Keith has $500 in a saving account at the beginning of the summer. He wants to have at
least $200 in the account. He withdraws $25 from his account each week for food,
clothes, and movie tickets. ("Withdraws" means he takes money out of his account.)
How many weeks can he withdraw $25 per week and still have at least $200 in the
account?


There’s a second question to this problem:
How many weeks can Keith withdraw $25 per week and still have at least $200 in the account? Write your answer in interval notation.

Answer:

let's define:

x = number of dimes

y = number of quarters.

Then the total amount of money that he has is:

x*$0.10 + y*$0.25

Now we know that:

"He has no more than 24 coins"

Then:

x + y ≤ 24

"...worth at least $3.50 combined"

x*$0.10 + y*$0.25 ≥ $3.50

Then we have two inequalities:

x + y ≤ 24

x*$0.10 + y*$0.25 ≥ $3.50

To graph these, it is easier to write them as linear equations in the slope-intercept form.

Then we need to isolate the y-variable in both equations.

we will get:

y ≤ 24 - x

y ≥ $3.50/$0.25 - x*$0.10/$0.25

In the first equation we have:

"y is smaller or equal than the line"

Then this is graphed with a solid line, and we shade all the region below the line

For the second equation, we have the inverse case, then it will be graphed with a solid line and we need to shade all the region above the line.

The solutions for the system will be all these values that are in both shaded regions.

The graph can be seen below.

In the graph, we can see that one acceptable solution can be:

x = 5

y = 15

or

x = 6

y = 16

The only other restriction we should add is:

x ≥ 0

y ≥ 0

Because Lincoln can not have a negative number of coins, so we can only find solutions in the first quadrant.

Answer:

16.79 %

Step-by-step explanation:

hythjuuhhhjuhhhh

Step-by-step explanation:

Head opposite angles

2x= 3x-42

x= 42°

the angles are 84°

Each of the pairs of opposite angles made by two intersecting lines is called a pair of vertical angles. The value of x is 42 and the measure of the two given angles is 84° each.

Each of the pairs of opposite angles made by two intersecting lines is called a pair of vertical angles.

The two of the given angles are vertically opposite angles, therefore, the measure of the two given angles will be the same.

(2x)° = (3x - 42)°

2x = 3x - 42

Subtract 2x from both sides of the equation and add 42 to both sides of the equation,

2x - 2x + 42 = 3x - 42 - 2x + 42

42 = 3x - 2x - 42 + 42

42 = x

Therefore, the value of x is 42. Now, the measure of each angle can be written as,

(2x)° = 2(42) = 84°

(3x - 42)° = 3(42) - 42 = 84°

Hence, the value of x is 42 and the measure of the two given angles is 84° each.

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Answer:

ultiply by 2 and then add 2

Step-by-step explanation:

....hi

Answer:

9x

Step-by-step explanation:

hshdhdhdxhhxhxhxhxhxhxhxhhxhxhxhhx

Answer:

9x or 15x

Step-by-step explanation:

-3x + 12x = 9x

-3 + 12 = 9,

or if you just straight out add

-3x + 12x = 15x

Answer:

184.26

Step-by-step explanation:

28.275 + 60 + 96 = 184.26

The fractional form is 7/10.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have to divide 7 by 10.

The common factor for 7 and 10

7 = 7 x 1

and, 10= 2 x 5 x 1

so, there is only one factor common is 1.

Thus, the fraction is 7/10.

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Answer:

none/0

Step-by-step explanation:

they ate all the cake.

now harry is gonna get sick

Answer:

79/79 or 1

Step-by-step explanation:

47+14+10+8=79

If Harry, Jack, Dave, and Mary all ate 79 slices in total, then there would be no more cake left since there are only 79 slices. The fraction answer would be 79/79 or 1, because they 79/79 is equivalent to 1.

Answer:

radius =3cm

volume of the sphere =4/3 πr^3

=4/3*22/7*3*3*3=88/7*3*3=88/7*9=792/7

=113.1cm^3

Answer:

787.5

Step-by-step explanation:

23×14=322

A=a+b /2h=15+34 /2·19=465.5

322+465.5=787.5

Answer:

The scatter plot would closely resemble a straight line with a positive slope, but causation  cannot be determined.

Step-by-step explanation:

Recall that causation and correlation are 2 different things. Say Taller people usually had a name that started with the letter “A” It's a correlation, but a name does not determine the height, so it's not causation. (I took the test and got it right too.)

The data has a strong, negative correlation, and a causal relationship exists between the team playing at home and winning would be imply about the football team winning at home.

It is an index that measures correlation between two variables, assuming values between -1 and 1.

If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

It also is the slope of the line of best fit.

The number of wins for a high school football team is measured for the season. When the team plays at home, it is generally believed that they will win.

Comparing the location of the game and the number of wins, a correlation coefficient of 0.891 is calculated.

The scatter plot would closely resemble a straight line with a negative slope. The data has a strong, negative correlation, and a causal relationship exists between the team playing at home and winning.

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Answer:

In a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability p(x), and then adding all these products together, giving. .

Step-by-step explanation:

I really hope this helps have a wonderful day

Answer:

38.5

Step-by-step explanation:

First do 77/2 then you get 38.5, if anything is wrong please tell me!!

Answer: 16cm

Step-by-step explanation:

The radius is half of the diameter so you would have to double the radius.

Answer:

16cm

Step-by-step explanation:

The diameter of a circle is double the radius, so if a circle has a radius of 8cm, it has a diameter of 16cm because that's double 8cm.

Answer:

-50 m

Step-by-step explanation:

its negative elevation because he is going down

Answers that equivalent to the expression 2x+3x+8-3x-2 would be the choices A and C. If you notice, in choice A, you have just combined all the like terms which results in 2x+6 and in Choice C, you have combined all your constants and the the two terms 2x and 3x resulting in 5x-3x+6 which all remain equivalent to he original given expression

Answer:

2x(x+3)(x-3)

Step-by-step explanation:

Answer:

4 pencils

Step-by-step explanation:

Note=  pencils costing 0. 90p

Given data

Balance= £10

pen= 3*1.45= £4.35

pencils=0.90p

change= £2.05

2.05= 10-4.35-90p

solve for p

2.05= 5.65-90p

collect like terms

5.65-2.05= 0.90p

3.6=90p

divide both sides by 90

p=3.6/0.90

p=4

Answer:

2 × 2 × 3 × 3 × 3

Answer:

2A=A+A

Step-by-step explanation:

2A=A*A, not A+A

Answer:

28,000

Step-by-step explanation:

Answer:

28,000

Step-by-step explanation:

if u multiply 6,827 by 4 u get 27,303  and 208, 000 is way off so is 240, 000 24,000 is off by 3,303 and 28, 000 is off by 697. so it's 28,000.

The total weight of the grain purchase is 5.5 tons when grain trader buys the following amounts from three suppliers: 3,200 pounds, 7,200 pounds and 600 pounds.

To find the total weight of the grain purchase in tons, we need to convert the weight from pounds to tons and then sum them up.

Given the weights from the three suppliers:

Supplier 1: 3,200 pounds

Supplier 2: 7,200 pounds

Supplier 3: 600 pounds

To convert pounds to tons, we divide the weight in pounds by the conversion factor of 2,000 (since there are 2,000 pounds in a ton).

Supplier 1's weight in tons: 3,200 pounds / 2,000 = 1.6 tons

Supplier 2's weight in tons: 7,200 pounds / 2,000 = 3.6 tons

Supplier 3's weight in tons: 600 pounds / 2,000 = 0.3 tons

Now, we can calculate the total weight by summing up the weights from each supplier:

Total weight in tons: 1.6 tons + 3.6 tons + 0.3 tons = 5.5 tons

Therefore, the total weight of the grain purchase is 5.5 tons.

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Answer:

c= -2

Step-by-step explanation:

Answer: 100,000,000,000,000

Step-by-step explanation:

1.0 x 10^14

since the exponent is positive that means we move the decimal to the right 14 times and you should get 100000000000000.0

Answer:

The equation is a contradiction: it has no solutions

Step-by-step explanation:

5(+2)−6(2−)=+10(+1)

5(x+2)−6(2−x)=x+10(x+1)5(x+2)-6(2-x)=x+10(x+1)5(x+2)−6(2−x)=x+10(x+1)

Solve

Distribute

5(+2)−6(2−)=+10(+1)

5+10−6(2−)=+10(+1)

Rearrange terms

Distribute

Subtract the numbers

Combine like terms

Distribute

Combine like terms

Add

2 to both sides of the equation

Simplify

Subtract 11 from both sides of the equation

Simplify

Result

0=12

Answer:

x = -11  (sorry if this is wrong)

Step-by-step explanation:

5(x+2)-6(2-x)=10(x+1)

5x +10 -12x + 6x = 10x + 10

-1x + 10 = 10x + 10

-10x        -10x

-11x + 10 = 10

        -10    -10

-11x = 0

----    ----

-11     -11

x = -11

Answer:

12565.11 teeth approximately cut cross the cutting surface per seconds.

Step-by-step explanation:

Since the diameter is 10inches, the circumference of the arm saw is 10π (circumference is πd where d is diameter).

The number of teeth on the cutting blade can be gotten by multiplying the diameter by 12 since we have 12 teeth per inch on the arm saw

Number of teeth on saw = 12 x 10π = 120π.

To get the number of teeth that cross the cutting surface in 2000rpm we multiple it by the total number of teeth in just one rpm.

So we have 2000 x 120π. But since we are asked to find it in revolution per seconds then 2000r/m = 2000r/60s ≈ 33.33

Therefore, we have

33.33 x 120π ≈ 12565.11 teeth

Answer:

Step-by-step explanation:

x=5

y=-5

Hence it lies in 4th quadrant.

x=r cos θ

5=r cos θ  ...(1)

y=r sin θ

-5 =r sin θ  ... (2)

square and add

(5)²+(-5)²=r²(sin ²θ  +cos ²θ  )

r²=25+25=50

r=±5√2

dividing

tan θ=-5/5=-1=-tan 45°=tan (180-45),tan(360-45)

θ=135°,315°

so polar coordinates are (5√2,315°) and (-5√2,135°)