1. Robbie opens an account at a local bank and deposits $100 every week into the account.
The account pays 2.4% interest, compounded weekly. How much is in the account after
three years?​

Answer:

False

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

-6

Step-by-step explanation: 2(n+5)=-2

Remove the bracket(expanding):

2×n+2×5=-2

2n+10=-2

collect like terms:

2n=-2+(-10)

2n=-12

Dividing both side by the coefficient of n i.e 2

2n/2=-12/2

n=-6

He sold 32 small watermelons and 17 large watermelons.

Step-by-step explanation:

Let,

Small watermelons = x

Large watermelons = y

Cost of one small watermelon = $7

Cost of one large watermelon = $10

According to given statement;

x = y+15   Eqn 1

7x+10y=394   Eqn 2

Putting value of x from Eqn 1 in Eqn 2

[tex]7(y+15)+10y=394\\7y+105+10y=394\\17y=394-105\\17y=289\\[/tex]

Dividing both sides by 17

[tex]\frac{17y}{17}=\frac{289}{17}\\y=17[/tex]

Putting y=17 in Eqn 1

[tex]x=17+15\\x=32[/tex]

He sold 32 small watermelons and 17 large watermelons.

Keywords: linear equations, substitution method

Learn more about linear equations at:

#LearnwithBrainly

Answer:

27 cats.

Step-by-step explanation:

The fraction of cats = 9 / (9 + 13) and dogs = 13 / ( 9 + 130

= 9/22 and 13/22

So the number of cats = (9/22) * 66

= 9 *3

= 27.

=

Answer:

x^2/3

Step-by-step explanation:

(x^5/6)/(x^1/6)=x^(5/6-1/6)=x^4/6

simplify 4/6, you get 2/3.

Answer: losing weight from 50lb to 40lb

Step-by-step explanation:

Answer:

50lb to 40lb

Step-by-step explanation:

When you multiply 50 lb to 40lb by 2, it makes 100 lb to 80 lb. 50lb to 40 lb is 20 percent change while 100 lb to 90 lb is 10 percent

Answer:

The final price is $ 22.68  And Proportional constant is 1.4  

Step-by-step explanation:

Given as :

The Original price = $ 16.20

The rate of increase = 40%

Let The final price = x

Now,

Final price after increase = initial price × ( 1 + [tex]\frac{\textrm Rate}{100}[/tex]

Or. Final price after increase = $ 16.20 × ( 1 + [tex]\frac{\textrm 40}{100}[/tex]

Or, Final price after increase = $ 16.20 × ( 1.4 )

∴ Final price after increase = $ 22.68

Now , Proportional constant = [tex]\frac{22.68}{16.20}[/tex]

I.e Proportional constant = 1.4

Hence The final price is $ 22.68  And Proportional constant is 1.4  Answer

Answer:

Part 40) [tex]y=-2x+9[/tex]

Part 41) [tex]y=5x+6[/tex]

Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Remember that

If two lines are parallel, then their slopes are the same

Part 40) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (4,1)

Given line y=-2x+7

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=-2[/tex]

step 2

Find the y-intercept b

we have

[tex]m=-2[/tex]

[tex](4,1)[/tex]

substitute in the linear equation

[tex]1=(-2)4+b[/tex]

solve for b

[tex]b=1+8[/tex]

[tex]b=9[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=-2[/tex]

[tex]b=9[/tex]

substitute

The equation of the line is

[tex]y=-2x+9[/tex]

Part 41) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (0,6)

Given line y=5x-3

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=5[/tex]

step 2

Find the y-intercept b

[tex]b=6[/tex] ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=5[/tex]

[tex]b=6[/tex]

substitute in the linear equation

[tex]y=5x+6[/tex]

Part 42) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (-5,-2)

Given line y=(2/3)x+1

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=\frac{2}{3}[/tex]

step 2

Find the y-intercept b

we have

[tex]m=\frac{2}{3}[/tex]

[tex](-5,-2)[/tex]

substitute in the linear equation

[tex]-2=(\frac{2}{3})(-5)+b[/tex]

solve for b

[tex]-2=-\frac{10}{3}+b[/tex]

[tex]b=-2+\frac{10}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=\frac{2}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

substitute

The equation of the line is

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Final answer:

To find the equation of a line that is parallel to a given line and passes through a specific point, use the fact that parallel lines have the same slope. Find the slope of the given line, substitute the slope and the point into the slope-intercept form of a line to find the y-intercept, and write the equation with the new slope and y-intercept.

Explanation:

To find the equation of a line that is parallel to a given line and passes through a specific point, we need to use the fact that parallel lines have the same slope. The given line, y = -2x + 7, has a slope of -2. So, the parallel line we need to find will also have a slope of -2.

Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope is -2 and the point (4,1) lies on the line, we can substitute these values into the equation to find the y-intercept:

y = -2x + b

1 = -2(4) + b

1 = -8 + b

b = 9

Therefore, the equation of the line that passes through (4,1) and is parallel to y = -2x + 7 is y = -2x + 9.

Answer:

[tex]17 + \frac{ - 18}{6} = 17 - 3 = 14[/tex]

The mean score on this test is 8.8, and the median score is 9.4.

In order to find the mean of the scores, we use the formula:

[tex]\[ \text{Mean} = \frac{\sum (X \cdot f)}{N} \][/tex]

where X is the score, f is the frequency, and N is the total number of scores. Applying this formula to the given data:

[tex]\[ \text{Mean} = \frac{(4 \cdot 1) + (5 \cdot 1) + (6 \cdot 1) + (7 \cdot 2) + (8 \cdot 1) + (9 \cdot 5) + (10 \cdot 5)}{1 + 1 + 1 + 2 + 1 + 5 + 5} \][/tex]

[tex]\[ \text{Mean} = \frac{4 + 5 + 6 + 14 + 8 + 45 + 50}{15} \][/tex]

Mean = [tex]\frac{132}{15}[/tex]

Mean = 8.8

So, the mean score is 8.8.

To find the median using the formula:

[tex]\[ \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times w \][/tex]

where:

- L is the lower class boundary of the median group,

- N is the total number of observations,

- F is the cumulative frequency of the group before the median group,

- f is the frequency of the median group,

- w is the width of the median group.

First, arrange the data and calculate cumulative frequencies:

Test Score  Frequency     Cumulative Frequency

3                    0                      0

4                      1                      1

5                      1                     2

6                       1                     3

7                       2                     5

8                       1                      6

9                       5                     11

10                     5                     16

The median position is [tex]\( \frac{N}{2} = \frac{16}{2} = 8 \)[/tex]  with a score of 9. The cumulative frequency before the median group is 6, and the frequency of the median group is 5.

Now, using the formula:

Median= 9 + [tex]\frac{8 - 6}{5} \times 1[/tex]

Median= 9 + [tex]\frac{2}{5}[/tex]

Median = 9 + 0.4

Median = 9.4

Therefore, the median score is 9.4.

Answer:

The sale price of a T-shirt is $24.

Step-by-step explanation:

1/4 off=25%=0.25

0.25*32=8

32-8=24

Answer:

He can spend $1363 for everything else.

Step-by-step explanation:

x+637<=2000

x<=2000-637

x<=1363

Answer:

300.407

Step-by-step explanation:

100*3=300

4*0.1=0.4

7*0.001=0.007

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

300+0.4+0.007

300.407

Answer:a total of 45 students per bus

Step-by-step explanation: 450-5= 445

445/10= 44.5

a total of 45 students per bus

Answer:

x=-1, y=-5. (-1, -5).

Step-by-step explanation:

y=-x-6

y=x-4

----------

-x-6=x-4

-x-x-6=-4

-2x-6=-4

-2x=-4+6

-2x=2

x=2/-2

x=-1

y=-1-4

y=-5

Answer:

Step-by-step explanation:

Hajdiabndodisba djdk

Answer:

x=8

Step-by-step explanation:

You divide both sides by 4 to get x alone.

Answer:

x = 8

Step-by-step explanation:

Answer: slope m = (y2 - y1)/(x2 - x1) so that  m = (2-(-1))/(5.3-4.5)

m = 3 / .8 = 3.75 or 15/4

Step-by-step explanation:

Answer:

[tex]A=10^0[/tex]

Step-by-step explanation:

Number 2.247 has 2 in ones place, 2 in tenths place, 4 in hundredths place and 7 in thousandths place.

This means you can rewrite this number as

[tex]2.247=2\times 1+2\times 0.1+4\times 0.01+7\times 0.001\\ \\2.247=2\times 10^0+2\times \dfrac{1}{10^1}+4\times \dfrac{1}{10^2}+7\times \dfrac{1}{10^3}[/tex]

So,

[tex]A=10^0\\ \\B=\dfrac{1}{10^1}\\ \\C=\dfrac{1}{10^2}\\ \\D=\dfrac{1}{10^3}[/tex]

Answer:

y=8.99+3

Step-by-step explanation:

we will make

x=how many large pizzas are sold

and a flat fee of $3 because they did delivery and do not pick it up them selves

so it would look like this

y=8.99x+3 to find the total cost

and it's not

y=8.99x-3 because they are not getting $3 dollars off their purchase!

Answer: Usually, a denominator should be bigger. If the numerator was bigger, it would make the fraction inproper, which you should convert into a mixed number.

Answer:denominator

Step-by-step explanation:

Answer:

y-2=2(x-6)

Step-by-step explanation:

y-y1=m(x-x1)

m=2

y-2=2(x-6)

Answer:

Twice.

Step-by-step explanation:

7 times 2 is 14.

So it can only go in 2x.

Answer:

Seven goes into 18 twice

Step-by-step explanation:

7×2=14

Answer:9 nickels and 19 dimes.

Step-by-step explanation:

Let [tex]n[/tex] be the number of nickels Kay has.

Let [tex]d[/tex] be the number of dimes Kay has.

Value of [tex]1[/tex] nickel is $[tex]0.05[/tex]

Value of [tex]n[/tex] nickels is $[tex]0.05n[/tex]

Value of [tex]1[/tex] dime is $[tex]0.1[/tex]

Value of [tex]d[/tex] nickels is $[tex]0.1dn[/tex]

Given that Kay has a total of [tex]28[/tex] coins.

So,[tex]n+d=28[/tex]                                                ...(i)

Given that Kay has a total value of $[tex]2.35[/tex]

So,[tex]0.05n+0.1d=2.35[/tex]                                 ...(ii)

Using (i) and (ii),

[tex]0.05n+0.1(28-n)=2.35\\0.05n+2.8-0.1n=2.35\\2.8-2.35=0.05n\\0.45=0.05n\\n=9[/tex]

[tex]d=28-n=28-9=19[/tex]

Answer:

[tex]\frac{x}{-3} =6\\x=-18[/tex]

x= -18

Answer: X = -18

Step-by-step explanation: In this problem, notice that x is being divided by -3 so to get x by itself, we need to multiply both sides of the equation by -3.

Notice that on the left side, the -3 and -3 cancel each other out so we're just left with x.

On the right side, we have 6 × -3 which is -18 so X = -18.

Finally, we can check our answer by plugging a -18 back into the original equation.

So we have -18 ÷ -3 = 6, which is a true statement which means that our answer is correct.

Image provided.

The only prime number that is a factor of 16 is 2, since 16 is a power of 2 (2⁴).

The student has asked to identify the only prime number that is a factor of 16. To find the factors of 16, we can break it down into its prime factors. The prime factorization of 16 is 2×4×4, which reduces further to 2×2×2×2 or 24. Since the prime factors of 16 are all 2s, the only prime number that is a factor of 16 is 2. It's important to note that a prime number is defined as a number that has exactly two distinct positive divisors: 1 and the number itself. In the case of 16, 2 is the only prime number that fits this definition and is a factor.

Answer:

Step-by-step explanation:

Answer:

Total bill=$51.75

Step-by-step explanation:

Step 1: Determine the cost of her meal

Cost of meal=$45

Step 2: Calculate the amount of the tip

Tip amount=15% of the cost of meal

where;

cost of meal=$45

replacing;

Tip amount=(15/100)×45=6.75

The tip amount=$6.75

Step 3: Total bill

The total bill can be expressed as;

Total bill=tip amount+subtotal

where;

tip amount=$6.75

cost of meal=$45

replacing;

Total bill=(45+6.75)=51.75

Total bill=$51.75

Answer:

40

Step-by-step explanation:

8 / (1/5)

When dividing fractions, the second fraction just flips upside down. Then you just multiply.

So it's now 8 * 5 = 40

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

[tex]x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})[/tex]

= [tex]35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1][/tex]

= [tex]35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)][/tex]

{Since sum of n natural numbers is given by [tex]\frac{1}{2} (n)(n + 1)[/tex]}

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

Answer:

J

Step-by-step explanation:

All of the other ones have a value of -5 except for J which has a value of 5.