If Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48 , what is the principal loan amount?

Since the lemonade recipe calls for the juice of 5 lemons, 2 cups of water, and 2 tablespoons of honey we can use mathematical operations to make different lemonades with the following recipes:

1) To make more lemonade taste the same as the original, we can use the multiplication operation on the above recipe as follows:

Lemons = 10

Cups of water = 4

Tablespoons of honey = 4

2) To make less lemonade taste the same as the original recipe, we can use the division operation as follows:

Lemons = 2.5

Cups of water = 1

Tablespoons of honey = 1

3) To make lemonade that has a stronger lemon taste than the original recipe, we can use the subtraction operation as follows:

Lemons = 4

Cups of water 1

Tablespoons of honey

4) To make lemonade that has a weaker lemon taste than the original recipe, we can use the addition operation as follows:

Lemons = 6

Cups of water 3

Tablespoons of honey = 3

Lemons = 5

Cups of water = 2

Tablespoons of honey = 2

1) Using the multiplication operation to make more lemonade taste the same as the original:

Lemons = 10 (5 x 2)

Cups of water = 4 (2 x 2)

Tablespoons of honey = 4 (2 x 2)

2) Using the division operation to make less lemonade taste the same as the original recipe:

Lemons = 2.5 (5 ÷ 2)

Cups of water = 1 (2 ÷ 2)

Tablespoons of honey = 1 (2 ÷ 2)

3) Using the subtraction operation to make lemonade that has a stronger lemon taste than the original recipe:

Lemons = 4 (5 - 1)

Cups of water 1 (2 - 1)

Tablespoons of honey = 1 (2 - 1)

4) Using the addition operation to make lemonade that has a weaker lemon taste than the original recipe:

Lemons = 6 (5 + 1)

Cups of water 3 (2 + 1)

Tablespoons of honey = 3 (2 + 1)

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Answer:

y = (2 + √2)/4   ;   y = (2 - √2)/4

Step-by-step explanation:

-8y² + 8y - 1 = 0

8y² - 8y + 1 = 0

discriminant = 64 - 4(8) = 64 - 32 = 32 = 2^4 * 2

y = (8 + [tex]\sqrt{2^4 * 2}[/tex])/16

(8 + 2²√2)/16

(8 + 4 √2) / 16

4(2+√2)/16

(2+√2)/4

y = (8 - [tex]\sqrt{2^4 * 2}[/tex])/16

(8 - 4√2) / 16

4(2-√2)/16

(2-√2)/4

Answer:no

Step-by-step explanation:

There is a property with triangles that the sum of two sides of a triangle should always be greater than the 3rd side.

Here if we take the two smaller sides their sum is 7 + 8 = 15 which is equal to the third side.

So it is not possible to construct a triangle with sides 7, 8, and 15 respectively.

The months when the temperature will be 0 °C are May and August.

A trigonometric function is a function that has the trigonometric ratios.

Temperature is the degree of hotness or coldess of a body.

Since the average monthly temperature of a particular city is T(m) = 10cos(πm/6) + 5 where m = number of months of year and January begins at m = 0.

To find the number of months in which the temperature would be 0°C. This means T(m) = 0.

So,  T(m) = 10cos(πm/6) + 5

0 = 10cos(πm/6) + 5

-10cos(πm/6) = 5

cos(πm/6) = 5/10

cos(πm/6) = -0.5

cos⁻¹cos(πm/6) = cos⁻¹(-0.5)

(πm/6) = π - π/6 or (πm/6) = 3π/2 - π/6 (since cos is negative int he second and third quadrant respectively)

πm/6 = 5π/6 or πm/6 = 8π/6

⇒ m = 5π/6 × 6/π or m = 8π/6 × 6/π

⇒ m = 5 or m = 8

Since m = 5 is May and m = 8 is August,

The months when the temperature will be 0 °C are May and August.

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The law for all large numbers with the central limit-theorem will tell us about how standard deviations doesn't as increase with medians. So b). false is correct.

The Law for all Large Number states that once pattern length has a tendency to infinity, the pattern imply equals to populace imply. The statements aren't contradictory. The Central Limit Theorem inform us that because the pattern length has a tendency to infinity, the of the distribution of pattern method methods the ordinary distribution.

The regulation of huge numbers has a completely vital position in possibility and statistics. It states that in case you repeat an test independently a huge variety of instances and common the result, what you got must be near the predicted value.

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Reciprocal of a = [tex]\frac{1}{a}[/tex]

What is Reciprocal ?

In Mathematics , reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n.

What are real numbers ?

In mathematics, a real number is a quantity that may be represented by an endless number of decimal expansions .

According to the given information

a ≠ 0

a is a real number

By the definition of reciprocal

Reciprocal of a will be the inverse of a = [tex]\frac{1}{a}[/tex]

Reciprocal of a = [tex]\frac{1}{a}[/tex]

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The length of the wrench handle 8.4 inches.

What is length?

Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The metre serves as the foundational unit of length in the International System of Units.

f = k/l

35 = k/6        

k = 210

f = 210/l

25 =210/l      

l = 8.4 inches

The length "L" (in inches) of a wrench handle has an inverse relationship with the force "F" (in pounds) required to remove a certain bolt. In the case of a handle that is 6 inches long, 35 pounds of power is required. The length of the wrench handle if the bolt needs to be loosened with 25 pounds of force is 8.4 .

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The given statement:

"the sum of a number and 10.7 is at most −3.2"

Is equivalent to the following inequality:

x + 10.7 ≤ -3.2

Here we have the following statement:

"the sum of a number and 10.7 is at most −3.2"

So let's define the variable "x" as "the number", we know that the sum between x and 10.7 is at most -3.2, we can say that the sum is equal to or smaller than -3.2

In that case, the symbol we need to use is: ≤

Then the inequality is:

sum ≤ -3.2

x + 10.7 ≤ -3.2

That is the statement written as an inequality.

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Answer:

A system of two linear inequalities in two variables is a set of two linear inequalities that involve two variables, such as x and y. A system of two linear equations in two variables is a set of two linear equations that involve two variables, also typically x and y.

There are several key differences between a system of two linear inequalities in two variables and a system of two linear equations in two variables:

Inequalities use symbols such as "less than" or "greater than" to indicate the relationship between the variables, whereas equations use the equal sign (=).

The solution to a system of linear inequalities is a region in the coordinate plane, whereas the solution to a system of linear equations is a single point.

The solution to a system of linear inequalities is found by graphing the inequalities on the coordinate plane and finding the region where they intersect, whereas the solution to a system of linear equations is found by solving the equations for the values of the variables.

The solution to a system of linear inequalities may include an infinite number of points, whereas the solution to a system of linear equations is always a finite number of points.

Overall, the main difference between a system of two linear inequalities in two variables and a system of two linear equations in two variables is the way in which the solutions are represented and found.

(i) At a total of 100 Songs the Charges for Company A and Company B will be Equal.

(ii) I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

Let, Songs Downloaded be x

Total Charges of Company A = 15 + 0.75*x

Total Charges of Company B = 0.9*x

(i) Total Charges by Company A = Total Charges by Company B

15 + 0.75*x = 0.9*x

15 = 0.15*x

x = 100 songs

(ii) Charges by Company A to Download 150 Songs = 15 + 0.75 * 150

= 15 + 112.5 = $127.5

Charges by Company B to Download 150 Somgs = 0.9 * 150 = $135

I would rather suggest to select Company A as the Total Charges to download 150 Songs is $127.5

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Answer:

18.6

Step-by-step explanation:

[tex]x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9[/tex]

Using these points, the correct graph is shown in option C.

Answer: 246.7

Step-by-step explanation:

10% of the time, the population mean will go below $1,500 or exceed $2,100.

Given that,

Assume that we have data on the annual spending on apparel of a sample of families. The probability that the population mean will fall below $1,500 or rise over $2,100 is ________% if we are 90% positive that the genuine population mean will be between $1,500 and $2,100.

We have to fill the blank.

We know that,

90% of the time, the real population mean will fall in the range of $1,500 and $2,100.

The genuine population mean will therefore most likely fall between $1,500 and $2,100, with a 90% probability.

So, the probability that it will fall outside of this range (i.e., be either less than $1,500 or beyond $2,100) is 100-90, or 10%.

Therefore, 10% of the time, the population mean will go below $1,500 or exceed $2,100.

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The equation of the quadratic function that models the height of the ball h(t) at time t is h(t) = −3(t − 4)² + 42

From the question, we have the following parameters that can be used in our computation:

The above parameters mean that

h(1) = 15

h(7) = 15

h max = 42

This also means that the leading coefficient of the function is negative

So, the possible equations from the options are

h(t) = −2(t − 4)² + 42

h(t) = −3(t − 4)² + 42

Calculate h(1) and h(7)

h(t) = −2(t − 4)² + 42

h(1) = −2(1 − 4)² + 42 = 24

h(7) = −2(7 − 4)² + 42 = 24

h(t) = −3(t − 4)² + 42

h(1) = −3(1 − 4)² + 42 = 15

h(7) = −3(7 − 4)² + 42 = 15

Hence, the function is h(t) = −3(t − 4)² + 42

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Answer: Answer is C

Step-by-step explanation:

I took the test and it gave me credit for this question

The number of sweets left in the box after giving 35% is 325.

There were 500 sweets in a box and Mrs. Miller has given out 35% as prizes. The number of sweets left in the box can be calculated as follows:

Therefore, the number of sweet left in the box = 500 - 35% of 500

number of sweet left in the box = 500 - 35 / 100 × 500

number of sweet left in the box = 500 - 17500 / 100

number of sweets left in the box = 500 - 175

= 325

Therefore, the number of sweets left in the box will be 325

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The linear functions in this problem are given as follows:

1. y = 1/3x + 3.

2. y = 2.

3. y = 3x - 1.

4. x = 1.

The slope-intercept definition of a linear function is presented as follows:

y = mx + b.

In which the coefficients are given as follows:

For item 1, the points are given as follows:

(-6, 1) and (-3,2).

When x increases by 3, increases by 1, hence the slope is given as follows:

m = 1/3.

Then:

y = 1/3x + b.

When x = -3, y = 2, then the intercept b is calculated as follows:

2 = 1/3(-3) + b

b = 3.

Thus the function is:

y = 1/3x + 3.

Then items 2 and 4 are given as follows:

For item 3, we have an intercept of -1, hence:

y = mx - 1.

When x = 3, y = 8, hence the slope m is calculated as follows:

8 = 3m - 1

3m = 9

m = 3.

Hence the function is:

y = 3x - 1.

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Answer:

Y= -1/9x-9 that's the answer, you're welcome

The equation of line which is perpendicular to the line q is given by

y = ( -1/9 )x - 9

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The point is P ( 9 , -10 )

Let the equation of line q be  y + 7 = 9 ( x + 4 )

Now , on simplifying the equation , we get

y + 7 = 9x + 36

Subtracting 7 on both sides of the equation , we get

y = 9x + 29

Now , the slope of the equation q is m₁ = 9

Now , since the line r is perpendicular to line q

The product of the slope is -1

So , m₁ x m₂ = -1

Substituting the values in the equation , we get

9 x m₂ = -1

Divide by 9 on both sides of the equation , we get

m₂ = -1/9

So , the slope of the line r m₂ = -1/9

The equation of line is given by y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -10 ) = -1/9 ( x - 9 )

On simplifying the equation , we get

y + 10 = -1/9 ( x - 9 )

y + 10 =  ( -1/9 )x + 1

Subtracting 10 on both sides of the equation , we get

y = ( -1/9 )x - 9

Therefore , the value of A is y = ( -1/9 )x - 9

Hence , the equation of line r is y = ( -1/9 )x - 9

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Answer:

Step-by-step explanation:

199/4

By using the concept of fraction, it can be calculated that

Jamal has the better record

What is a fraction?

Suppose there is a collection of objects and a part of the collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction.

The upper part of the fraction is called numerator and the lower part of the fraction is called denominator.

This is a word problem on fraction

Portion of free throws Jamal made in the last ten games = [tex]\frac{7}{9}[/tex]

Portion of free throws Brian made in the last ten games = [tex]\frac{5}{8}[/tex]

To compare between [tex]\frac{7}{9}[/tex] and [tex]\frac{5}{8}[/tex]

LCM of 9 and 8 = 72

[tex]\frac{7}{9} = \frac{7 \times 8}{9 \times 8} = \frac{63}{72}[/tex]

[tex]\frac{5}{8} = \frac{5 \times 9}{8 \times 9} = \frac{45}{72}[/tex]

As [tex]\frac{63}{72} > \frac{45}{72},[/tex]

So [tex]\frac{7}{9} > \frac{5}{8}[/tex]

So, Jamal has the better record

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Answer:

B

Step-by-step explanation:

5x + 30 - 18x - 18 = 10

-13x + 12 = 10

Answer:

See below   ( you have it correct !)

Step-by-step explanation:

See image below....sometimes it is easier to see these things if you extend some lines a bit:

The total area of the Sea of Japan and the Southern Ocean is 2.1334 × 10⁷ km². The correct option is the first option 2.1334 × 10⁷ km²

From the question, we are to calculate the total area of the sea and ocean

From the given information,

"The area of the Sea of Japan is 1.007 × 106 km²"

and

"The area of the Southern Ocean is 2.0327 × 107 km²"

Thus,

The total area of the sea and ocean = 1.007 × 10⁶ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 0.1007 × 10⁷ km² + 2.0327 × 10⁷ km²

The total area of the sea and ocean = 2.1334 × 10⁷ km²

Hence, the total area is 2.1334 × 10⁷ km²

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In the octagon, the measurement of the largest exterior angle is 90°.

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words, poly, which means numerous and gon, means sides.

The given exterior angles of the octagon are,

x°, 2x°, 3x°, 4x°, 5x°, 7x°, 8x°, and 10x°.

The sum of the exterior angle of the octagon is 360°.

Implies that,

x + 2x + 3x + 4x + 5x + 7x + 8x + 10x = 360

40x = 360

x = 9

The largest exterior angle = 10 x  = 10 × 9 = 90°.

The required largest exterior angle is 90°.

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5.3

80/15=5.3

which means each person completed 5.3 puzzles

On solving the given equation  y=(x-2)(x-4) the point on the graph are as follows:

(4,0), (2,0), (5,3), (3,-1) &(0,8)

What is a graph?

A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.

It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.

It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.

1)

let   y=0

0=(x-2)(x-4)

i.e. x = 4 and 2

2)

Let x =0

y=(0-2)(0-4)

y=8

3)

Let x = 3

y=(3-2)(3-4)

y=-1

4)

Let x = 5

y=(5-2)(5-4)

y=3

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Answer:

Before 1913, federal government revenues came mainly from taxes on goods—tariffs on imported products and excise taxes on items like whiskey.

Step-by-step explanation:

What was the tax rate in 1913?

The act levied a tax of one percent on all incomes above the exemption with additional surtax rates imposed for progressively higher incomes. Those surtax rates started at one percent for those making $20,000 or more and topped out at a mere six percent on incomes in excess of $500,000.

The Area of the shaded part is 3.44 cm²

The formula used to find the Area of a circle is given by

Where r is the radius of the circle

The formula used to find the Area of a Square is given by

Here we know

The radius of the circle = 2m

As we know Area of a Circle = 2πr

=> Area of given circle = 2(3.14)2 = 12.56 cm²

Area of circle = 12.56 cm²

As we can see the circle is inscribed in a square

Then the Length of the side square = diameter of the circle

=> Length of side = 2 × Radius of circle = 2 × 2 cm = 4 cm

Length of side = 4 cm

As we know Area of the square = side²

=> Area of given square = 4 × 4 = 16 cm²

Now using the above value we will friend the area of the shaded part

Area of shaded part = Area of the square - Area of the circle

= 16 cm² - 12.56 cm² = 3.44 cm²

Therefore,

The Area of the shaded part is 3.44 cm²

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Answer: 28 inches

Hope this helps!!! :)