please help me! i don't know how to work this out.

the n th term is n^2+20 work out the first three terms of the sequence. how many terms in the sequence are less than 50

Han's mixture has a higher concentration of orange juice concentrate, it is likely to taste stronger compared to Clare's mixture.

To determine whose orange juice mixture tastes stronger, we can compare the concentration of orange juice in each mixture. The concentration of orange juice can be measured by the ratio of orange juice concentrate to the total liquid volume.

Let's calculate the concentration for each mixture:

For Clare's mixture:

- Water: [tex]\(2\frac{1}{2}\)[/tex] cups

- Orange juice concentrate: [tex]\(\frac{1}{3}\)[/tex] cup

Total liquid volume: [tex]\(2\frac{1}{2} + \frac{1}{3} = \frac{7}{2} + \frac{1}{3} = \frac{21}{6} + \frac{2}{6} = \frac{23}{6}\) cups[/tex]

Concentration of orange juice concentrate in Clare's mixture: [tex]\(\frac{\frac{1}{3}}{\frac{23}{6}} = \frac{1}{3} \times \frac{6}{23} = \frac{2}{23}\) (ratio)[/tex]

For Han's mixture:

- Water: [tex]\(1\frac{2}{3}\)[/tex] cups

- Orange juice concentrate: [tex]\(\frac{1}{4}\)[/tex] cup

Total liquid volume: [tex]\(1\frac{2}{3} + \frac{1}{4} = \frac{5}{3} + \frac{1}{4} = \frac{20}{12} + \frac{3}{12} = \frac{23}{12}\) cups[/tex]

Concentration of orange juice concentrate in Han's mixture: [tex]\(\frac{\frac{1}{4}}{\frac{23}{12}} = \frac{1}{4} \times \frac{12}{23} = \frac{3}{23}\) (ratio)[/tex]

Comparing the concentrations:

- Clare's mixture has a concentration of [tex]\(\frac{2}{23}\)[/tex] orange juice concentrate.

- Han's mixture has a concentration of [tex]\(\frac{3}{23}\)[/tex] orange juice concentrate.

Since Han's mixture has a higher concentration of orange juice concentrate, it is likely to taste stronger compared to Clare's mixture.

The probable question maybe:

Clare mixes 2(1)/(2) cups of water with (1)/(3) cup of orange juice concentrate. Han mixes 1(2)/(3) cups of water with (1)/(4) cup of orange juice concentrate. Whose orange juice mixture tastes stronger? Explain or show your reasoning.

Number of text messages Keisha sent: 16

Number of text messages Miguel sent: 21

Number of text messages Pablo sent: 32

Step-by-step explanation:

Total messages sent = 69

Let,

Messages sent by Keisha = x

Messages sent by Miguel = y

Messages sent by Pablo = z

According to given statement;

x+y+z=69    Eqn 1

y=x+5    Eqn 2

z=2x    Eqn 3

Putting Eqn 2 and 3 in Eqn 1

[tex]x+(x+5)+2x=69\\x+x+5+2x=69\\4x=69-5\\4x=64[/tex]

Dividing both sides by 4;

[tex]\frac{4x}{4}=\frac{64}{4}\\x=16[/tex]

Putting x=16 in Eqn 2

[tex]y=16+5=21[/tex]

Putting x=16 in Eqn 3

[tex]z=2(16)=32\\[/tex]

Number of text messages Keisha sent: 16

Number of text messages Miguel sent: 21

Number of text messages Pablo sent: 32

Keywords: addition, linear equation

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Final answer:

To determine the number of classes at which the total cost for both options is the same, we can set up an equation. When attending 6 classes in a month, the total cost for both options will be the same, which is $60.

Explanation:

To determine the number of classes at which the total cost for both options is the same, we can set up an equation. Let x be the number of classes attended in a month.

For the membership option, the total cost is $60 per month.

For the walk-in option, the total cost is $10 multiplied by the number of classes attended.

Setting up the equation, we have:

60 = 10x

Dividing both sides by 10, we find:

x = 6 classes

So, when attending 6 classes in a month, the total cost for both options will be the same.

Using this value of x, we can find the total amount. For the membership option, it would be $60. For the walk-in option, the total amount is $10 multiplied by 6 classes, which is $60 as well.

Answer:

The point (0,4) doesn't make either equation true.

Step-by-step explanation:

Consider the equations.

[tex]y=-2x[/tex] and [tex]y=x+3[/tex]

We need to determine the point (0,4) make either equation true.

Substitute x=0 and y=4 in [tex]y=-2x[/tex]

[tex]4=-2(0)[/tex]

[tex]4=0[/tex]

Which is false.

Substitute x=0 and y=4 in [tex]y=x+3[/tex]

[tex]4=(0)+3[/tex]

[tex]4=3[/tex]

Which is false.

Hence, the point (0,4) doesn't make either equation true.

Answer:

x= -2 and y=1

Step-by-step explanation:

Given equations:

             -3x - 4y = 2

             3x + 3y = -3

Adding these two equations, we get:

            3y - 4y = -1 ⇒ y=1

           ⇒ 3x + 3(1) = -3 ⇒ x=-2

Answer:

5 is the greatest number of cups we can make.

Step-by-step explanation:

Given: 50 red bears, 25 blue bears and 35 green bears.

Now, finding the greatest number of cups we can make with same number of each colour in cups.

∴ we will be using greatest common factor (GCF) to know the number of cups.

[tex]50= 5\times 5\times 2\\\\25= 5\times 5\\\\35= 5\times 7[/tex]

∴ [tex]GCF= 5[/tex]

5 is the greatest number of cups we can make with same number of each colour.

Answer:

sin 39 = BS / 500

0.629320391 * 500 = BS

BS = 314.6601955 feet

ie. h = 314.66 feet

Answer:

404.9 m

Step-by-step explanation:

In the attached file

The range of function is { 0, -6, -9}

Given that the function is:

[tex]f(x) = \frac{-3}{4}x - 6[/tex]

Also given its domain is (-8, 0, 4)

To find: Range of the function

Domain of the function is possible input of the function that is "x" and range of the function is possible output of the function that is f(x)  

As there are only three input values for "x" that are (-8, 0, 4) we can determine the range by calculating value of f(x) for each of the x

For x = 8:

[tex]f(-8)=\frac{-3}{4} \times(-8)-6=6-6=0[/tex]

[tex]f(-8)=0[/tex]

For x = 0:

[tex]\begin{array}{l}{f(0)=\frac{-3}{4} \times(0)-6=-6} \\\\ {f(0)=-6}\end{array}[/tex]

For x = 4:

[tex]\begin{array}{l}{f(4)=\frac{-3}{4} \times(4)-6=-3-6=-9} \\\\ {f(4)=-9}\end{array}[/tex]

Thus the range of function is { 0, -6, -9}

To find the number, subtract 37 from both sides of the equation and isolate 'x'. The number is 54.

To find the number, let's represent it with the variable 'x'. The problem states that when 17 is added to the number, the result is 37 less than twice the number.

Mathematically, this can be represented as:

x + 17 = 2x - 37

To solve for 'x', we can start by subtracting 'x' from both sides of the equation:

17 = x - 37

Next, we can add 37 to both sides to isolate 'x':

54 = x

Therefore, the number is 54.

Answer:

50 gallos of 70%

100 gallons of 85%

Step-by-step explanation:

x = amount of 70% antifreeze

y = amount of 85% antifreeze 

   EQUATION 1:   x + y = 150    (total of 150 gallons mixed) 

   EQUATION 2:  .70x + .85y = .80(x + y)

    Multiply second equation by 100 on both sides to remove the decimals           70x + 85y = 80(x + y)  

  70x + 85y = 80x + 80y   (distributive)     

  70x - 80x + 85y - 80y = 0          

 -10x + 5y = 0      

Now we have the following system of equations:        

     x  +  y = 150     

  -10x +5 y = 0  

 Multiply the first equation by 10 to get opposite coefficients for x;  add the equations to eliminate x        

  10x + 10y = 1500       

 -10x + 5y =       0     

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

                15y = 1500    

 Solve for y            15y = 1500                y = 100

x+100=150    x=50

Answer:

6

Step-by-step explanation:

(3/4)/(1/8)=(3/4)(8/1)=3*2/1=6/1=6

Answer: 2/5

Step-by-step explanation:

slope = change in y/change in x (y2-y1/x2-x1)

slope (using points (50,3) and (60,7)) = 7-3/60-50 = 2/5

Answer:

$3

Step-by-step explanation:

3 blobs for 1.50

that means 1 blob is (1.50 / 3) which is 50 cents per blob

0.50 * 6 = 3 dollars for 6 blobs

The question is about cost ratios. Given that 3 blobs are worth $1.50, a single blob is worth $0.50. Therefore, 6 blobs would cost $3.00.

The question is asking about cost ratios. In the presented situation, there are 3 blobs for every $1.50. We can say that the cost of one blob is $1.50 divided by 3, which is $0.50. If we are looking for the cost of 6 blobs, we simply multiply the cost of one by 6, which gives us $3.00. Therefore, 6 blobs cost $3.00.

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Good evening ,

Answer:

Step-by-step explanation:

Look at the photo below for the details.

:)

Answer:

25x+300=y

Step-by-step explanation:

The equation represents Tonya's profit, y, for working x for hours is

y = 25x - 300

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Tonya's profit will depend on how many hours she works and how much she earns from tutoring.

Let's assume she works x hours, then she earns 25x dollars from tutoring.

However, she also has to pay the monthly rent of $300 regardless of how many hours she works.

Therefore, her profit y can be calculated as follows:

y = 25x - 300

This equation takes into account both her revenue (25x) and her expenses (the fixed cost of $300 for rent), and gives us her profit as the difference between the two.

Thus,

The equation represents Tonya's profit, y, for working x for hours is

y = 25x - 300

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Answer:D) No, because for some x's there are more than one y's.

Step-by-step explanation:The definition of a function states that for every x there is only one y. If you look at the data table for an x- value of 8 there are 2

different y-values 7 and 9. Therefore the correct answer is No, because for some x's there are more than one y's.

Answer:

the answer is D

Step-by-step explanation:

Answer:

x=510/7

Step-by-step explanation:

51/70=x/100

cross product

70*x=51*100

70x=5100

x=5100/70

x=510/7

x =72.86. This means that 51 out of 70 is equivalent to 72.86%.

51/70 = x/100.

51 * 100 = 70 * x.

5100 = 70 x

5100 / 70 = x.

The result is x = 72.86.

So, x = 72.86.

This means 51 out of 70 is equivalent to 72.86 out of 100 as a percentage.

Answer:

a = [tex]\frac{w + 4 - 3b}{6}[/tex]

Step-by-step explanation:

Given

w = 3(2a + b) - 4 ( add 4 to both sides )

w + 4 = 3(2a + b) ← distribute parenthesis

w + 4 = 6a + 3b ( subtract 3b from both sides )

w + 4 - 3b = 6a ( divide both sides by 6 )

[tex]\frac{w+4-3b}{6}[/tex] = a

Answer:

The answer is pi and 3pi

Step-by-step explanation:

Answer:

pi and 3 pi

Step-by-step explanation:

the second one is: (B) x=pi/2 and (D) x=3pi/2

:)

Answer:

B)     b = 240 - 5 x is the required expression to decipher the situation.

Step-by-step explanation:

The amount paid to the club in the advance = $240

Amount deducted in each visit = $5

Let us assume the number of times the club visited = x

So, the amount deducted in x visits  = x ( $5)  = 5x

Let b : amount Left after x visits

So, Amount left after x visits  = Advance Amount - Deductions after x visits

⇒  b = $240 - 5x

or , b = 240 - 5x is the required expression to decipher the situation.

Answer:

Giselle pays $240 on advance

Each time she uses ,$5 is deducted

Let no of time she use be x

So, Amount deducted = 5x

As Giselle pays $240 in advance

So 5x amount will be deducted from $240 to get net amount

So b= 240-5x

B) is Correct

Answer:

Step-by-step explanation:

[tex]10=2\cdot\boxed{5}\\\\45=3\cdot3\cdot\boxed{5}\\\\GCF(10,\ 45)=\boxed{5}[/tex]

Answer:

44.

Step-by-step explanation:

Let, x= white marbles

and y= yellow marbles

Now, according to the first condition

x + y = 58 … (1)

According to the second condition,

x= 3y+2

Or, 3y - x = -2 … (2)

Adding (1) and (2)

4y= 56

Or, y= 14 ... (3)

Now, putting (3) in (1)

x = 44

Therefore there are 44 White marbles and 14 yellow marbles.

Answer:

The area of the rectangular playroom is 260 feet² .

Step-by-step explanation:

Given:

The perimeter of the rectangular playroom is 72 feet and it's width is 10 feet.

Now, to find its area we need the length .

So, putting the formula of perimeter we get it's length:

Let the length be l .

Perimeter = 2( length + width)

[tex]72=2(l+10)[/tex]

[tex]72=2l+20[/tex]

subtracting both sides from 20:

[tex]72-20=2l+20-20[/tex]

[tex]52=2l[/tex]

Dividing both sides by 2:

[tex]52\div2=2l\div2[/tex]

[tex]26=l[/tex]

Length is 26 feet.

And, to get the area we put the formula of finding the area:

[tex]Area=length\times width[/tex]

[tex]Area=26\times 10[/tex]

[tex]Area=260[/tex]

Therefore, the area of the rectangular playroom is 260 feet² .

Final answer:

To determine the area of the rectangular playroom at Miss Pittypat's Day Care, we calculate the length using the perimeter and width provided, then multiply the length by the width. The playroom's area is found to be 260 square feet.

Explanation:

The question involves calculating the area of a rectangle when given the perimeter and the width. To find the length, we first use the perimeter formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Since the perimeter is given as 72 feet and the width is 10 feet, we can solve for the length:

72 = 2l + 2(10)

72 = 2l + 20

52 = 2l

l = 26 feet

Once we have the length, we calculate the area by multiplying the length by the width:

Area = l × w

Area = 26 ft × 10 ft

Area = 260 square feet

Therefore, the area of the rectangular playroom is 260 square feet.

Answer:

THE  FIRST ONE IS -3<1

THE SECOND ONE IS 7.11>-7.1

THE THIRD ONE IS 16 OVER 5

I DON'T KNOW THE LAST TWO SORRY

Answer:

#1

# 1

x=4

don't know number 4 and 5

so i think it is

7 and 9

[3,4]

Step-by-step explanation:

Answer:

[tex]y=0.15x[/tex]

Step-by-step explanation:

Given:

Original price of the ticket is [tex]x[/tex]

Price after using the coupon is [tex]y[/tex]

Coupon discount is 85% of [tex]x=0.85x[/tex]

Therefore, the price after applying coupon is given as the difference of the original price and the coupon discount. That is,

[tex]y=x-0.85x=x(1-0.85)=0.15x\\\therefore y=0.15x[/tex]

The graph is shown below. The graph passes through the origin as the above relationship is a proportional relationship.

The line [tex]y=0.15x[/tex] strictly remains in the first quadrant as both [tex]x[/tex] and [tex]y[/tex] can't be negative as they represent price of tickets and price can never have negative values. Hence, only the first quadrant has both the values of [tex]x[/tex] and [tex]y[/tex] positive.

$1331 is invested at 7% and $5566 is invested at 6%

Step-by-step explanation:

The formula of the simple interest is I = P r t, where

Assume that Sherry invested $P in the first account

∵ Sherry invested $P in the first account at 7% interest for 1 year

∵ I = P r t

∴ The interest of the 1st account = P( [tex]\frac{7}{100}[/tex] )(1)

∴ The interest of the 1st account = 0.07 P

∵ Sherry also invested $242 more than four times that amount at

   6% for 1 year

- Multiply P by 4 and add 242 to the product

∴ Sherry invested in the 2nd account (4P + 242)

∵ I = P r t

∴ The interest of the 2nd account = (4P + 242)( [tex]\frac{6}{100}[/tex] )(1)

∴ The interest of the 2nd account = 0.06(4P + 242)

- Simplify it

∴ The interest of the 2nd account = 0.24 P + 14.52

∵ Sherry receives $427.13 in interest after one year

- Equate the 1st interest and the 2nd interest and equate the sum

  by 427.13

∴ 0.07 P + 0.24 P + 14.52 = 427.13

∴ 0.31 P + 14.52 = 427.13

- Subtract 14.52 from both sides

∴ 0.31 P = 412.61

- Divide both sides by 0.31

∴ P = 1331

∵ She invested (4P + 242) in the 2nd account

- Substitute P by 1331

∴ She invested in the 2nd account = 4(1331) + 242 = 5566

∴ She invested $1331 at 7% interest

∴ She invested $5566 at 6% interest

$1331 is invested at 7% and $5566 is invested at 6%

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Answer: 67

Step-by-step explanation: