The owner of a ski resort estimates that a new 4-person ski lift will cost $5,000,000. The owner begins making payments on March 1 and every three months thereafter for 5 years into an account that earns 4% annual interest compounded quarterly. What payment amount must the owner make to have the cost of the ski lift in 5 years? Round your answer to the nearest cent.

Answer:

32⅘

(using indices)

32 = 2⁵

= 2⁵ × 1⅘

= 2²⁰

⁵

= 2⁴ = 16

Answer:

y = 8/5

Terms:

3y, -2y, y

Leading term:
3y

Step-by-step explanation:

Subtract by 17 from all sides

[tex]3y+17-17=-2y+25-17[/tex]

Simplify

[tex]3y=-2y+8[/tex]

Add term 2y

[tex]3y+2y=-2y+8+2y[/tex]

Simplify further

[tex]3y + 2y = 5y\\= 5y\\5y = 8[/tex]

Divide all sides by 5

[tex]\frac{5y}{5}=\frac{8}{5}[/tex]

Cancel the current leading term, 5y, simplify one last time

[tex]y=\frac{8}{5}[/tex]

Answer:

y =  [tex]\frac{8}{5}[/tex]  or  [tex]1\frac{3}{5}[/tex]  or  [tex]1.6[/tex]  ✅

Step-by-step explanation:

[tex]3y+17=-2y+25[/tex]

                 ⬆️

Move the variable to the left-hand side and change its sign

              ⬇️

[tex]3y+17+2y=25[/tex]

      ⬆️

Move the constant to the right-hand side and change its sign

                      ⬇️

[tex]3y+2y=25-17[/tex]

   ⬆️

Collect like terms

⬇️

[tex]5y=25-17[/tex]

           ⬆️

Subtract the numbers

       ⬇️

[tex]5y=8[/tex]

  ⬆️

Divide both sides of the equation by 5

  ⬇️

[tex]\frac{5y}{5} =\frac{8}{5}[/tex]

  ⬇️

Solution

[tex]y=\frac{8}{5}[/tex]  ✅

Alternative form

[tex]y=1\frac{3}{5} , y=1.6[/tex]  ✅

I hope this was helpful!

Have a blessed day! (✿◠‿◠)

Answer:

A

Step-by-step explanation:

[tex](-3-i)+(5+6i) \\ \\ =-3-i+5+6i \\ \\ =2+5i[/tex]

Answer: 11

Step-by-step explanation:

the answer is 11 all it is asking for is finding the mode which simply means the highest group of repeated numbers

The mode of the frequency distribution based on the table is age 11 with 12 students.

Mode can be defined as the most occurring value in a statistical distribution. It is also the most repeated number.

According to the table given;

Age 9 = 3 students

Age 10 = 10 students

Age 11 = 12 students

Age 12 = 1 students

Based on this information, the age with the most number of students is age 11.

Therefore, the mode is 11

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Step-by-step explanation:

based on the story told I expected completely different questions.

but for the actually asked question the whole thing about gaining our not gaining weight is competent irrelevant. ignore it.

so, all we need to do is looking at the row totals.

27.4% of the participants took 1 vitamin.

49.5% of the participants took more than 1 vitamin.

so, 49.5% + 27.4% = 76.9% of all participants are taking vitamins in some form.

therefore, the second answer option is correct.

The expressions matched with their correct pairs is

(-8)(-2.2)     →    17.6

(-3.4)(5)      →    -17

(-9.5)(-2)    →     19

(3.8)(-5)     →    -19

From the question, we are to match the tiles to the boxes to form correct pairs

To do this, we will simplify the expressions

Multiplying

-8 × -2.2

= 17.6

Multiplying

-3.4 × 5

= -17

Multiplying

-9.5 × -2

= 19

Multiplying

3.8 × -5

= -19

Hence, the expressions matched with their correct pairs is

(-8)(-2.2)     →    17.6

(-3.4)(5)      →    -17

(-9.5)(-2)    →     19

(3.8)(-5)     →    -19

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Answer:

Solutions: x=1.

Step-by-step explanation:

Answer: Less than

Step-by-step explanation:

The symbols || indicate absolute value.

Absolute value changes a number into it's distance from 0 on the number line.  As such, |27| = 27, but |-9| = 9.

Thus, |-5| = 5, and 5 > -5

|-5| > -5

Hope it helps

Answer:

Less than

Step-by-step explanation:

-5 is negetive 5 and |−5| means "positive 5", or just 5

Answer: The preimage and final image are the same point

This applies to every point in the xy plane.

======================================================

Explanation:

Let's say we started with the example point of (5,7)

Put the coordinates of the point into the T(x,y) transformation

We'll replace every x with 5 and every y with 7

So,

T(x, y) = (x+3, y-1)

T(5, 7) = (5+3, 7-1)

T(5,7) = (8, 6)

What does this mean? It means that the original preimage point (5,7) moves to (8,6). This is a shift of 3 units right and 1 unit down.

------------------

Now we'll plug the coordinates of that result, the (8,6), into the transformation of S(x, y) = (x-3, y + 1)

Plug in x = 8 and y = 6 to get...

S(x, y) = (x-3, y + 1)

S(8, 6) = (8-3, 6 + 1)

S(8, 6) = (5, 7)

We have gone from (8,6) to (5,7). We're back where we started.

The second transformation of (x-3, y+1) shifts 3 units left and 1 unit up. Notice both of these undo the original "3 units right and 1 unit down" from earlier. So this is why we get back to the starting point. It's not a coincidence.

Therefore, transformation T and transformation S are inverse transformations of one another. They undo each other. It's like taking a step forward (transformation T) and then taking a step back (transformation S)

In terms of algebra, it's like how multiplication and division are inverses of each other.

As you can probably guess, there's nothing particularly special about (5,7). I chose two random numbers. Pick whatever two favorite numbers you want for x and y. Plug them into T(x,y) and then whatever that result is, plug it into S(x,y) to notice you should get back to your original choice of (x,y). I recommend GeoGebra as a useful tool to help with geometric transformations.

Answer:

I dont understand it bc the pic is blurry

Step-by-step explanation:

Please mark Branliest

Answer:

b = 8 , m = - 5

Step-by-step explanation:

For this question we can use simulteanous equations to solve for m and b.

We first come up with 2 equations.

Given the first condition:

23 = -3m + b

b - 3m = 23 (Equation 1)

Now the Second Condition:

-7 = 2m + b

b + 2m = -7 (Equation 2)

Now, we will use Equation 1 - Equation 2 to eliminate b to solve for m.

-3m - (+2m) = 23 - ( - 7)

- 5m = 30

m = 30 ÷ -6 = -5

Now we substitute m into Equation 1 to solve for b.

b - 3(- 5) = 23

b + 15 = 23

b = 23 - 15 = 8

Answer: m=-6    b=5

Step-by-step explanation:

f(x)=mx+b

f(-3)=23     f(2)=7

[tex]\displaystyle\\\left \{ {{23=(m)(-3)+b} \atop {-7=(m)(2)+b}} \right. \ \ \ \ \left \{ {{23=-3m+b\ \ \ \ (1)} \atop {-7=2m+b\ \ \ \ (2)}} \right.[/tex]

Subtract equation (2) from equation (1):

-30=5m

Divide both parts of the equation by 5:

-6=m

Thus, substitute m=-6 in (2):

-7=(-6)(2)+b

-7=-12+b

-7+12=-12+b+12

5=b

Hence,

y=-6x+5

If 13 cents per yard is the price, and there was $8.63 left on the card, the yards of ribbon  Leila bought is 49 yards of ribbon.

To determine the number of yards of ribbon Leila bought, we need to calculate the difference between the initial balance on the prepaid debit card and the remaining balance after the purchase.

Initial balance: $15.00

Remaining balance: $8.63

The difference between these two amounts represents the amount spent on the ribbon:

$15.00 - $8.63 = $6.37

Now, we can calculate the number of yards of ribbon by dividing the amount spent by the price per yard:

$6.37 / $0.13 = 49

Therefore, Leila bought 49 yards of ribbon.

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[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{-7 -1}{3 -5} \implies \cfrac{ -8 }{ -2 }\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{4}(x-\stackrel{x_1}{5})[/tex]

[tex]y-1=4x-20\implies y=4x-19\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Based on the transformaion of point A, the coordinate of the point she would end up is (3, -4)

The complete question is added at the end of this solution

From the question, we have the following point

Starting point = (-3, 5)

The movement is given as

9 units down and 6 units to the right

The above can be represented mathematically as

(x, y) = (x + 6, y - 9)

When the above translation is applied on point A, we have the following equation

A' = (-3 + 6, 5 - 9)

Evaluate the sum and he difference in the above equation

A' = (3, -4)

Hence, the coordinate of the point she would end up is (3, -4)

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Complete question

The coordinates (the x- and y-values) for point A are (−3, 5).

If Samantha moved point A 9 units down and 6 units to the right, at what point would she end up?

Answer:

y = -x + 5

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is -1. Substituting into point-slope form, we get the equation to be

[tex]y+2=-(x-7)[/tex]

which rearranges into slope-intercept form as follows:

[tex]y+2=-x+7 \\ \\ y=-x+5[/tex]

Answer:

y=-x+5

Step-by-step explanation:

In linear equation the number of Republicans  are 225  and the number of Democrats are 259 .

What in mathematics is a linear equation?

Let Republicans  = x

then Democrats = x + 34

x + x + 34 = 484

2x + 34 = 484

2x = 484 - 34

2x =   450

 x = 450/2

  x  = 225

x + 34  =  225 + 34  ⇒  259

Therefore ,the number of Republicans  are 225  and the number of Democrats are 259 .

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The probability that the selected number is even is 7/15.

The probability that the selected number is a multiple of 4 is 1/5.

The probability that the selected number is a prime number is 2/5.

Based on the information illustrated, the following can be deduced:

Even numbers = 2, 4, 6, 8, 10, 12, 14.

Multiple of 4 = 4, 8 and 12.

Prime numbers = 2, 3, 5, 7, 11, and 13.

Therefore, the probability that the selected number is even will be:

= 7/15.

The probability that the selected number is a multiple of 4 is:

= 3/15 = 1/5.

The probability that the selected number is a prime number is:

= 6 / 15

= 2/5.

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The orders from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:

Brenda < Tim  < Carlton < Ali

Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1, 2, 3, 4, 5, 6, 7, 8… and so on.

If the information is sorted from highest to lowest, it is said to be in descending order. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are arranged in descending order. In other words, if the numbers are arranged from the largest to the smallest number, it is said to be in descending order.

We can write, four friends went scuba diving today,

Ali dove = 70 feet,

Tim went down = 50 feet,

Carl dove = 65 feet,

Brenda reach = 48 feet below sea level.

To determine the order from the person whose death was closest to the surface to the person whose death was the farthest from the surface.

Arrange in ascending order of distance from sea level.

Brenda < Tim  < Carlton < Ali

48feet < 50 feet < 65 feet < 70 feet

Therefore,

The order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:

Brenda < Tim  < Carlton < Ali.

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Hi could u ask the question a bit clearer?

Answer:between 28000 km and 32000 km

Step-by-step explanation:

The mean of all ninth grader's scores in the city is 80.32

From the question, we are to determine the mean score for all ninth graders in the city

From the given information,

Mariner High school

Mean score is 75 and the frequency is 265

Everett High school

Mean score is 90 and the frequency is 326

Jackson High school

Mean score is 69 and the frequency is 154

Thus,

The mean score for all ninth graders

= (265×75 + 326×90 + 154×69)/ (265 + 326 + 154)

= (19875 + 29340 + 10626)/745

= 59841/745

= 80.32

Hence, the mean is 80.32

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Perimeter of computer chip = 14.428 * ( [tex]10^{-7}[/tex] ) meters .

Given : length = 7.18×10⁻⁷ meters

            breadth = 3.4×10⁻⁹ meters    

To find = perimeter of computer chip

Formula for perimeter of a rectangle :      

Perimeter = 2 ( length + breadth )

Calculations :

Perimeter = 2 [ (  7.18×10⁻⁷ ) + ( 3.4×10⁻⁹ ) ]

On simplifying ,

                = 2 [ [tex]10^{-7}[/tex] ( 7.18 + 0.034 )

            = 2 [  [tex]10^{-7}[/tex] ( 7.214 ) ]

              = 14.428 * ( [tex]10^{-7}[/tex] ) meters

Hence , perimeter = 14.428 * ( [tex]10^{-7}[/tex] ) meters .

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Answer:

0.5 feet of snow

Step-by-step explanation:

6 inches is half of a foot because 1 foot = 12 inches.

6 inches / (12 inches / 1 foot) = 0.5 feet of snow

Answer:

1/2

Step-by-step explanation:

Since 13+13= 26 we know that 13 or 1/2 are girls

The following are the results:

[container 1] = aₙ = aₙ₋₁  ₊  4.5 ; a₁ = 0

[container 2] = aₙ = ₋4.5 ₊ 4.5n

[container 3] = 68 , 57 , 46 , 35 , 24, ..

[container 4] = aₙ = 79 ₋ 11n

[container 5] = 12 , 19 , 33 , 40

[container 6] = aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Given the sequence is : 0,4.5,9,13.5,18,..

recursive formula = aₙ=a₍ₙ₋₁₎+4.5 where a₁ = 0

Explicit formula = aₙ = a₁ ₊ (n ₋ 1)4.5

= 0 ₊ (n ₋ 1)4.5

aₙ = ₋4.5 ₊ 4.5n

b. given, we have recursive formula: aₙ = aₙ₋₁  ₋ 11 ; a₁ = 68

here we have the common difference as 11, and the initial term is 68.

hence the sequence will be 68 , 57 , 46 , 35 , 24, ..

Explicit formula = a₁ ₊ (n ₋ 1)11

aₙ = 68 ₊ 11n ₋ 11

aₙ = 79 ₋ 11n

c. the explicit formula is given, aₙ = 5 ₊ 7n

here we have the common difference as 7.

so the sequence is 12,19,33,40

and the recursive formula is aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Hence we get the acquired results.

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The area that would be painted will be 144 square feet

From the question, we are to determine the area of the cube-shaped shed that was painted

From the given information,

The cube-shaped shed has 6-foot high walls

From the formula for the surface area of a cube,

Surface area = 6s²

Where s is the measurement of a side

A cube has six sides

Since, the floor and ceiling are not painted,

The area of the shed that was painted will be

Surface area painted = 4s²

s = 6 feet

Thus,

Surface area painted = 4 × 6²

Surface area painted = 4 × 36
Surface area painted = 144 square feet

Hence, the area that would be painted will be 144 square feet  

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Answer: the bus's speed on the level road was 65 milles per hour

Step-by-step explanation:

Let the bus's speed on the level road is x mph

Hence, the bus's speed on the winding road is (x-20) mph

Thus,

3(x)+5(x-20)=420

3x+5x-100=420

8x-100=420

8x-100+100=420+100

8x=520

Divide both parts of the equation by 8:

x=65 mph

Answer:

9=11

Step-by-step explanation: