Mike practices the cello every 5 days and the piano every 13 days. Mike practiced both the piano and the cello today. How many days will pass before he practices them both on the same day again?​

Answer:

A line parallel to this line will have slope 4/5.

Step-by-step explanation:

2 parallel lines will have the same slope.

y = mx + c is the general form of the slope-intercept formula of a line, the slope is given by m.

y = 4/5 x - 3

-we see by comparing the 2 equations that the slope of this line (m) is 4/5.

Final answer:

The slope of a line parallel to the one given by the equation y = 4/5x - 3 is 4/5. This maintains the definition that parallel lines have identical slopes.

Explanation:

The slope of a line that is parallel to the line represented by the equation y = 4/5x - 3 is 4/5. This is because parallel lines have the same slope. In the context of algebra and straight lines, the slope of a line is a measure of its steepness, commonly identified as 'm' in the slope-intercept form y = mx + b, where 'b' is the y-intercept. Each of the provided figures and examples illustrate that the slope of a straight line remains constant regardless of other changes.

Looking specifically at the equation y = 4/5x - 3, this is in slope-intercept form where the coefficient of 'x' is the slope, which is 4/5. Therefore, any parallel line would have the same slope of 4/5.

Let [tex]x[/tex] be the amount (in L) of the 40% solution to be used, and [tex]y[/tex] the amount (L) of the 20% solution. The chemist wants a new solution of 50 L, so that

[tex]x+y=50[/tex]

Each L of the 40% solution contributes 0.4 L of salt, while each L of the 20% solution contributes 0.2. The new solution should have a concentration of 25% salt, so that

[tex]0.4x+0.2y=0.25(x+y)=12.5[/tex]

Now

[tex]x+y=50\implies y=50-x[/tex]

[tex]0.4x+0.2y=12.5\implies0.4x+0.2(50-x)=12.5\implies0.2x=2.5[/tex]

[tex]\implies\boxed{x=12.5}\implies\boxed{y=37.5}[/tex]

To make a 50 L solution containing 25% salt, the chemist should use 25 L of the 40% salt solution and 0 L of the 20% salt solution.

To solve this problem, we can use the method of mixing solutions. Let x represent the amount of the 40% salt solution used, and 50-x represent the amount of the 20% salt solution used. The amount of salt in the 40% solution is 0.4x, and the amount of salt in the 20% solution is 0.2(50-x). Since the new solution will contain 25% salt, the amount of salt in the new solution is 0.25(50). Setting up an equation, we have:

Simplifying the equation, we get:

The chemist should use 25 L of the 40% salt solution and 25 - 25 = 0 L of the 20% salt solution to make 50 L of the new solution containing 25% salt.

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The absolute value of  I-32I = 32

For given question,

We need to find the absolute value of -32

We know that, for any number 'a',

the absolute value of a is |a| = a (positive value)

|-32| = 32

Therefore,  the absolute value of  I-32I = 32

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Answer:

Difference = 2.25°

Step-by-step explanation:

Here we are given that at depth the Temperature T is inversely proportional to the depth x.

[tex]T[/tex] ∝ [tex]\frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{x}[/tex]

Where 4500 is constant

Now we have to find the difference in the temperature at 1200 mts and 3750 mts

1. x=1200

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{1200}[/tex]

[tex]T= 3.75[/tex]

2. x=3750

[tex]T= 4500 \times \frac{1}{x}[/tex]

[tex]T= 4500 \times \frac{1}{3750}[/tex]

[tex]T=1.2[/tex]

Hence Difference is

T = 3.75 -1.20

= 2.25

Therefore The difference of the temperature at 1200 mts and 3750 mts is T=2.25°

[tex]\bf \begin{cases} f(x)=&x^2+3\\\\ g(x)=&\cfrac{x+2}{x}\\\\ (f\circ g)(x)=&f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(2)=\cfrac{(2)+2}{(2)}\implies g(2)=\cfrac{4}{2}\implies g(2)=\boxed{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{x=2}{f(~~g(2)~~)}=\left( \boxed{2} \right)^2+3\implies f(~~g(2)~~)=4+3\implies \stackrel{(f\circ g)(2)}{f(~~g(2)~~)}=7[/tex]

Answer:

y=3

Step-by-step explanation:

Lets make y the subject of the equation by bringing the like terms together through mathematical operations.

10=2y+4

2y=10-4

2y=6

y=3

Answer:

15/8

Step-by-step explanation:

for 1 batch=5/2 pounds

for 3/4 batch=[5/2]×(3/4)

Answer: Michael will need 15/8 pounds of apples.

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the amount of apples that a batch of applesauce needs (2 1/2) by the number of batches of applesauce that Michael wants to make (3/4).

Mathematically speaking;

2 1/2 x 3/4 = ([2x2+1] / 2 ) x 3/4 = 5/2 x 3/4 = (5x3) / (2x4) = 15/8  

He will need 15/8 pounds of apples.

Answer:

Option a) Hyperbola

Step-by-step explanation:

The number of mice in the field after 1 year is 221 mice.

Given data:

If the population of mice in the field grows exponentially, we can use the exponential growth formula to determine the future population.

The exponential growth formula is given by:

P(t) = P₀ * e^(kt)

Where:

P(t) is the population at time t,

P₀ is the initial population,

e is Euler's number (approximately 2.71828), and

k is the growth rate.

So, the initial population (P₀) is 3 mice, and after five months, the population (P(t)) is 18 mice.

18 = 3 * e^(5k)

Dividing both sides by 3, we get:

6 = e^(5k)

To solve for k, we can take the natural logarithm (ln) of both sides:

ln(6) = 5k

k = ln(6) / 5 ≈ 0.35835

So, the growth rate is k = 0.3583

Now that we have the growth rate, determine the population after 1 year (12 months).
Substituting the values into the formula:

P(12) = 3 * e^(0.35835 * 12)

Calculating this expression, we find:

P(12) ≈ 3 * e^(4.3) ≈ 3 * 73.699 ≈ 221.09

Hence, it is expected that there will be approximately 221 mice in the field after 1 year if the population grows exponentially.

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Final Answer:

After 1 year, the field is expected to have approximately 221 mice.

Explanation:

To solve this exponential growth problem, we'll use the exponential growth formula:
[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population at time t,
- [tex]\( P_0 \)[/tex] is the initial population size,
- r is the growth rate,
- e is Euler's number (approximately 2.71828),
- t is the time in consistent units.
We need to find the growth rate r using the information that we have (the initial population [tex]\( P_0 \)[/tex] is 3, and after 5 months,[tex]\( P(5) \)[/tex] is 18). Then, we'll calculate the population after 1 year (12 months).
Let's apply the given values to the formula at t = 5 months:
[tex]\[ 18 = 3 \times e^{5r} \][/tex]
Now we need to solve for r. We start by dividing both sides of the equation by 3:
[tex]\[ 6 = e^{5r} \][/tex]
Next, we take the natural logarithm (ln) of both sides to solve for r. The natural logarithm of [tex]\( e^{5r} \)[/tex] is equal to 5r:
[tex]\[ \ln(6) = 5r \][/tex]
Now we divide by 5:
[tex]\[ \frac{\ln(6)}{5} = r \][/tex]
We can use a calculator to find r. The natural logarithm of 6 is approximately 1.79176, so:
[tex]\[ r = \frac{1.79176}{5} \\\\\[ r \approx 0.358352 \][/tex]

Now that we have the monthly growth rate r, we can use it to find the population after 12 months. Plugging r, [tex]\( P_0 \)[/tex], and t = 12  months into the exponential growth formula, we get:
[tex]\[ P(12) = 3 \times e^{0.358352 \times 12} \][/tex]
Using a calculator, we compute the value of [tex]\( e^{0.358352 \times 12} \)[/tex], which is approximately [tex]\( e^{4.300224} \)[/tex].
[tex]\[ P(12) = 3 \times e^{4.300224} \][/tex]
Using a calculator to find [tex]\( e^{4.300224} \)[/tex], we get a value of approximately 73.699.
[tex]\[ P(12) = 3 \times 73.699 \\\\\[ P(12) \approx 221.097 \][/tex]
Since we can't have a fraction of a mouse, we would round to the nearest whole number.

Thus, after 1 year, the field is expected to have approximately 221 mice.

Answer:

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the given base

# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3

Step-by-step explanation:

* Lets explain how to solve the problem

- She has three vertices of the parallelogram

- The vertices are (12 , 2) , (5 , 2) , (1 , 5)

∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates

∴ The length of the base of the parallelogram is 12 - 5 = 7 units

- In parallelogram each two opposite sides are equal and parallel

∴ The opposite side to the base is 7

∴ The x coordinate of the missing point equal the x-coordinate of the

  point (1 , 5) + the length of the base

∴ The x coordinate of the missing vertex  = 1 + 7 = 8

∵ The y-coordinate of the missing vertex is the same with the

   y-coordinate of the point (1 , 5)

∴ The y-coordinate of the missing vertex is 5

∴ The missing vertex is (8 , 5)

- The area of the parallelogram is A = bh, where b is the base of it

  and h is the height of this base

- Remember the height must be perpendicular on the base

∵ The perpendicular distance between the two parallel bases is the

  difference between the y-coordinates of the two points each one

  belong to one of the two parallel bases

∴ The height of the parallelogram = 5 - 2 = 3 units

∴ Its area = 7 + 3 = 21 units ²

* The error she made:

# She did not find the correct vertex; it should be at (8, 5)

# She used the wrong length for the base; it should be 7, like the

   given base

# She used a side length of the parallelogram for the height instead

  of a line segment perpendicular to the base; the height should be 3

Answer:

The Answer is Indepentant.

Step-by-step explanation:

The reason that the answer is Indepentant is that you don't rely on the other thing. Like you have a bag of marbles. You pick one and you put it back. You haven't changed anything. You put the marble back and restored the marble.

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Independent events are not afftected by the others outcomes.

If outcomes of an event doesn't affect the outcomes of other event, the events are called independent events, i.e. they are independent to each other.

Example : "Rolling dice" and "getting good marks in exam" are independent events, because the outcomes of "rolling dice" doesn't affect the outcome of the event "getting good marks in exam".

By seeing the definition & description of independent events given above, we can say that,

One of the independent events can not affected by the another one. Each independent event's outcomes are independent too.

So,the independent events are not affected by the others outcomes.

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Answer:

12

Step-by-step explanation:

You want the costs to be the same so set them equal.

180+10t=25t

Subtract 10t on both sides:

180. =15t

Divide both sides by 15:

180/15. =t

12. =t

So t=12 would give us the costs being the same.

Answer:

Step-by-step explanation:

The given functions are

[tex]C(t)=180+10t\\C(t)=25t[/tex]

To answer the question, we just need to solve this system. We are gonna replace the second function into the first one,

[tex]C(t)=C(t)\\180+10t=25t\\15t=180\\t=\frac{180}{15}=12[/tex]

Therefore, after 12 months, the service contracts will cost the same.

Answer:

40

Step-by-step explanation:

6*6/6*-2i/2i*6/2i*-2i

Answer:

40

Step-by-step explanation:

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

The product is 0 if one of the factors is 0.

(4 - 10)(4 - 4)

= (4 - 10)*0

= 0

Answer:

A. (x - 10)(x - 4)

Step-by-step explanation:

Let x=4

O A. (4 - 10)(4 - 4) = -6 * 0 = 0

OB. (4 + 4)(4 - 10) = 8* -6 = -48

O C. (4 + 6)(4 - 2) = 10 * 2 = 20

OD. 4*4(4-6)=16*-2 = -32

Answer:

This is an acute triangle

Step-by-step explanation:

Pythagoras theorem is used to determine if a triangle is right, acute or obtuse

If the sum of squares of two shorter lengths is greater than the square of third side then the triangle is an acute triangle.

If the sum of squares of two shorter lengths is less than the square of third side then the triangle is an obtuse triangle.

If the sum of squares of two shorter lengths is equal the square of third side then the triangle is a right triangle.

so,

[tex](40)^2 = (37)^2 + (24)^2\\1600 = 1369+576\\1600<1945[/tex]

As 1600<1945, the given triangle is an acute triangle ..

Answer:

2750

Step-by-step explanation:

5500 ÷ 2 (multiplying by 50% is the same as dividing by 2)= 2750

50% of 5500 commuters is calculated as 2750. Hence, 2750 commuters carpool to work.

To find the number of commuters who carpool, we'll use a very basic principle in mathematics: percentage calculation. The problem states that 50% of the 5500 commuters carpool to work. To find the number of commuters carpooling, we multiply the total number of commuters by the percentage of those who carpool. In mathematical terms, it looks like this:(50/100) * 5500 = 2750. Therefore, 2750 commuters carpool to work.

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[tex]3x^2 - x+ 7 =0\\\Delta=(-1)^2-4\cdot3\cdot7=1-84=-83\\x\in\emptyset[/tex]

no real solutions

Answer:

-a,2b

Step-by-step explanation:

here is your answer

Answer:

Option C

Step-by-step explanation:

In this question coordinates of rhombus WXYZ are given as W(0, 4b), X(2a, 0), Y(0, −4b), and Z(−2a, 0).

Now we have to find the coordinates of midpoint of WZ as part of the proof.

Since mid point of two points (x, y) and (x', y') is represented by

[tex](\frac{x+x'}{2}[/tex]  [tex]\frac{y+y'}{2})[/tex]

For midpoint of WZ,

[tex](\frac{0-2a}{2}[/tex]  [tex]\frac{4b+0}{2})[/tex]

= (-a, 2b)

Option C will be the answer.

Answers: A: cube D: prism B: cone (not including the vertex) F : Cylinder

CORRECT ANSWER!!!!!!

Using the piling method, polygons alone can be used to construct a cube, pyramid, and prism. Discs alone can be used to construct a cylinder.

The piling method involves stacking two-dimensional shapes to create three-dimensional solids. Using this method, the following can be constructed:

3(5-1)+1

(15-3)+1

12+1

13

[tex]\huge{\boxed{13}}[/tex]

Substitute. [tex]3(5-1)+1[/tex]

Subtract. [tex]3*4+1[/tex]

Multiply. [tex]12+1[/tex]

Add. [tex]\boxed{13}[/tex]

Answer:

1/3

Step-by-step explanation:

Multiplicative inverse means we want to end up with 1

3 * what = 1

Divide each side by 3

3* what /3 = 1/3

what = 1/3

The multiplicative inverse of 3 is 1/3

Answer:

1/3

Step-by-step explanation:

The mult. inverse of 3 is 1/3.

Answer:

The hourly fee charged by the teacher was $32.10.

Step-by-step explanation:

A music teacher charged for [tex]2\frac{1}{2}[/tex] hour = $80.25

To calculate the hourly fee of the teacher, we have to divide 80.25 by 2.5

Therefore, hourly fee of the teacher [tex]=\frac{80.25}{2.5}[/tex]

                                                            = $32.10

The hourly fee charged by the teacher was $32.10.

To find the possible combinations of pens and notebooks Amanda can purchase, we need to consider her budget and the cost of each pen and notebook. The correct graph representing these combinations is Graph B.

To find the possible combinations of pens and notebooks that Amanda can purchase, we need to consider her budget and the cost of each pen and notebook.

Each pen costs $2 and each notebook costs $3.

Let's assume Amanda buys x number of pens and y number of notebooks.

So, the total cost of pens would be 2x and the total cost of notebooks would be 3y.

Given that Amanda has $30 to spend, we can set up the equation: 2x + 3y = 30.

To graph this equation, we can plot different points that satisfy this equation.

The graph that represents the possible combinations of pens and notebooks Amanda can purchase would be a line passing through points where the x-coordinate represents the number of pens and the y-coordinate represents the number of notebooks.

Answer: The correct graph is Graph B.

Amanda allocates $30 for pens and notebooks. Each pen costs $2, and each notebook is $3. The inequality 2P + 3N ≤ 30 is solved algebraically (P ≤ 15, N ≤ 10) and graphically, considering whole numbers for precision.

Amanda is limited to spending $30 on pens and notebooks. With each pen costing $2 and each notebook priced at $3, the total cost equation is C = 2P + 3N. The corresponding inequality is 2P + 3N ≤ 30.

Algebraically, solving for P and N involves finding values when N = 0 and when P = 0.

When N = 0:

2P ≤ 30

P ≤ 15

When P = 0:

3N ≤ 30

N ≤ 10

So, the solution is P ≤ 15 and N ≤ 10.

For a graphical representation:

Draw a coordinate plane.

Plot the points (15, 0) and (0, 10).

Shade the region below and to the left of the line formed by connecting these points.

The question probable may be:

Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook costs $3.  write inequality showing the relationship and solve them also solve them graphically.

Answer:

X = 21

Step-by-step explanation:

X- 12 = 9

Add 12 to each side

X- 12+12 = 9+12

X = 21

The divisor is 4.033 because it divides 198,200. Rounded to the nearest whole number, it is 4 because 0 is less than 5, so the next highest (whole) place is unchanged.

For this case we have a division where:

If we want to round the divisor to the nearest whole number we have:

4.033 is equivalent to 4, because:

3 is less than 5, then we have 4.03

3 is less than 5, so we have 4.0 equivalent to 4.

Answer:

The divisor remains as 4, rounded to the nearest whole number.

Answer:

1.5

Step-by-step explanation:

As the common difference is not same for all terms, the given sequence is a geometric sequence

the standard formula for a geometric sequence is:

[tex]a_n=a_1r^{n-1}[/tex]

The formula to calculate common ratio is:

[tex]r =   \frac{a_n}{a_{n-1}}[/tex]

Dividing the term by previous term

So,

r = 12/8 = 18/12 = 27/18 = 1.5

The value for common ratio will be:

1.5 ..

Answer:

3/2

Step-by-step explanation:

3/2 is the value

Answer:

12+[(3*8-8)÷4]=16

Step-by-step explanation:

The given expression is:

12+3*8-8÷4=16

Now to insert parenthesis in this statement to make it equality statement we will follow the rule of BODMAS:

BODMAS stands for Bracket, Of, Division,Multiplication,Addition, Subtraction.

It explains the order of expression to solve an expression. If an expression contains (), {}, [], we have to solve or simplify the brackets first and then division, multiplication,addition and subtraction from left to right.

Now take an example of the given statement and place parenthesis:

12+3*8-8÷4=16

12+[(3*8-8)÷4]=16

According to BODMAS rule simplify the terms inside () completely and then [ ].

12+[(24-8)÷4]=16

12+[16÷4]=16

When we divide 16 by 4, it gives the answer 4.

12+ 4 =16

16 = 16

Hence we have made the statement true by inserting parenthesis in order. 12+[(3*8-8)÷4]=16 ....

Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We have with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer:

[tex]\large\boxed{m=-\dfrac{1}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (2, 3) and (4, 2). Substitute:

[tex]m=\dfrac{2-3}{4-2}=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]

Other method.

Look at the picture.

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

[tex]\Delta y=-1\\\\\Delta x=2[/tex]

Substitute:

[tex]m=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]

Answer:

4cm, 11cm, 21cm

Step-by-step explanation:

4(x + 1)(x + 11)

4(x ^ 2 + 12x + 44)

x ^ 2 + 12x + 11 = 231

x ^ 2 + 12x + 11 - 231 = 0

x ^ 2 + 12x - 220 = 0

(x - 10)(x + 22) = 0

x = 10 and x = - 22

4cm , 11cm , 21cm

Both values of x are 10 and -22

The dimension of the cuboid is 4cm by 11cm by 21cm

The formula for calculating the volume of a cuboid is expressed as:

Volume of a cuboid = Length * Width * Height

Given the following parameters

Length = 4 cm

Width = (x+1) cm

Height = (x+11) cm

Volume = 924cm³

Substitute into the formula as shown:

924 = 4(x+1)(x+11)

Factorize

924 = 4(x²+11x + x + 11)

924/4 = x²+12x+11

231 = x²+12x+11

Swap

x²+12x+11 = 231

x²+12x = 231 - 11

x²+12x = 220

x²+12x - 220 = 0 (Proved)

On factorizing

x²+12x - 220 = 0

x²+22x-10x - 220 = 0

x(x+22)-10(x+22) = 0

(x-10)(x+22) = 0

x = 10 and -22

Hence both values of x are 10 and -22

Get the dimensions

Length = 4cm

Width = x+ 1 = 10 + 1 = 11cm

Height = x+11 = 10 + 11 = 21cm

Hence the dimension of the cuboid is 4cm by 11cm by 21cm

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