right angle triangle then triangles are congruent"

According to above statement if AB and DE are hypotenuse of Δ ACB and  Δ DCE respectively then either

AC = DC    (leg)

BC = EC     (leg)

In order to prove  congruence of triangles using HL theorem, AC must be equal to DC.

So option C is correct.

Answer:

C ) AC=DC

Step-by-step explanation:

edge 2021

Answer:

Jasmine can load maximum of 25 boxes with herself on the elevator.

Step-by-step explanation:

Given:

Weight of Jasmine = 150 lb

Weight of each boxes  = 72 lb

Load elevator can carry = 2000 lb

we need to find the number of boxes that can be loaded

Let number of boxes be 'x'

Now we know that Maximum load the elevator can carry is 2000 lb.

So We can say Weight of jasmine plus Number of boxes multiplied by Weight of each boxes should be less than or equal to Load elevator can carry.

Framing in equation form we get;

[tex]150+72x\leq 2000[/tex]

Solving the equation we get:

We will first Subtract 150 on both side;

[tex]150+72x-150\leq 2000-150\\\\72x\leq 1850[/tex]

Now Dividing both side by 72 by using Division property we get;

[tex]\frac{72x}{72}\leq \frac{1850}{72}\\\\x\leq 25.69[/tex]

Hence Jasmine can load maximum of 25 boxes with herself on the elevator.

Answer:

50 grams

Step-by-step explanation:

Let the amount of cheese required by the recipe be "x"

Ann increased 60% from original amount and then used up 80 grams. Thus:

Original, increased by 60%, became 80

This translated to algebraic equation would be:

x + 0.6x = 80

Note:  60% = 60/100 = 0.6

So we can solve the above equation for "x" and get our answer. Shown below:

[tex]x + 0.6x = 80\\1.6x=80\\x=\frac{80}{1.6}\\x=50[/tex]

Hence,

the recipe required 50 grams of cheese

Answer:

Graph of the following function is attached with the answer.

Domain : ( - ∞ , + ∞ )

Range : ( 3 , + ∞ )

Step-by-step explanation:

[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]

Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.

So, Domain : ( - ∞ , + ∞ )

The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:

Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

I would say it as "the letter F is greater than negative four."

Option a. 26; the cheetah's rate in miles per hour is the correct answer.

Step-by-step explanation:

Given

[tex]f(x) = 6x+8\\g(x) = x-2[/tex]

As the function f is in miles and function g is is hours, and we are dividing the function f by function g so the new unit will be:

miles/hour = miles per hour

Now

[tex]\frac{f}{g}(x)= \frac{f(x)}{g(x)}\\\frac{f}{g}(x) = \frac{6x+8}{x-2}[/tex]

We have to find (f/g)(3) so putting 3 in place of x

[tex]\frac{f}{g}(x) = \frac{6(3)+8}{-2}\\= \frac{18+8}{1}\\= 26[/tex]

Hence,

Option a. 26; the cheetah's rate in miles per hour is the correct answer.

Keywords: Functions, function operations

Learn more about functions at:

#LearnwithBrainly

Answer:

See proofs below

Step-by-step explanation:

a) Suppose that aRb. Let y∈Sa , then y∈A and yRa. We have that yRa and aRb. Since R is a partial order, R is a transitive relation, therefore yRa and aRb imply that yRb. Now, y∈A and yRb, thus y∈Sb. This reasoning applies for all y∈Sa that is, for all y∈Sa, y∈Sb, threrefore Sa⊆Sb.

b) Suppose that Sa⊆Sb. Since R is a partial order, R is a reflexive relation then aRa. Thus, a∈Sa. The inclusion Sa⊆Sb implies that a∈Sb, then aRb.

c) Denote this set by S={Sb:b∈B}. We will prove that supS=Sx with x=supB.

First, Sx is an upper bound of S: let Sb∈S. Then b∈B and since x=supB, x is an upper bound of B, then bRx. Then b∈Sx. Now, for all y∈Sb, yRb and bRx, then by transitivity yRx, thus y∈Sx. Therefore Sb⊆Sx for all Sb∈S, which means that Sx is an upper bound of S (remember that the order between sets is inclusion).

Now, let's prove that Sx is the least upper bound of S. Let Sc⊆A be another upper bound of S (in the set F). We will prove that Sx⊆T.

Because Sc is an upper bound, Sb⊆Sc for all b∈B. Thus, if y∈Sb for some b, then y∈Sc. That is, if yRb then yRc. In particular, bRb then bRc for all b∈B. Thus c is a upper bound of B. Byt x=supB, then xRc. Now, for all z∈Sx, zRx and xRc, which again, by transitivity, implies that z∈Sc. Therefore Sx⊆Sc and Sx=sup S.

In a partial order set, if aRb, then Sa ⊆ Sb. If Sa ⊆ Sb, then aRb. If B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}.

a) To show that if aRb, then Sa ⊆ Sb, we need to prove that if x ∈ Sa, then x ∈ Sb. Since x ∈ Sa, that means xRa holds. And since aRb, we can conclude that xRb holds as well. Therefore, x ∈ Sb, which implies that Sa ⊆ Sb.

b) To show that if Sa ⊆ Sb, then aRb, we need to prove that if aRb does not hold, then Sa ⊆ Sb does not hold. If aRb does not hold, it means that b is not in Sa. However, if Sa ⊆ Sb, it implies that every element in Sa is also in Sb. Hence, we arrive at a contradiction, which proves that if Sa ⊆ Sb, then aRb.

c) To show that if B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}, we need to prove that Sx is an upper bound for {Sb : b ∈ B} and that it is the least upper bound. Since x is the least upper bound for B, this means that every element of B is contained in Sx. Therefore, Sx is an upper bound for {Sb : b ∈ B}. Additionally, if there exists an upper bound U for {Sb : b ∈ B}, then every element of {Sb : b ∈ B} must be contained in U. Since Sb is a subset of Sa for every b ∈ B, it follows that every element of Sa is contained in U. Therefore, Sa ⊆ U for every a ∈ A. In particular, Sx ⊆ U, which proves that Sx is the least upper bound for {Sb : b ∈ B}.

https://brainly.com/question/31435349

#SPJ12