Jack lives in a house worth $172000 and pays $13760 in taxes. Write an equation to represent the relationship

For the given scenario the mean changes from 80.42 to 82.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, the average high temperatures in degrees for a city are 58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57.

Now, average = (58+61+71+77+91+100+105+102+95+82+66+57)/12

= 965/12

= 80.42

If a value of 101° is added to the data, then the new average is

(965+101)/(12+1)

= 1066/13

= 82

Therefore, for the given scenario the mean changes from 80.42 to 82.

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Malia can't buy 75 water bottles and 100 pairs of socks because it is not a solution to the system.

Here we have a graph of inequalities, and we just need to see if the pair (75, 100) is a solution.

The solutions of the system are all the points in the intersection of the two shaded areas (in this case are all the points in the green area)

Now, clearly the point (75, 100) is not a solution

Even if you evaluate that in the first inequality:

x + y ≥ 200

we get:

75 + 100 ≥ 200

175 ≥ 200

which is false.

So no, Malia can't buy 75 water bottles and 100 pairs of socks.

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The level of scale of measurements is the ratio scale for the data of the average weight of newborn babies in ounces.

A ratio scale is a numerical scale with a genuine zero and uniform distances between adjacent points. A zero on a ratio scale, in contrast to an interval scale, indicates complete lack of the variable being measured. Examples of ratio scales include length, area, and population.

As, There are four scales of measurement: Nominal, Ordinal, Interval, and Ratio.

First, The categories in this scale are given names, hence the label "nominal." There is no innate hierarchy among the categories. Simply said, it is impossible to say that one category is superior to or better than another.

Ordinal scale: It is possible to rationally organise the various categories in a meaningful order. The distinction between the categories is not "meaningful," nevertheless.

Interval scale: Doubling has no significance, but values (not categories) can be arranged and have substantial differences. The lack of a "absolute zero" is the reason of this.

Scale of ratios: The values can be arranged in a way that makes a meaningful difference, and doubling also makes a difference. "Absolute zero" exists.

As a result, the ratio scale for the level of measurements is used to determine the average weight of newborn babies.

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Only Euna successfully constructed an equilateral triangle inscribed in a a circle.

An equilateral triangle's sides are congruent, which indicates that they are all the same length. The inner angles are all equal (60°), as well. Equilateral is a compound word made up of the words "equi," which means equal, and "lateral," which means side. Thus, an equilateral triangle is one that has three sides of equal length. An equilateral triangle in geometry is a triangle whose three sides are equal in length. An equilateral triangle is also equiangular in the conventional Euclidean geometry, meaning that each of the three internal angles is 60 degrees and that all three are congruent with one another.

So, Euna successfully constructed an equilateral triangle inscribed in a a circle.

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Answer:

2

Step-by-step explanation:

mangoes left=10-5-2-1=2

Step-by-step explanation:

In order to make a profit R > C

So let's make those equal first

R = C

[tex]6.56x = 10.063 + 1.09x[/tex]

Let's get X alone by subtracting 1.09x from both sides.

[tex]5.47x = 10.063[/tex]

Next we divide by 5.47

[tex]x = 1.83[/tex]

Rounding up to 2, looks like Anna needs to only sell 2 books to start making a profit

The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.

Algebra is the examination of ideational signs while reasoning the manipulation of all those thoughts.

The big square block represents the 1 unit. And each small block represents 0.01 units.

The number of small blocks which are marked by the color in one shot is 32 which means 0.32 units.

And these processes are done six times, then the expression that represents the condition is given as,

6 x 0.32 = 1.92

The multiplication equation best represents the figure will be 6 x 0.32 = 1.92. Then the correct option is B.

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Answer:

They would need 35 cups of rice.

Step-by-step explanation:

4 x 5 = 20

7 x 5 = 35

a) The total time taken in hours is 0.75 hours

b) The amount of all-purpose flour needed is not given in the question.

c) The thickness of the dough in centimetres is not given.

d) The amount of salt needed per scone is not given.

e) The amount of butter needed per scone is not given.

f) It will be ready for consumption by 15:30

g) 356°F in °C can be calculated using the formula:

°C = (356°F - 32°) / 1.8 = 180°C.

a) Total preparation and cooking time = 30 minutes + 15 minutes = 45 minutes = 0.75 hours

b) To bake 36 scones, we need:

36 scones * all-purpose flour needed to bake 1 scone = all-purpose flour needed to bake 36 scones

The amount of all-purpose flour needed is not given.

c) The thickness of the dough in centimetres is not given.

d) Mrs. Msimango baked 48 scones, so the number of teaspoons of salt required would be:

48 scones * teaspoons of salt needed per scone = teaspoons of salt needed for 48 scones

The amount of salt needed per scone is not given.

e) Mrs. Msimango baked 48 scones, so the number of millilitres of butter required would be:

48 scones * ml of butter needed per scone = ml of butter needed for 48 scones

The amount of butter needed per scone is not given.

f) If Mrs. Msimango started making the scones at 14:55, they would be ready to eat at 14:55 + 0.75 hours = 15:30.

g) 356°F in °C can be calculated using the formula:

°C = (356°F - 32°) / 1.8 = 180°C

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The solution will lie on the number line from (-∞ , 0)

An inequality is the representation of an algebraic statement with two non-equal values. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

One of the following options is available for resolving an inequality: Add the same amount to each side, deduct the same amount from each side, multiply each side by the same positive number, or split each side in half. If you multiply or divide each side by a negative value, the inequality sign must be reversed.

Given,

(x-0)(x-6)<0

⇒ x < 0 and x < 6

the solution will lie on the number line from -∞ to 0.

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Answer:

21°

Step-by-step explanation:

For this right-angled triangle:

∠M = angle in question

Side LM = Hypotenuse

With respect to ∠M:

Side LN = Opposite side

Side MN = Adjacent side

Trigonometric function applied:

sin∠M = [tex]\frac{opposite}{hypotenuse}[/tex]

           = [tex]\frac{8}{22}[/tex]

 ∠M = [tex]sin^{-1} (\frac{8}{22})[/tex]

          = 21.32°

  ∠M  = 21° (Rounded to the nearest degree)

Answer:

∠M = 21°

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

Therefore, substitute the given values into the sine ratio and solve for ∠M:

[tex]\implies \sin(M)=\dfrac{8}{22}[/tex]

[tex]\implies M=\arcsin \left(\dfrac{8}{22}\right)[/tex]

[tex]\implies M=21.323686...^{\circ}[/tex]

[tex]\implies M=21^{\circ}\sf\;(nearest\;degree)[/tex]

Therefore, the measure of ∠M to the nearest degree is 21°.

the system is inconsistent Infinitely many solutions.

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A' stands for "matrix," Aij.

The given matrix is [tex]\left[\begin{array}{ccccc}1&0&0&0&0\\0&1&0&0&0\\0&0&1&0&0\\0&0&0&1&0\\0&0&0&0&1\\0&0&0&0&0\end{array}\right][/tex]

This is a linearly dependent matrix a row is 0.

Hence, the system is inconsistent Infinitely many solutions.

Hence the element s₂₃ of the given matrix is -2

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Answer:

h = F/4g

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

6 - 3/4x + 1/3 = 1/2x + 5

6 - 9/12x + 4/12 = 6/12x + 5  If I multiply all the way through by 12 I will eliminate the fraction

72 - 9x + 4 = 6x+ 60

Answer: Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk.

We know that:

x + y = 7 (because you want 7 days of supply)

And the protein content per serving of Designer Whey is 18g and the protein content per serving of Muscle Milk is 20g. So:

18x + 20y = 412 (because you want 412g of protein)

And the carbohydrate content per serving of Designer Whey is 4g and the carbohydrate content per serving of Muscle Milk is 8g. So:

4x + 8y = 108 (because you want 108g of carbohydrates)

We can now use the above two equations to solve for x and y. We'll start by solving for x in terms of y:

18x + 20y = 412

18x = 412 - 20y

x = (412 - 20y)/18

Now we can substitute this expression for x into the equation for the carbohydrates:

4x + 8y = 108

4((412 - 20y)/18) + 8y = 108

1664 - 80y + 8y = 1080

1664 = 1080 + 80y

584 = 80y

y = 7.3

Since y must be an integer, we'll round it down to 7. So y = 7. We can now use either equation to find x:

18x + 20y = 412

18x + 20 * 7 = 412

18x = 412 - 140

18x = 272

x = 15.1

Since x must be an integer, we'll round it up to 15. So x = 15.

Therefore, you should combine 15 servings of Designer Whey and 7 servings of Muscle Milk in order to meet your requirements.

Step-by-step explanation:

Answer:

k = 176

Step-by-step explanation:

16 = k/11

16 * 11 = k/11 * 11

176 = k

Because k is being divided by 11 on the right-hand side of the equation, we would need to multiply both sides by 11 to undo the division operation done to k so we can isolate it.

Answer:

27.52

Step-by-step explanation:

1m =1.09 yards

30/1.09 = 27.52

Answer:

An inequality in mathematics is a statement that compares two values, with the use of inequality symbols like < (less than), > (greater than), ≤ (less than or equal to), ≥ (greater than or equal to), and ≠ (not equal to). For example, the inequality "5 > 2" states that 5 is greater than 2. Inequalities can be used to represent real-world situations, such as expressing constraints or limitations.

Step-by-step explanation:

Answer:

Step-by-step explanation:

tan L = 8/15

Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

If the ratio is 5: 3, (girls: boys) we can use this equation to figure out how many boys there are if there are 35 girls:

We can see that in the ratio 5: 3, 5 is being multiplied by 0.6 to get three. If the relationship between the numbers 5 and 35 stays proportional, we multiply 35 by 0.6.

Therefore, the ratio of girls to boys is 35: 21, meaning there are 21 boys.

The height of the right cylinder is 0.011 inches approximately.

Volume Definition:

Every three-dimensional object occupies some space. It is being determined how big this area is. Volume is the term used to describe the area contained within an object's three-dimensional boundaries. It is referred to as the object's capability on sometimes.

‘Volume’ is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Now in the given question,

Circumference,

[tex]2\pi r[/tex] = [tex]\frac{41}{4}[/tex]

[tex]r=\frac{41}{8\pi }[/tex]

V = 9 cubic inches

volume of cylinder = πr²h = 3.14×[tex]\frac{41}{8\pi }^2[/tex]×h

h = (9)÷(3.14×[tex]\frac{41}{8\pi }^2[/tex]) = 0.011 inches

therefore the height of the cylinder is 0.011 inches approximately.

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Answer:

The area of the irregular figure is 8.1 ft² (rounded to the nearest tenth).

Step-by-step explanation:

The irregular figure is made up of:

[tex]\boxed{\begin{aligned}\sf Area\;of\;triangle&=\sf \dfrac{1}{2} \times base \times height\\\\&=\sf \dfrac{1}{2} \times 2.8 \times 3.6\\\\&=\sf 1.4 \times 3.6\\\\&=\sf 5.04 \; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \; of\;semicircle&= \sf \dfrac{1}{2} \pi r^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times (1.4)^2\\\\&= \sf \dfrac{1}{2}\times 3.14 \times1.96\\\\&= \sf 1.57 \times1.96\\\\&= \sf 3.0772\; ft^2\end{aligned}}[/tex]

[tex]\boxed{\begin{aligned}\sf Area \;of\;irregular\;figure&=\sf Area\;of\;triangle+ Area\;of\;semicircle\\\\&=\sf 5.04+3.0772\\\\&=\sf 8.1172\\\\&=\sf 8.1\; ft^2\;(nearest\;tenth)\end{aligned}}[/tex]

Therefore, the area of the irregular figure is 8.1 ft² rounded to the nearest tenth.

Before solving for fractions, you must know what you're doing. This will list information you should know to solve fraction problems.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters

[tex]\frac{5}{12} + \frac{1}{4}[/tex] is our equation, so let's solve this step by step,

Common Denominator

As you can see, the fractions have unlike denominators. An unlike denominator is when 2 or more fractions have different denominators. One of our denominators is 12 and the other is 4, so this shows we have unlike denominators. The way we get the denominators to be the same is multiplying. Its a quicker method to easily make them the same. We can also skip count until the numbers meet:

12: 12,

4: 4, 8, 12

The fraction denominator can be 12. We can also prove that it is 12 by showing the Least Common Denominator, or LCD. LCD (5/12, 1/4) = 12.

[tex]\frac{5}{12}[/tex] × [tex]\frac{1}{1}[/tex] = [tex]\frac{5}{12}[/tex] . We multiply this by [tex]\frac{1}{1}[/tex] because the denominator is already 12.

[tex]\frac{1}{4}[/tex] × [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{12}[/tex].  We multiply this by [tex]\frac{3}{3}[/tex]  so we can make the denominator 12.

Adding the fractions

Now that we have our equation, [tex]\frac{5}{12}[/tex]  + [tex]\frac{3}{12}[/tex], we can easily add the fractions.

We do not add the denominators, however, we do add the numerators. We can express this as [tex]\frac{5+3}{12}[/tex]. 5 + 3 = 8. So, the numerator is 8. This means our answer is [tex]\frac{8}{12}[/tex].

Reduce

As your question says the sum must be in simplest form, you must reduce the answer to get it in simplest form. To reduce, you must divide. [tex]\frac{8}{12}[/tex] can be reduced, or divided by 4 to get it to simplest form. [tex]\frac{8}{12}[/tex] ÷ [tex]\frac{4}{4}[/tex] = [tex]\frac{2}{3}[/tex].

Answer

Simplest form: [tex]\frac{2}{3}[/tex]

Not in its simplest form: [tex]\frac{8}{12}[/tex]

The coordinates can be determined by using mid point formula. Here the coordinates vertex C is (2,8), vertex A is (0,2) and vertex T is (6,4)

Here the midpoints are (1,5) , (4,6), (3,3).

By using mid point equation, x₁+x₂/2 = 1

So x₁+x₂ = 2  --------------------> eq 1

x₂+x₃/2 = 3

x₂+x₃ = 6   -----------------------> eq 2

x₁+x₃/2 = 4

x₁+x₃ = 8 -----------------------> eq 3

Adding equations 1,2,3

2( x₁+x₂+x₃) = 16

 x₁+x₂+x₃ = 8 ---------------> 4

Determining x-coordinates

Subtracting equation 1 from 4

x₁+x₂+x₃ -(x₁+x₂) = 8-2

 x₃ = 6

Similarly subtracting equation 2 from 4

x₁+x₂+x₃ -(x₂-x₃) = 8-6

x₁ = 2

Subtracting 3 from 4

x₁+x₂+x₃ -(x₁+x₃) = 8-8

x₂ = 0

Determining y coordinates

y₁+y₂/2 = 5

y₁+y₂ = 10 ----------------> 5

y₁+y₃/2 = 6

y₁+y₃ = 12 ----------------> 6

y₂+y₃/2 = 3

y₂+y₃ =6   -------------->  7

Adding equations 5,6 and 7

2(y₁+y₂+y₃) = 28

y₁+y₂+y₃ = 14 -----------------> 8

Subtracting equations 5,6 and 7 from 8

y₁+y₂+y₃ -(y₁+y₂) =14 - 10

y₃ = 4

y₁+y₂+y₃ -( y₂+y₃) = 14- 6

y₁ = 8

y₁+y₂+y₃-(y₁+y₃) = 14- 12 = 2

So the coordinates are (x₁ , y₁) =(2,8)

                                       (x₂, y₂) = (0, 2)

                                       (x₃, y₃) = (6,4)

So the coordinates of C,A and T are (2,8) , (0,2) and (6,4) respectively.

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The formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) can be proven using the trigonometric identities.

Starting with the definition of cosecant:

cosec (A + B) = 1/sin (A + B)

Using the sum-to-product identity:

sin (A + B) = sinA cosB + cosA sinB

Substituting this expression into the definition of cosecant:

cosec (A + B) = 1 / (sinA cosB + cosA sinB)

Using the difference-to-product identity:

sinA - sinB = 2sin((A - B)/2)cos((A + B)/2)

Dividing both numerator and denominator by 2sin((A - B)/2)cos((A + B)/2), we get:

cosec (A + B) = (sinA cosB - cosA sinB) ÷ (sinA + sinB)(sinA - sinB)

Therefore, the formula cosec (A + B) = sinA cosB - cosA sinB ÷ (sinA + sinB)(sinA - sinB) has been proven.

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