Which expressions are equivalent to 4(4a+5)4(4a+5)4, left parenthesis, 4, a, plus, 5, right parenthesis ?

To determine the time necessary for an investment to grow from $9,500 to $12,600 at an interest rate of 5.75% compounded quarterly, the compound interest formula is rearranged and solved for time, yielding approximately 6.6 years.

To find out how long it takes for an investment to grow from $9,500 to $12,600 with an interest rate of 5.75% compounded quarterly, we use the formula for compound interest: A = P(1 + r/n)^(nt), where:

In this case, we're solving for t, so we rearrange the formula: t = ln(A/P) / (n * ln(1 + r/n)). Substituting the provided values:

Thus, t = ln(12600/9500) / (4 * ln(1 + 0.0575/4)). After calculating, we find that t ≈ 6.6 years, rounded to the nearest tenth of a year.

The person must leave the money in the bank for approximately 5.4 years until it reaches $12600, with interest compounded quarterly.

To find out how long it takes for the investment to reach $12600 at a 5.75% interest compounded quarterly, we can use the formula for compound interest:

[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]

Where:

- A is the amount of money accumulated after t  years, including interest.

- P is the principal amount (the initial amount of money).

- r is the annual interest rate (in decimal).

- n is the number of times interest is compounded per year.

- t is the time the money is invested for, in years.

We want to find t, so we can rearrange the formula to solve for t:

[tex]\[ t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)} \][/tex]

Given:

- P = 9500

- A = 12600

- r = 0.0575  (5.75% expressed as a decimal)

- n = 4 (quarterly compounding)

Substituting these values into the formula:

[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + \frac{0.0575}{4}\right)} \][/tex]

[tex]\[ t = \frac{\log\left(\frac{12600}{9500}\right)}{4 \cdot \log\left(1 + 0.0575/4\right)} \]\[ t \approx \frac{\log(1.32631579)}{4 \cdot \log(1.014375)} \]\[ t \approx \frac{0.12224324}{4 \cdot 0.00570388} \]\[ t \approx \frac{0.12224324}{0.02281552} \]\[ t \approx 5.361 \][/tex]

Rounded to the nearest tenth, it takes approximately 5.4 years for the investment to reach $12600 at 5.75% interest compounded quarterly.

The cost of renting the apartment for n months can be simplified to 800n + 1050. To rent the apartment for 2 years, the cost is $20,250.

To simplify the expression, we can distribute the 800 to both terms inside the parentheses:

Combining these terms gives us:

800n + 800 + 250

By combining like terms, we get the simplified expression:

800n + 1050

To find the cost of renting the apartment for 2 years (24 months), we substitute n = 24 into the simplified expression:

800(24) + 1050 = 20,250

Therefore, the apartment costs $20,250 to rent for 2 years.

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Answer:

4 people per square mile

Step-by-step explanation:

----Population density = number of people divided by land area.

Back I 2005,the population density of the US was: 295500000/3806000= 77.6 people per square miles.

----If the population increased by 5.1%,the new population of residents in the US will be

100% + 5.1% = 105.1%

105.1/100 × 295500000

= 310,570,500.

--- The new population density of the US in 2015 will be

310,570,500 ÷ 3,806,000

= 81.6 persons per square mile

---- To find out the difference in population from 2005 to 2015,we have to do nothing else but subtract the Population Density (PD) of 2015 from 2005

81.6 - 77.6 = 4 persons per square mile

Answer:

96[tex]cm^3[/tex]

Step-by-step explanation:

To determine how much additional wax was needed to make the taller candle, we determine the volume of each of the candles and find the difference in their volumes

First Candle

Volume=Height X Length X Width

=12 X 4 X 6

=288[tex]cm^3[/tex]

Second Candle

The second candle is 4cm higher

Volume=Height X Length X Width

=16 X 4 X 6

=384[tex]cm^3[/tex]

Difference in Volume = 384-288 =96[tex]cm^3[/tex]

Therefore, 96[tex]cm^3[/tex] of additional wax was used to make the second candle.

Answer:

24

Step-by-step explanation:

First do parenthesis:

3*(9+1)-6 -> 3*(10)-6

Then do multiplication:

3*(10)-6 -> (30)-6

Then complete it with subtraction:

(30)-6 -> (24)

So your answer would be 24!

PEMDAS= Parenthesis, Exponents, Multiplication, Division, Add, Subtract.

Answer:

P (-1 , 0)

Step-by-step explanation:

M (-6 , 2)      N (9 , -4)     P (x , y)

horizontal distance of M and N = 9 - (-6) = 15

vertical distance of M and N = 2 - (-4) = 6

1/3 from x coordinate of M (-6): -6 + 15/3 = -1    This is x coordinate of point P

1/3 from y coordinate of M (2): 2 - 6/3 = 0    This is y coordinate of point P

P (x , y)  i.e P (-1 , 0)

check: distance of MP = √(-1 - (-6))² + (0 - 2)² = √29 = 5.385

distance of PN = √(-1 - 9)² + (0 - (-4))² = √116 = 10.77

MP / PN = 5.385 / 10.77 = 0.5 = 1/2

The values of x and y that partition the line segment MN into the ratio 1:2 are x = 3 and y = -4.

To determine the values of x and y that partition the line segment MN into the ratio MP:PN = 1:2, we can use the section formula. The section formula states that the coordinates of a point P(x,y) that partitions a line segment with endpoints M(x1, y1) and N(x2, y2) into the ratio m: n are given by:

x = (nx1 + mx2) / (m + n)

y = (ny1 + my2) / (m + n)

In this case, M(-6, 2) and N(9, -4), and the ratio is 1:2. Plugging these values into the section formula, we get:

x = (2*9 + 1*(-6)) / (1 + 2) = 3

y = (-4*2 + 2*(-4)) / (1 + 2) = -4

Therefore, the values of x and y that partition the line segment MN are x = 3 and y = -4.

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Answer:

1 6   p i   s q u a r e s   i s    m y    f i n a l    a n s w e r ! ! !   y o u r   w e l c o m e

Answer:

C

Step-by-step explanation:

the variables in this system of equations are b and p these represent distance walked.

4b + 5p = 2 represents the total amount of time the walk takes

b + p = 8 represents the total distance walked :)

The answer isn't A only because the word problem states that from her house to the beach, it should be represented as b. And p for the beach to the park.

Answer:

x^2-9x+8

Step-by-step explanation:

(2x^2-5x+3)-(-x^2+4x-5)

Open the bracket first

2x^2-5x+3+x^2-4x+5

Collect like terms

2x^2+x^2-5x-4x+3+5

x^2-9x+8

So the final answer is x^2-9x+8

Answer:

110 degrees

Step-by-step explanation:

the angles are alternate exterior angles which means that they are the same

Answer:

110

Step-by-step explanation:

The angles are the same according to the corresponding angle postulate.

Answer:

.48

Step-by-step explanation:

The total number of tiles is

24+6+10+10 =50 tiles

P(blue) = number of blue tiles/total

            = 24/50

             =.48

Answer:

Buying the 1kg is a better value.

Step-by-step explanation:

okay so 1000g for every 1kg

so first we will find out how much the 600g would cost if it was 1kg

(ill be using $ instead of £)

600g/$4.25=1000g/? (finding the question mark which will be "x")

you cross multiply so 600x = 4.25×1000

600x = 4250

then cancel out the 600 so x is left, since the 600 is multiplying into the x, you would divide it out to cancel. so

600x=4250

_________     <(dividing)

600     600

so it would be

x= 7.08

which means it is $7.08 which is NOT better for value because it is 9 cents more than just buying the 1kg.

Answer:

3% unlikely

Step-by-step explanation:

if there are 10 marbles you can try to get 1 white, 1 blue, 1 red is't 3/10 = .3

Answer:

Blue 60%

Red 30%

White 10%

Answer:

x = 4.92

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hypotenuse

sin 38 = x/8

Multiply each side by 8

8 sin 38 = x/8 *8

8 sin 38 = x

4.925291803 =x

Answer:

r2+A

Step-by-step explanation:

lalalalalalalalalalalalala

Answer:                      Received cold medicine  Did not receive cold medicine

Cold lasted longer than 7 days             23                                 20

Cold did not last longer than 7 days     27                                30

Step-by-step explanation:

i hope it helps

To complete the two-way frequency table, calculate the values for each cell based on the given information.

To complete the two-way frequency table, we need to fill in the missing values. Given that there are 100 participants in total, we can calculate the value for each cell. Starting with the top left cell, which represents participants who received the cold medicine and had their cold last longer than 7 days, the value would be 27. Similarly, we can calculate the values for the other cells in the table.

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The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.

The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points

Arrange the data points from smallest to largest.

If the number of data points is odd, the median is the middle data point in the list.

If the number of data points is even, the median is the average of the two middle data points in the list.

Given data ,

From the given boxplot we can deduce the following points:

On Friday: Q₁ = 200, Q₂ = 215, Q₃ = 220 and IQR = 20.

On Saturday: Q₁ = 190, Q₂ = 205, Q₃ = 210 and IQR = 20.

And , the median of the data on Friday is M₁ = 220

And , the median of the data on Saturday is M₂ = 205

So , scores on Friday have a greater median than the scores on Saturday

Hence , the median is solved

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The complete question is attached below :

A bowling team participates in a two-day tournament and records the scores for each team member on both days. The scores for both days are represented by the box plots below.

A. The scores on Friday and the scores on Saturday have the same median and interquartile range.

B. The scores on Friday have a greater median and a greater interquartile range than the scores on Saturday.

C. The scores on Friday have a greater interquartile range than the scores on Saturday, but both data sets have the same median.

D. The scores on Friday have a greater median than the scores on Saturday, but both data sets have the same interquartile range.

Answer:

student b has 4 more movies

Step-by-step explanation:

Answer:

4 more

Step-by-step explanation:

Step-by-step explanation:

[tex]a \: \: \: \: 1 \\ \\ b \: \: \: \: 4 \\ \\ c \: \: \: \: 3 \\ \\ d \: \: \: \: 2[/tex]

Answer:

D

Step-by-step explanation:

For some side lengths to create a triangle, any two of the side lengths must have an added length together of less than the third leg. Otherwise, the vertices would simply not be able to be connected by the lines. In a), 3+5=8, but since it is not more, the triangle will not be able to be formed (it would basically just be a line.) In B, 7+8< 16. In C, there is the same situation as with the first example (4+15=19). Finally, in the last one, 5+7>12, and all of the side lengths work out. Therefore, the correct answer is D. Hope this helps!

Hope this will help u...

Answer:

9u(v²u+v³-5u³)

Hope this Helps You !!!

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Answer:

9.9 cm²

Step-by-step explanation:

Base = 2.6x3 which is 7.8/ 2 is 3.9.

Faces = 4x3 which is 12/2 is 6

Then, add those together to get 9.9

Answer:

Vijay cannot fit all the cubes into the box, he can only fit 20 cubes into the box

10 x 2 = 20 cubes

He would need 5 boxes to fit all the cubes

Hope this helps <3

Answer:

5

Step-by-step explanation:

According to the question, A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12.We are now asked to find the height of the frustum.

---The height of this frustum is equal to the distance of its smaller base from the center of the sphere.

Therefore,it is assigned the pattern

H = √(r1² - r2²

Where r1 is the radius of the sphere

And r2 is the radius of the other base of the frustum

H is the height that we are looking for

H = √(13² - 12²)

= √( 169 - 144 )

= √ 25

H = 5

Final answer:

The height of the frustum inscribed in a sphere with a radius of 13 and one base having a radius of 12 is found to be 10 units using the Pythagorean theorem.

Explanation:

To find the height of the frustum inscribed in a sphere of radius 13, where one base is a great circle of the sphere, and the other base has radius 12, we can use geometry and Pythagorean theorem.

Consider the right triangle formed by the radius of the sphere, half of the frustum height (since the center of the sphere is midway of the frustum's height for the configuration given), and the radius of the smaller base of the frustum.

The radius of the sphere is 13, and the radius of the smaller base is 12.

Using the Pythagorean theorem (a² + b² = c²), we can find the half-height of the frustum.

So, we have:

122 + b² = 132

144 + b² = 169

b² = 25 => b = 5

Thus, the full height (h) of the frustum is 10 units.

The 5 th term of the given expression is 330[tex](6x)^{7}( 6y)^{4}[/tex].

Step-by-step explanation:

Given,

[tex](6x+6y)^{11}[/tex]

To find the 5th term of the given expression.

Formula

In a binomial series [tex](a+b)^{n}[/tex], the r th term is = nC(r-1) [tex]a^{n-r-1} b^{r-1}[/tex], where,

nC(r-1) = [tex]\frac{n!}{(r-1)!(n-r+1)!}[/tex]

Now,

Putting, n=11, r = r, a=6x and b=6y we get,

5 th term = 11C4[tex](6x)^{7}( 6y)^{4}[/tex]

= [tex]\frac{11!}{4!7!}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]

= [tex]\frac{11X10X9X8X7!}{7!X4X3X2X1}[/tex][tex](6x)^{7}( 6y)^{4}[/tex]

= 330[tex](6x)^{7}( 6y)^{4}[/tex]

Here is the answer.

Answer: 21

Step-by-step explanation:

1/3 = 7

7 * 3 = 21

1/3 = 7/21

Answer:

21

Step-by-step explanation:

Given:

[tex](y-4 x)\left(y^{2}+4 y+16\right)[/tex]

Resulting form = [tex]y^{3}+4 y^{2}+a y-4 x y^{2}-a x y-64 x[/tex]

To find:

The value of a in the polynomial.

Solution:

[tex](y-4 x)\left(y^{2}+4 y+16\right)[/tex]

Using distributive property:

[tex]a(b+c)=a b+a c[/tex]

[tex](y-4 x)(y^{2}+4 y+16)=y(y^{2}+4 y+16)-4 x(y^{2}+4 y+16)[/tex]

Now multiply each of the first term with each of the second term.

                     [tex]=y y^{2}+y \cdot 4 y+y \cdot 16+(-4 x) y^{2}+(-4 x) \cdot 4 y+(-4 x) \cdot 16[/tex]

Applying plus minus rule: [tex]+(-a)=-a[/tex]

                    [tex]=y^{2} \cdot y+4 y\cdot y+16 y-4 y^{2} x-4 \cdot 4 y x-4 \cdot 16 x[/tex]

Apply the exponent rule: [tex]a^{b} \cdot a^{c}=a^{b+c}[/tex]

                    [tex]=y^{3}+4 y^2+16 y-4 y^{2} x-16 y x-64 x[/tex]

Let us compare this with the given resulting form:

                   [tex]=y^{3}+4 y^{2}+a y-4 x y^{2}-a x y-64 x[/tex]

On comparing above two expression, we get a = 16.

The value of a in the polynomial is 16.

Answer:

a^n=-9+(n-1).5

Step-by-step explanation:

Arithmetic sequence=a+(n-1)d

a=-9

n=?

d=+5

Arithmetic sequence=-9+(n-1)5

=-9+5n-5

Collect like terms

-9-5+5n

-14+5n

So the final answer is

an=-9+(n-1).5

If the technician charges $327.50, then the technician worked 5.95 hours.

To determine how many hours the computer technician worked, we need to set up an equation based on the information provided. Let:

- [tex]\( F \)[/tex] represent the flat rate for home visits.

- [tex]\( h \)[/tex] represent the number of hours worked.

- [tex]\( 55h \)[/tex] represent the hourly charge ($55 per hour).

The total charge is given as $327.50. The equation for the total charge is:

[tex]\[F + 55h = 327.50\][/tex]

Without the flat rate [tex]\( F \)[/tex] provided, we can't determine [tex]\( h \)[/tex] exactly. However, let's assume that [tex]\( F \)[/tex] is included in the total cost as a constant and solve for [tex]\( h \)[/tex] based on the given rate per hour.

First, let's isolate [tex]\( h \):[/tex]

[tex]\[55h = 327.50 - F\\\\h = \frac{327.50 - F}{55}\][/tex]

Since the exact flat rate [tex]\( F \)[/tex] isn't given, let's assume it's zero for this case:

[tex]\[h = \frac{327.50}{55}\][/tex]

Now, calculate [tex]\( h \):[/tex]

[tex]\[h = \frac{327.50}{55} = 5.95 \text{ hours}\][/tex]

Therefore, if the technician charges $327.50 for 5.95 hours worked and assuming no flat rate, the technician worked approximately [tex]\( 5.95 \)[/tex] hours.

The complete question is:

A computer technician charges a flat rate for home visits plus $55 per hour. If the technician charged $327.50, then the technician worked how many hours?

Answer: c

Step-by-step explanation:

[tex]x^2+4x-45[/tex]

[tex](x+9)(x-5)[/tex]

Answer:

c

Step-by-step explanation: