A bathtub can hold a maximum of 50 gallons of water. Water can be drained out of the tub at a rate of 2 gallons per minute. If the tub is initially completely filled by a faucet at a rate of 1 gallon per minute, how long will it take to drain the full tub if the drain is opened but the faucet is kept on?

Answer:

Step-by-step explanation:

You know that 3 pennies are involved, because $0.68 cannot be made without them.

Then 6 coins must make up 65¢. If 1 is a quarter, then the remaining 40¢ must be made using 5 coins. 4 dimes is too few, and 8 nickels is too many. However 3 dimes and 2 nickels is just right.

Bobby gave the cashier 1 quarter, 3 dimes, 2 nickels, 3 pennies.

Answer:

0.65

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

In this problem we have

[tex]x=4+4+13+13=34[/tex]

because

total of three=4

total of jack=4

total of club=13

total of diamond=13

[tex]y=52\ cards[/tex]

substitute

[tex]P=\frac{34}{52}=0.65[/tex]

Answer:

  C = (7, 6)

Step-by-step explanation:

The problem statement tells us the relation between the points is ...

  (B-A)/(C-A) = 2/7

  7(B -A) = 2(C -A) . . . . . . multiply by 7(C-A)

  7B -7A +2A = 2C . . . . . add 2A

  C = (7B -5A)/2 . . . . . . . divide by 2

  C = (7(2, -4) -5(0, -8))/2 = (14, 12)/2 . . . . . fill in the values of A and B

  C = (7, 6)

Answer:

Part a) 30+m

Part b) $36

Step-by-step explanation:

Part a) Identify an expression that represents the amount Susan spent on the fruits

The complete question in the attached figure

Let

m ------> the number of apples

n -----> the number of oranges

q ----> the amount Susan spent on the fruits

we know that

m+n=15 ----> (in total she needs 15 fruits)

n=15-m -----> equation A

q=3m+2n ----> equation B

Substitute equation A in equation B

q=3m+2(15-m)

q=3m+30-2m

q=30+m -----> expression that represents the amount Susan spent on the fruits

Part b) Identify the amount she spent if she bought 6 apples

we know that

If m=6 apples

substitute the value of m in the expression of Part a)

q=30+m -----> q=30+6=$36

The money that club make $ 639.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

The Spanish club began the year with $15.00 in its account.

At the end the club had = $654. 75

so, the Club earned

= 654. 75- 15

= 639.75

Hence, the money club make $ 639.75

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Answer:

  15 cups

Step-by-step explanation:

To make 15 lattes, Charles will triple his recipe, so use 3×5 = 15 cups of milk.

Answer:

  $300

Step-by-step explanation:

30% of $1000 is ...

  0.30 × $1000 = $300

Answer:

$300

Step-by-step explanation:

If there is a 30% reserve requirement on a $1,000 deposit, there must be $300 set aside as a member bank reserve.

30% of $1000 = $300

Answer:  [tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Given : An opaque bag contains 5 green marbles, 3 blue marbles and 2 red marbles.

Total marbles = 5+3+2=10

Now, if it given that the a red marble is already drawn, then the total marbles left in the bag = 10-1=9

But the number of blue marbles remains the same.

Now, the probability of drawing a blue marble given the first marble was red :-

[tex]=\dfrac{\text{Number of blue marbles}}{\text{Total marbles left}}\\\\=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Hence, the required probability = [tex]\dfrac{1}{3}[/tex]

Answer:

C

Step-by-step explanation:

Answer:

The answer to your question is: 16x + 3

Step-by-step explanation:

Step 1 :      f(x) = 8x² + 3x

                f(x +h) =  8(x + h)² + 3( x + h)

                f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

                f (x + h) = 8x² + 16xh + 8h² + 3x + 3h

Step 2 f(x+h) - f(x) =  8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

                              = 8x² + 16xh + 8h² + 3x + 3h - 8x² -3x

                              = 16xh + 8h² + 3 h

Step 3 f(x + h) - f(x)/ h = h(16x + 8h + 3) /h

                                    = 16x + 8h + 3

Step 4 lim  f(x + h) - f(x)/ h = lim 16x + 8h + 3  = lim 16x + 8(0) + 3 = 16x + 3

        h ⇒0                           h ⇒0                     h ⇒0

Here, we are required to find the slope of the tangent line to the graph of the given function at any point.

The correct answer is 16x + 3.

The four step process to find the slope of the tangent line to the graph at any point is as follows;

First step (1):

f(x +h) = 8(x + h)² + 3( x + h) and yields;

f(x + h) = 8( x² + 2xh + h²) + 3( x + h)

and, f (x + h) = 8x² + 16xh + 8h² + 3x + 3h.

Second step(2):

F(x+h) - f(x) = 8x² + 16xh + 8h² + 3x + 3h - ( 8x² + 3x)

and, F(x+h) - f(x) = 16xh + 8h² + 3 h

Third step (3):

{F(x+h) - f(x)} / h = (16xh)/h + (8h²)/h + (3 h)/h

This in turn yields;

{F(x+h) - f(x)} / h = 16x + 8h + 3.

Fourth step(4):

lim f(x + h) - f(x)/ h =

h=>0

lim 16x + 8h + 3 = lim 16x + 8(0) + 3 = 16x + 3

h=>0. h=>0

Therefore, the slope of the tangent line to the graph of the given function at any point is;

16x + 3.

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Answer:

y = 2x - 1

Step-by-step explanation:

Note the difference between consecutive terms of y are constant, that is

1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 9 - 7 = 2

Thus the equation is of the form y = 2x ± c ← c is a constant

Substitute values of x to determine the required value of c

x = 0 : 2 × 0 = 0 ← require to subtract 1 for y = - 1

x = 1 : 2 × 1 = 2 ← require to subtract 1 for y = 1

x = 2 : 2 × 2 = 4 ← require to subtract 1 for y = 3, and so on

Thus the required equation is

y = 2x - 1

Answer:

Step-by-step explanation:

From the problem statement, we can setup the following equation:

[tex]125,000 = 45,000 + 125E[/tex]

where [tex]E[/tex] is the number of employees being trained.

Solving for [tex]E[/tex] will give us the answer:

[tex]125,000 = 45,000 + 125E[/tex]

[tex]80,000 = 125E[/tex]

[tex]E = 640[/tex]

[tex]\text{Hello there!}\\\\\text{The most that they can spend is \$125,000}\\\\\text{We know that the fixed cost of the program is \$45000}\\\\\text{They also need to pay \$125 for each employee}\\\\\text{We need to solve:}\\\\125000-45000=80000\\\\\text{Now divide 80,000 by 125 to see how many employees they can train}\\\\80000\div125=640\\\\\boxed{\text{They can train 640 employees}}[/tex]

The best approximation of the solution is represented by the ordered pair, (0.7,-1.5), the correct option is C.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The system of equations are equations that have a common solution.

The equations are:

y = 2x-3

y = -5x +2

The ordered pair that is the best approximation of the solution is the point at which for a given value of x, the system of the equation has the same y value.

From the table, it can be seen that for x = 0.7, the y value for both the equation is similar, -1.5 and -1.6.

Therefore, (0.7, -1.5).

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Answer:

The horizontal speed of the truck is 102.39 km/hr.

Step-by-step explanation:

Given that,

Speed of airplane = 125 km/h

Angle = 35°

We need to calculate the horizontal speed

Using formula of horizontal speed

[tex]u_{x}=u\cos\theta[/tex]

Where, u = speed

Put the value into the formula

[tex]u_{x}=125\times\cos35^{\circ}[/tex]

[tex]u_{x}=102.39\ km/hr[/tex]

Hence, The horizontal speed of the truck is 102.39 km/hr.

Answer:

v = 102.4 km/h

Step-by-step explanation:

Given:-

- The speed of the airplane, u = 125 km/h

- the angle the airplane makes with the ground, θ = 35°

Find:-

How fast must a truck travel to stay beneath an airplane?

Solution:-

- For the truck to be beneath the airplane at all times it must travel with s projection of airplane speed onto the ground.

- We can determine the projected speed of the airplane by making a velocity (right angle triangle).

- The Hypotenuse will denote the speed of the airplane which is at angle of θ from the truck travelling on the ground with speed v.

- Using trigonometric ratios we can determine the speed v of the truck.

                                  v = u*cos ( θ )

                                  v = (125 km/h) * cos ( 35° )

                                  v = 102.4 km/h

- The truck must travel at the speed of 102.4 km/h relative to ground to be directly beneath the airplane.

By the law of total probability,

[tex]P(A\cap B)=P[(A\cap B)\cap C]+P[(A\cap B)\cap C'][/tex]

but the events A, B, and C are mutually independent, so

[tex]P(A\cap B)=P(A)P(B)[/tex]

and the above reduces to

[tex]P(A)P(B)=P(A)P(B)P(C)+P(A\cap B\cap C')\implies P(A\cap B\cap C')=P(A)P(B)(1-P(C))=P(A)P(B)P(C')[/tex]

which is to say A, B, and C's complement are also mutually independent, and so

[tex]P(A\cap B\cap C')=0.5\cdot0.8\cdot(1-0.3)=0.12[/tex]

By a similar analysis,

[tex]P(A\cap B'\cap C)=P(A)P(B')P(C)=0.03[/tex]

[tex]P(A'\cap B\cap C)=P(A')P(B)P(C)=0.12[/tex]

These events are mutually exclusive (i.e. if A and B occur and C does not, then there is no over lap with the event of A and C, but not B, occurring), so we add the probabilities together to get 0.27.

Final answer:

The probability that exactly two of the independent events A, B, and C occur is 0.43, calculated by adding the probabilities of each possible pair of events occurring while the third does not.

Explanation:

The student is seeking the probability that exactly two out of the three events A, B, and C occur given their individual probabilities P(A) = 0.5, P(B) = 0.8, and P(C) = 0.3, and the fact that they are mutually independent events. To find this, we ned to consider the three scenarios where exactly two events occur: A and B, A and C, and B and C. The probability for each scenario is found by multiplying the probabilities of the two events occurring and then multiplying by the probability of the third event not occurring.

For example, the probability of A and B both occurring but not C is P(A) × P(B) × (1 - P(C)). To find the total probability that exactly two events occur, we sum up the probabilities of all three scenarios:

P(A and B but not C) = P(A) × P(B) × (1 - P(C))

P(A and C but not B) = P(A) × (1 - P(B)) × P(C)

P(B and C but not A) = (1 - P(A)) × P(B) × P(C)

We then calculate and sum these probabilities:

P(A and B but not C) = 0.5 × 0.8 × (1 - 0.3) = 0.5 × 0.8 × 0.7 = 0.28

P(A and C but not B) = 0.5 × (1 - 0.8) × 0.3 = 0.5 × 0.2 × 0.3 = 0.03

P(B and C but not A) = (1 - 0.5) × 0.8 × 0.3 = 0.5 × 0.8 × 0.3 = 0.12

Adding these probabilities together provides the final answer:

Σ P(exactly two events) = 0.28 + 0.03 + 0.12 = 0.43

Therefore, the probability that exactly two of the events A, B, and C occur is 0.43.

Answer:

The fraction of the area of ACIG represented by the shaped region is 7/18

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

In the square ABED find the length side of the square

we know that

AB=BE=ED=AD

The area of s square is

[tex]A=b^{2}[/tex]

where b is the length side of the square

we have

[tex]A=49\ units^2[/tex]

substitute

[tex]49=b^{2}[/tex]

[tex]b=7\ units[/tex]

therefore

[tex]AB=BE=ED=AD=7\ units[/tex]

step 2

Find the area of ACIG

The area of rectangle ACIG is equal to

[tex]A=(AC)(AG)[/tex]

substitute the given values

[tex]A=(9)(10)=90\ units^2[/tex]

step 3

Find the area of shaded rectangle DEHG

The area of rectangle DEHG is equal to

[tex]A=(DE)(DG)[/tex]

we have

[tex]DE=7\ units[/tex]

[tex]DG=AG-AD=9-7=2\ units[/tex]

substitute

[tex]A=(7)(2)=14\ units^2[/tex]

step 4

Find the area of shaded rectangle BCFE

The area of rectangle BCFE is equal to

[tex]A=(EF)(CF)[/tex]

we have

[tex]EF=AC-AB=10-7=3\ units[/tex]

[tex]CF=BE=7\ units[/tex]

substitute

[tex]A=(3)(7)=21\ units^2[/tex]

step 5

sum the shaded areas

[tex]14+21=35\ units^2[/tex]

step 6

Divide the area of  of the shaded region by the area of ACIG

[tex]\frac{35}{90}[/tex]

Simplify

Divide by 5 both numerator and denominator

[tex]\frac{7}{18}[/tex]

therefore

The fraction of the area of ACIG represented by the shaped region is 7/18

Answer:

  20 ft

Step-by-step explanation:

The tree's shadow is 34/8.5 = 4 times the length of the person's shadow, so the tree is 4 times a tall as the person:

  4×5 ft = 20 ft . . . . . the height of the tree

_____

Shadow lengths are proportional to the height of the object casting the shadow.

Using the ratio given from the shadow of the 5-foot person, we set up a proportion and solve for the height of the tree, which is 20 feet.

The question is asking about the height of a tree, which can be figured out through a method called similar triangles in geometry. In this case, Phil, Melissa, Noah, and Olivia observed a 5-foot tall person casting an 8.5-foot shadow and a tall tree casting a 34-foot shadow.

From this, we can set up a proportion to find out the height of the tree. This would look like 5/8.5 = x/34, where x is the height of the tree. Cross multiplying and solving for x gives us x = (5*34)/8.5, which equals to 20 feet. Therefore, the height of the tree is 20 feet.

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Answer:

  (x, y, z) = (1-z, z, z) . . . . . . . an infinite number of solutions

Step-by-step explanation:

Use the first equation to substitute for x in the remaining two equations.

  (-5y +4z +1) -2y +3z = 1 . . . . substitute for x in the second equation

  -7y +7z = 0 . . . . . . . . . . . . . . simplify, subtract 1

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

__

  2(-5y +4z +1) +3y -z = 2 . . . . substitute for x in the third equation

  -7y +7z = 0 . . . . . . . . . . . . . . subtract 2; collect terms

  y = z . . . . . . . . . . . . . . . . . . . . divide by -7; add z

This is a dependent set of equations, so has an infinite number of solutions. Effectively, they are ...

  x = 1 -z

  y = z

  z is a "free variable"

Answer:

  (a) |s - x| ≤ 3/16

  (b) 4 15/16 ≤ x ≤ 5 5/16

Step-by-step explanation:

(a) The absolute value of the difference from spec must be no greater than than the allowed tolerance:

  |s - x| ≤ 3/16

__

(b) Put 5 1/8 for s in the above equation and solve.

  |5 1/8 - x| ≤ 3/16

  -3/16 ≤ 5 1/8 -x ≤ 3/16

  3/16 ≥ x -5 1/8 ≥ -3/16 . . . . multiply by -1 to get positive x

  5 5/16 ≥ x ≥ 4 15/16 . . . . . . add 5 1/8

Pieces may be between 4 15/16 and 5 5/16 inches in length.

An absolute value inequality can be used to represent the acceptable range of lengths for a piece of wood in a woodshop class. For a specified length of 5 1/8 inches, the acceptable lengths for the piece would be between 4 15/16 inches and 5 5/16 inches.

Your task in woodshop class is to cut pieces of wood to within 3/16 inch of the teacher's specifications. The difference between the specification s and the measured length x of a cut piece is represented by (s-x).

(a) You can represent this situation with the absolute value inequality |s - x| ≤ 3/16, which shows that the difference between the specification and the measured length must be less than or equal to 3/16 inch.

(b) If the length of one piece is specified to be s = 5 1/8 inches, you can substitute that value into the inequality to find the acceptable range of lengths: |5 1/8 - x| ≤ 3/16. Solving the inequality gives you the range 5 - 3/16 inches ≤ x ≤ 5 + 3/16 inches, or between 4 15/16 inches and 5 5/16 inches.

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Answer:

  The line of reflection is at y = x+6.

Step-by-step explanation:

The perpendicular bisector of AA' is a line with slope 1 through the midpoint of AA', which is (-4, 2). In point-slope form, the equation is ...

  y = 1(x +4) +2

  y = x + 6 . . . . . . . line of reflection

Answer:

Step-by-step explanation:

Given that When n is divided by 21, the remainder is an odd number.

i.e. [tex]n=21m+k[/tex] where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

[tex]n=28c+3[/tex], where c is a positive integer

This can be written as

[tex]n=4(7c)+3\\n=7(4c)+3[/tex]

Since n is giving odd remainder when divided by 21,

we get r =3 as n is a multiple of 7 +3

Answer:

The answer to your question is:  The last option is correct

Step-by-step explanation:

Just remember thta when we divide by a negative number, the inequality changes, then,

                            - 125 ≥ -135      divide by -5

                              25  ≤ 27

Answer:

25 < 27 not 25 ≤ 27

Step-by-step explanation:

-125 ≥ -135

on the number, you count through -125 before -135, so -125 is greater but not equal to -135.

-125/ -5  > -135/ -5

= 25 < 27

25 is less than 27. They are not equal.

The opportunity cost of Susan attending college for a year is $51,400 ($11,400 of actual college expenses and $40,000 of foregone income from her previous job).

The opportunity cost of attending college is determined not only by the actual expenditure but also by the income you forgo by not working. In Susan's case, her actual expenses include $8,000 for tuition, $900 for books, and $2,500 for food, which total to $11,400. However, since she quit her $40,000 a year job to attend college, that lost income is also part of her opportunity cost. So, we add the lost income to her college expenses to get the total opportunity cost. Therefore, the opportunity cost of Susan attending college for the year would be $51,400 ($40,000 + $11,400).

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Answer:

l = 10.5 cm and A = 21 cm2

Step-by-step explanation:

Area is w*l

Perimeter is 2(w+l)

Replacing the information known in the problem you can get the length with the perimeter

P = 2(w+l)

25 = 2(2+l)

12.5 = 2 + l

10.5 cm = l

with the length now you can find the area

A = w*l

A = 2*10.5

A = 21 cm2

Answer:

y=-8(x+6)

Step-by-step explanation:

The equation of a line is [tex]y=mx+b[/tex] where m is the pending and b is the y intercept,

First we are going to calculate m:

If you have two points [tex]A=(x_{1},y_{1})\\B=(x_{2},y_{2})[/tex],

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case we have A=(-5,-8) and B=(-7,8)

[tex]x_1=-5, y_1=-8\\x_2=-7,y_2=8[/tex]

Replacing in the formula:

[tex]m=\frac{8-(-8)}{(-7)-(-5)}\\\\m=\frac{16}{-2} \\\\m=-8[/tex]

Then [tex]y=-8x+b[/tex].

We have to find b, we can find it replacing either of the points in [tex]y=-8x+b[/tex]:

Replacing the point (-5,-8):

[tex]y=-8x+b\\-8=-8.(-5)+b\\-8=40+b\\-8-40=b\\-48=b[/tex]

Or replacing the point (-7,8):

[tex]y=-8x+b\\8=-8.(-7)+b\\8=56+b\\8-56=b\\-48=b[/tex]

The answer is the same with both points.

Then we have:

y=-8x-48

y=-8(x+6)

Answer:

  225%

Step-by-step explanation:

You can figure the percentage change from ...

  percentage change = ((new value)/(old value) -1) × 100%

  = (26/8 -1) × 100% = (3.25 -1) × 100% = 225%

Because there are 4 inside angles the sum of the four angles must equal 360 degrees.

Add the angles to equal 360:

4x + 3x + 2x + 3x = 360

Simplify:

12x = 360

Solve for x by dividing both sides by 12:

x = 360 /12

x = 30

Now you have x, solve for each angle:

ABC = 4x = 4 x 30 = 120 degrees.

BCD = 3x = 3 x 30 = 90 degrees.

CDA = 2x = 2x 30 = 60 degrees.

DAB = 3x = 3 x 30 = 90 degrees.

C. It's important to know that a four sides figure needs the inside angles when added together need to equal 360 degrees.

Good morning ☕️

____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)