What Is the equation of a line that passes through the coordinates (4,1) and (1,4)

The money in the account at the end of 5 years is 2208.16

The formula for calculating the compound interest is expressed according to the formula:

Compound interest = P(1+r)^t

Given the following parameters

Principal = 2000

rate = 2 % = 0.02

time = 5 years

Substitute

A = 2000(1+0.02)^5

A = 2000(1.02)^5

A = 2208.16

Hence the amount of money that will be in that account at the end of 5 years is 2208.16

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The mean of the number of hours spent watching television is 15.75

The mean absolute deviation of the number of hours spent watching television is 6.625.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10 +  11 + 22 + 7 + 17 + 17 + 20 + 31 + 0 + 12 + 19 + 23) / 12 = 189/12 = 15.75

Mean absolute deviation is the average of the sum of the absolute difference between the numbers and the mean.

MAD =  1/n ∑ l x - m(x) l

(|10 - 15.75) + |11 - 15.75| + |22 - 15.75| + |7 - 15.75| + |17 - 15.75|+ |17 - 15.75| + |20 - 15.75| + |31 - 15.75| + |0 - 15.75| + |12 - 15.75| + |19 - 15.75| + |23 - 15.75|

= (5.75 + 6.75 + 6.25 + 8.75 + 1.25 + 1.25 + 4.25 + 15.25 + 15.75 + 3.75 + 3.25 + 7.25) / 12 = 6.625

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Answer:  38.46

Step-by-step explanation:

             ↓

   38.456 It means round by 0.05, so when you round you look at the place value after the specified digit.

The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.

Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.

Where P exists at the origin and line segment is a horizontal one.

The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).

The segment exists not a horizontal or vertical line:

The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].

Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).

where neither P nor Q exists at the origin.

Use the end points of the segment PQ to estimate the components of the directed segment.

[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]

= (6,-4)

The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are

[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]

To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.

Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

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Answer:

half of a foot

Step-by-step explanation:

The value of x is 14 °

The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.

In ΔOPQ,

∠O = (2x- 5)°

∠P = (3x-8)°

∠Q= (10x- 17)°

Thus by angle sum property of triangle we know:

∠O+ ∠P + ∠Q = 180

thus 2x - 5 + 3x - 8 + 10x - 17 = 180

15x - 30 = 180

= 15 x = 180 + 30

= 15 x = 210

= x= 210 / 15

= x = 14 .

Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °

∠P = (3x-8)° = 3× 14 - 8 = 44°

∠Q= (10x- 17)° = 10 × 14 - 17 = 123°

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The triangle ABC has an area of 50 square cm

From the question, the given parameters are:

The given parameters above mean that:

The triangles ABC and PQR are similar triangles

So, the area of the triangle ABC is then calculated as

Area of △PQR = Area of △ABC x (AC/PR)²

Substitute the known values in the above equation

So, we have the following equation

Area of △PQR = 8 x (2.5)²

Evaluate the product

Area of △PQR = 50

Hence, the area of the triangle ABC is 50 square cm

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The two column proof of the given angles are;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

Statement 4; x = 28°

Reason 4; Algebra

From the attached image, we can complete the two column proof as follows;

Statement 1; m∠AOB = 180°

Reason 1; Sum of angles on a straight line sums up to 180°

Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB

Reason 2; Opposite angles

Statement 3; x + 3x + x + 12 = 152

Statement 3; Substitution

From statement 3, we can use algebra to find x as;

x + 3x + x + 12 = 152

5x + 12 = 152

5x = 152 - 12

5x = 140

x = 28°

Thus;

Statement 4; x = 28°

Reason 4; Algebra

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Answer:

y=-1

y=43

x=14

Step-by-step explanation:

So, you have the equation: [tex]y=-4x+15[/tex], and if we know one value we can easily solve for the other using some algebraic manipulation.

Find y when x=4.

For this we know one value, "x", and the other "y" value is unknown. This is actually not to hard if you notice that the equation we're given expresses the value of "y" in terms of "x".

So let's plug in the x-value: [tex]y=-4(4)+15\implies y=-16+15=-1[/tex]

So we get: y=-1, which turns out to be the solution!

Find y when x=-7

This is a similar process, so let's just get straight into it and plug x as -7

[tex]y=-4(-7)+15\\y=28+15\\y=43[/tex]

This is our solution, y=43

Find x when y = -41

So this case is a bit different since we're given the y-value and not the x-value, and as I mentioned the equation represents the value of y in terms of x.

We still do a similar process, except we'll use some more algebraic manipulation, but let's start by plugging in the known value:

[tex]-41=-4x+15[/tex]

Let's move the constant, 15, to the other side by subtracting by 15 to cancel both sides.

[tex]-56 = -4x[/tex]

Now we want to get the x alone, and the only "operation" being done on the x, is that it's being multiplied by the coefficient of -4. To cancel this out we want to divide both sides by -4 to maintain equality & cancel out the coefficient of -4 to one, which is just 1 * x which can be expressed as x as it's implied the coefficient is 1

[tex]14=x[/tex]

Now we have our solution!

In the picture there are 4 graphs.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

Given that,

In the picture there are 4 graphs.

We have to find the domain and range of the each function using inequality or set-builder notation.

A function's domain is the set of values that we are allowed to enter into our function.

This set consists of the values of the x-axis for a function like f. (x).

The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.

1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).

2nd graph we get domain as [-4,4] and range as [3,-1].

3rd graph we get domain as [-4,1] and range as [1,-4].

4th graph we get domain as (-∞,4] and range as (-∞,-2].

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The number of atoms of each element in CO2 are; Number of O atoms = 2 and Number of C atoms = 1

The number of atoms present in the molecule of an element is known as its Atomicity. For Example: In the H2O molecule, its atomicity is 3 as it has 2 molecules of hydrogen and 1 molecule of oxygen

Similarly, for the antiperspirant  Al₂Cl(OH)₅. the number of atoms in each element can be found as follows;

Number of Al atoms = 2

Number of Cl atoms = 1

Number of H atoms = 1 x 5 = 5

Number of O atoms = 1 x 5 = 5

Applying the above to our question gives;

Number of C atoms = 1 atom

Number of O atoms = 2 Atoms

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Answer:

97 miles

Step-by-step explanation:

pls mark brainlest

Answer:

97 miles

Step-by-step explanation:

65 mph * 1.5 hours = 97 miles

The solution of the given expression will be ( 2.4 x 10⁸ ).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that 2 x 10⁸ = 20 × 10⁷. The sum of the two exponential numbers will be calculated as:-

Sum = 2 x 10⁸  + ( 4 x  10⁷ )

Sum = 20 x  10⁷ + ( 4 x  10⁷ )

Sum = ( 20 + 4 ) x  10⁷

Sum  = 24 x  10⁷

Sum = 2.4 x 10⁸

Therefore, the solution of the given expression will be ( 24 x 10⁷ ).

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The scale of the map given the area of the desert and the area of the scale drawing is 1 square inch represents 2,500 square miles.

A scale drawing is either a larger or smaller image of another image or object. A scale drawing is enlarged or reduced using a scale. A map is a smaller scale drawing of an area. The scale is used to keep the proportion of the dimensions between the scale drawing and the original place similar.

In order to determine the scale of the drawing, divide the original square area by the square area of the scale drawing.

Scale of the drawing = original dimensions / dimensions of the scale drawing

25,000 square miles / 10 square inches = 2,500 square miles

The scale is 1 square inch represents 2,500 square miles. or 1 : 2,500.

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Answer:

2[tex]\sqrt{10}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]

given

[tex]\sqrt{5}[/tex] × [tex]\sqrt{8}[/tex]

= [tex]\sqrt{5(8)}[/tex]

= [tex]\sqrt{40}[/tex]

= [tex]\sqrt{4(10)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex]

= 2[tex]\sqrt{10}[/tex]

For given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'

Part A:

We need to write the converse to the conditional statement.

The converse of given conditional statement would be:

'If it is a television, then the object has a remote.'

Part B:

We need to write a biconditional statement from the conditional statement.

A biconditional statement of the given conditional statement would be:

'The object has a remote if and only if it is a television.'

Part C:

We need to validate the above biconditional statement.

The biconditional statement is true because the conditional statement and the converse are true.

Therefore, for given conditional statement 'If the object has a remote, then it is a television.'

Part A: converse to the conditional statement

'If it is a television, then the object has a remote.'

Part B: a biconditional statement

'The object has a remote if and only if it is a television.'

Part C: validation of biconditional statement

The biconditional statement is true because the conditional statement and the converse are true.

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Answer:

MP = 19

Step-by-step explanation:

MP = MN + NO + OP

we require to find OP and MN before we can evaluate MP

NO + OP = NP , that is

8 + OP = 15 ( subtract 8 from both sides )

OP = 7

and

MN + NO = M0 , that is

MN + 8 = 12 ( subtract 8 from both sides )

MN = 4

Then

MP = MN + NO + OP = 4 + 8 + 7 = 19

Answer:

Cost Function is:

c = 4n

Or, using n as a function variable, we write:

c(n) = 4n

Step-by-step explanation:

c represents total cost
n represents notebook

4 represents cost per notebook

Answer:

151, 29, 151

Step-by-step explanation:

[tex]m\angle 2=29^{\circ}[/tex] (vertical angles)

[tex]m\angle 1=m\angle 3=151^{\circ}[/tex] (linear pair)

Answer:

[tex]m \angle 1= \boxed{159}\;^{\circ}\\\\m \angle 2= \boxed{21}\;^{\circ}\\\\m \angle 4= \boxed{21}\;^{\circ}[/tex]

Step-by-step explanation:

Angles on a straight line sum to 180°.

⇒ m∠3 + m∠4 = 180°

⇒ 159° + m∠4 = 180°

⇒ m∠4 = 21°

Vertical Angle Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Applying the Vertical Angle Theorem:

The multiplication of 92 by 43 using standard algorithm is 3956.

A standard algorithm or method in elementary mathematics is a certain computation technique that is typically taught for resolving particular mathematical issues.

To be more organized and effective, a typical algorithm uses the same steps each time we multiply, add, subtract, or divide.

Math problems are typically solved by aligning the places, starting with the ones on the right, moving on to the tens place, adding in any carryover numbers or regrouping if subtracting and so on.

Therefore, the multiplication is:

= 92 × 43

= 3956

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Answer:

60

Step-by-step explanation:

10 + 10 + 10 + 10 + 10 + 10 = 60

Answer:

60

Step-by-step explanation:

Everytime you are multiplying by 10, you add a 0 to the number that you are multiplying by. In this case, the 6 turns into 60. This is a trick for the multiples of 10. Hope this helps!

The difference between of the cost of the phones in the USA and the UK is $51. 2

Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.

It is also known as the rate at which a currency is exchanged to another currency

From the information given, we have that;

We also have that;

The exchange rate is expressed as;

£1 = $1.36

Now, let's convert the cost from dollars to euros, we have;

If £1 = $1.36

Then, £920 = $x

cross multiply, we have;

x = 920 × 1. 36

x = $1251. 36

Now, let's find the difference between the cost in the USA and UK, we have;

=  $1251. 36 - $1200

= $51. 2

Hence, the difference is $51. 2

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Answer:

Circumference 87.92 ft

Step-by-step explanation:

You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.

14×2=28

28×3.14=87.92

Answer:

1024

Step-by-step explanation:

4^5

= 4*4*4*4*4

= 16*4*4*4

= 64*4*4

= 256*4

= 1024

Using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds

The cost of the oranges = 3.16 pounds

The cost of the peaches = 1.15 pounds

The cost of the apples = 2.24 pounds

Then the total bill = The cost of the oranges + The cost of the peaches + The cost of the apples

Here we have to use the addition

Substitute the values in the equation

Then the total bill = 3.16 + 1.15 + 2.24

= 6.55 pounds

Hence, using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds

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Answer:

9

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]

Answer:

c. Yes, she is correct because 0.45 and 0.333 are rational numbers. The sum of two rational numbers is a rational number.

Answer: 960

Step-by-step explanation:

Let the number of pennies Keiko's bank hold be x

Now, According to the question,

[tex]\frac{1}{6} \times x+320=\frac{1}{2} \times x[/tex]

⇒ [tex]\frac{1}{6} \times x+320=\frac{x}{2}[/tex]

⇒ [tex]\frac{(x+1960)}{6}=\frac{x}{2}[/tex]

⇒ 2(x + 1920) = 6x

⇒ 2x + 3840 = 6x

⇒ 6x - 2x = 3840

⇒ 4x = 3840

⇒ [tex]x = \frac{3840}{4}[/tex]

⇒ x = 960

Hence, the total number of pennies Keiko's bank hold = 960.