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What are the similarities and differences between number 1 and 3?

What are the similarities and differences do you see between 3 and 4

For example:
Similar: both arithmetic/linear/common difference
Different: #1 is discrete #3 is continuous

WILL GIVE BRAIN

Using simple interest, the amounts invested into each account are given as follows:

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = P(1 + rt)

In which:

The amount of interest after t years is given by:

I(t) = Prt

You invest $8,000 in 3 investment accounts, hence:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

From the rates of the account, we have that:

The amount invested in the glass account was double the amount invested in the metal account, hence:

[tex]P_3 = 2P_2[/tex]

The yield was a total of $280 at the end of one year, hence:

[tex]I_1 + I_2 + I_3 = 280[/tex]

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

From the first and the third equations, we have that:

[tex]P_1 + P_2 + P_3 = 8000[/tex]

[tex]P_1 + 3P_2 = 8000[/tex]

[tex]P_1 = 8000 - 3P_2[/tex]

Hence the amount of the metal investment can be found as follows:

[tex]0.02P_1 + 0.04P_2 + 0.05P_3 = 280[/tex]

[tex]0.02(8000 - 3P_2) + 0.04P_2 + 0.05(2P_2) = 280[/tex]

[tex]0.08P_2 = 120[/tex]

[tex]P_2 = \frac{120}{0.08}[/tex]

[tex]P_2 = 1500[/tex]

Hence the other investments are given as follows:

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he needs 3 pints of mango

Answer:3

Step-by-step explanation:

If the ratio is 1:5 that means that the number of pints of apple juice is multiplied by 5 to get the nimber of pints of mango juice

Considering the expression of a line, the correct answer is option a.) the relationship between the line that passes through (-1, -8) and (4,-4) and the line that passes through (2, -9) and (7,-5) is parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

In this case, you can calculated in this case:

Being (x₁, y₁)= (-1; -8) and (x₂, y₂)= (4; -4), the slope m can be calculated as:

m= (-4 - (-8))÷ (4 - (-1))

m= (-4 + 8)÷ (4 + 1)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-8= 4/5× (-1) + b

-8= -4/5 +b

-8 + 4/5= b

-36/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 36/5.

Being (x₁, y₁)= (2; -9) and (x₂, y₂)= (7; -5), the slope m can be calculated as:

m= (-5 - (-9))÷ (7 - 2)

m= (-5 + 9)÷ (5)

m= 4÷ 5= 4/5

Considering point 1 and the slope m, you obtain:

-9= 4/5× (-2) + b

-9= -8/5 +b

-9 + 8/5= b

-37/5=b

The equation of the line that passes through the pair of points (-1, -8) and (4,-4) is y=4/5x - 37/5.

You can see that the lines y=4/5x - 36/5 and y=4/5x - 37/5 have the same slope of 4/5 and different ordinates to the origin. So, this lines are parallel.

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Answer:

f(4) = 11

Step-by-step explanation:

f(x) = 3 x -1

Let x = 4

f(4) = 3*4 -1

     = 12-1

     = 11

f (x) = 3x - 1

f (4) = 3 × 4 - 1

f (4) = 12 - 1

f (4) = 11

Hope Helpful :-;

Answer: 11

Step-by-step explanation:

8x + 7 = 9x - 4

7 = x - 4

11 = x

Answer:

Length = 15

Step-by-step explanation:

The problem can be solved by dividing the total length of the rope (90-feet) by the total pieces you want from the rope (6 pieces). This information can be used to make this equation

90 feet / 6 pieces

Which equals

90 feet / 6 pieces = 15 feet/piece        (15 feet per peice)

Hope this helps :)

Answer:

9

Step-by-step explanation:

[tex]p(x)=4x^6+x^2+4 \\ \\ p(1)=4+1+4=9[/tex]

Answer:

$3337.92

Step-by-step explanation:

$3.66 x 912 = $3337.92

Answer: The answer I came up with is:  $237,737

The rate of interest is 10% and the sum is Rs 10,1000.

The interest calculated on the principal and the interest accrued over the prior period is known as compound interest. Compound interest is commonly abbreviated C.I. in mathematics.

The compound interest formula is given by

Compound Interest = Amount – Principal

Here, the amount is

[tex]A=P(1+\frac{r}{100} )^{n}[/tex]  where,

A = amount

P = principal

r = rate of interest

n = time (in years)

Given:

C.I. of a sum of money in 3 years = Rs 13310

C.I. of a sum of money in 4 years = Rs 14641

Let the principal be P and the rate of interest be r%

Then, according to the question,

For 3 years:

[tex]13310=P(1+\frac{r}{100} )^{3}[/tex]       ..... (1)

For 4 years:

[tex]14641=P(1+\frac{r}{100} )^{4}[/tex]       ..... (2)

Dividing equation (2) by (1), we obtain

[tex]\frac{14641}{13310} =(1+\frac{r}{100} )[/tex]

⇒[tex]\frac{14641-13310}{13310} =\frac{r}{100}[/tex]

⇒[tex]\frac{1331}{13310} =\frac{r}{100}[/tex]

⇒[tex]r=\frac{100}{10}[/tex]

⇒ r = 10%

Now, substituting r in equation (1),

[tex]13310=P(1+\frac{10}{100} )^{3}[/tex]

⇒[tex]13310=P(\frac{1331}{1000} )[/tex]

⇒P = Rs 10,000

Therefore, the rate of interest is 10% and the sum is Rs 10,1000.

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The value of x if T is the midpoint segment XY is 14.

The midpoint is the middle point of a line segment.

It is equidistant from both endpoints.

The midpoint is halfway between the two end points.

Therefore, the end point of the segment is XY.

The midpoint is T.

Hence,

XY = XT + YT

XT = 3x - 14 = YT

XY = 8x - 56

Let's find the value x.

Therefore,

8x - 56  = 3x - 14 + 3x - 14

8x - 56 = 6x - 28

8x - 6x = -28 + 56

2x = 28

divide both sides by 2

x = 28 / 2

x = 14

Therefore, the value of x is 14

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Answer: 6, 48 and 7, 56 and 9, 72 and 10,80

Step-by-step explanation:

By solving the given equation (y = 0.43x + 5) we know that the cost of renting the car is $215 when we plan to drive 489 miles.

So, y = 0.43x + 5 where 'x' is car driven and 'y' is the cost of renting.

Now, solve for y when the value of x is 489.

Rounding off: y = $215

Therefore, by solving the given equation we know that the cost of renting the car is $215 when we plan to drive 489 miles.

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Answer:

20

Step-by-step explanation:

The sum of the exterior angles of a polygon add to 360.  360 divided by 18 is 20.

Answer:

26000:48000

26000/48000

26/48(cancel the zeros)

13/24

fractional form=13/24

The equation for the hourly rate is 55x = 1578.5

For double hourly rate for overtime, it is 55 x 2x= 1578.5

Given

Antonia makes X dollars for regular hours

And 2x dollars for over time

Since he works 55 hours this week he works 8 hours a day

Hence the equation is as follows

55x = 1578.5

x= $28.7

In case of double payment during overtime

He gets double amount as following equation

55 x 2x

55 x 2(28.7) =  $3157

Hence the equation to find his hourly rate is 55x = 157.85

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Answer:

u= 30

Step-by-step explanation:

the sum of all angles on a triangle is 180* so u add the others (120+30)

that brings it to 150 then 180-150=30*

the answer is this

4 4/8.

Answer:

y = 5, 3

x = 155, 171

(y = 5, x = 155)

(y = 3, x = 171)

Step-by-step explanation:

(8y - 15) = (y²)

-8y + 15          -8y + 15

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

y² - 8y + 15 = 0

(y - 5) (y - 3) = 0

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

y = 5, 3

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

y² + x = 180

(5)² + x = 180

25 + x = 180

-25         -25

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

x = 155

(3)² + x = 180

9 + x = 180

-9            -9

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

x = 171

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

I really hope this helps!

Answer: 13

Step-by-step explanation:

As the sum of the angles of a triangle is 180, we have that 39 + 90 + 3x+12 = 180.

3x = 180 - 39 - 90 - 12

3x = 39

x = 13

Answer:

1. 5- (-8) = 13

2. -3 1/2 - 4 1/2 = -7 1/2

3. -7 - 4 = -11

4. -0.5 - 3.5 = -4

Step-by-step explanation:

1. 5- (-8) =

5 + 8

13

2. -3 1/2 - 4 1/2 =

-7 1/2

3. -7 - 4 =

-11

4. -0.5 - 3.5 =

-4

Answer:

c because if the number next to the underlined is above 5 u round up under 4 u round down

Step-by-step explanation:

Answer: c. 76

Step-by-step explanation: 0.758 to the hundredth place is 0.76 because numbers5 and above round up.

Check the picture below.

The most appropriate choice for Independent event and multiplicative counting rule will be given by

This is known as multiplicative counting rule.

What is Independent event and multiplicative counting rule?

Event that is not dependent on any other event is called independent event.

Let A and B be two independent events.

P(A∩B) = P(A) [tex]\times[/tex] P(B)

If two independent events occur m ways and n ways respectively then both the event together will happen in mn ways.

Here,

Let first event occur [tex]n_1[/tex] ways, second event occur [tex]n_2[/tex] ways, third event occurs [tex]n_3[/tex] ways and so on

Also assuming that the events are independent

The event together can happen [tex]n_1 \times n_2 \times n_3\times...[/tex] ways

This is known as multiplicative counting rule.

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Answer:

When A = 0 and y = 1 and C = 2

0x + 1y = 2

y = 2 No matter what x is, y will always be 2 and this will create a horizontal line.

Step-by-step explanation:

We can conclude that the probability of the randomly selected person does not use any facility is 0.

So, the probability that the selected person does not uses any facility:

Therefore, we can conclude that the probability of the randomly selected person does not use any facility is 0.

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Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.