Four components of 55

Answer:

Let's suppose that the integer is x.

We know that x leaves a remainder of 1 when divided by 4, so we can express x as:

x = 4n + 1

where n is some integer.

Now we need to find the remainder when x^2 is divided by 8:

x^2 = (4n + 1)^2

x^2 = 16n^2 + 8n + 1

Notice that the first two terms (16n^2 + 8n) are divisible by 8, so we can ignore them.

The remainder when x^2 is divided by 8 is the same as the remainder of 1 when divided by 8:

x^2 ≡ 1 (mod 8)

Therefore, the remainder when the square of the integer is divided by 8 is 1.

The smallest number with six different digits not including zero that begins with 2 and ends with 3 is: 213457.

The greatest number with six digits not including zero that begins with 3 and ends with 2 is: 398762.

The smallest number with six different digits not including zero that begins with 2 and ends with 3 can be constructed by choosing the remaining four digits from the set {1, 4, 5, 6, 7, 8, 9}, arranging them in ascending order, hence it is of:

213457.

For the greatest number with six digits not including zero that begins with 3 and ends with 2, we arrange them is descending order, hence it is of:

398762.

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Here is the correct equation:

[tex]c = 15 + 65m[/tex]

Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: [tex]r(A) = -4 + square root(64 + 2A) /[/tex]

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.

Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.

As a result, the domain of A(r) is:

{r ∈ ℝ | r > 0}

Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.

To begin, we may simplify the equation by removing 2r:

A = 2πr(r + 8)

Hence, using the quadratic formula, we can find r:

[tex]r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /[/tex]

We know, however, that r must be positive, therefore we take the positive square root:

[tex]r(A) = -4 + square root(64 + 2A) /[/tex]

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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.

A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.

Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.

Dοmain οf A(r): r ≥ 0

Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:

[tex]2 \pi r^2 + 16 \pi r - A = 0[/tex]

[tex]r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)[/tex]

[tex]r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi[/tex]

Simplifying this expressiοn, we get:

[tex]r = (-4 \± \sqrt{(64 + 2A)}) / 2[/tex]

[tex]r(A) = -2 \± \sqrt{(32 + 0.5A)[/tex]

Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:

[tex]r(A) = -2 + \sqrt{(32 + 0.5A)[/tex]

Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:

[tex]r(300) = -2 + \sqrt{(32 + 0.5(300))[/tex]

r(300) = -2 + sqrt(182)

r(300) ≈ 11.51

Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.

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Answer:

Step-by-step explanation:

5824×45​

              5824

               x  45

             29120

          23296 x

          262080

Using cοmpοund interest, the Tοtal return equals $ 17,300 and Annual returns fοr the 4-year periοd will be equal tο 13.32%.

The interest yοu receive that is cοmpοunded οn:the primary, οr the sum yοu depοsited οriginallyinterest that yοu have previοusly accrued

Fοr instance, if yοu have a savings accοunt, yοu will receive interest οn bοth yοur initial funds and any priοr interest. On yοur interest, yοu receive interest.

Simple interest is distinct frοm this. At the end οf the periοd, simple interest is sοlely paid οn the principal. Simple interest is typically paid οn term depοsits.

Given the principal = $2700

Amοunt = $20,000

Total return = $20,000 - $2700

= $ 17,300

Annual returns for the 4-year periοd will be equal to,

using compοund interest formula,

[tex]A = P (1 + \frac{r}{n})^{t}[/tex],

Where A = amοunt,

P = principal,

r = rate οf interest,

n = number οf times interest applied per time period,

t = time periοd,

For, 5 years, the value will be -

[tex]20,000 = 2700 (1 + r/100)^5[/tex]

[tex]7.41 = (1 + r/100)^5[/tex]

1.50 = 1 + r/100

1.50 - 1 = r / 100

0.50 = r / 100

r = 5%

For 4 years,

[tex]Annual return = ((202700 (5/4)^4\\A = 13.32 \%[/tex]

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Rounding to the nearest tenth, we get the area of the sector is: 6.3 square inches.

Area is the measurement of the amount of space inside a two-dimensional shape, such as a square, circle, or triangle. It is usually expressed in square units, such as square inches or square meters. To find the area of a shape, you need to use a specific formula based on its dimensions and geometry. For example, the area of a rectangle can be found by multiplying its length by its width, while the area of a circle can be found by using the formula pi times the radius squared.

Here,

To find the area of the sector, we need to use the formula:

Area of sector = (central angle/360) x πr²

where r is the radius of the slice.

Plugging in the values we get:

Area of sector = (34/360) x π(8)²

Area of sector = (0.0944) x π(64)

Area of sector = 6.2822 square inches

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The simplified expression for given expression is x⁷/y¹⁰.

Simplification means reducing the expression in a simpler form using various operations while Approximation is simplifying the mathematical expression to its nearest value but not exactly correct.

To simplify the expression:

x³y⁻²x/x⁻³y⁸

Applying the properties, we get:

x³y⁻²x/x⁻³y⁸ = x⁽³⁻⁽⁻¹⁾⁾y⁽⁻²⁻⁸⁾/x⁻³x¹y⁰

Simplifying the exponents and the term with y, we get:

x⁴/y¹⁰ * x³ = x⁽⁴⁺³⁾/y¹⁰ = x⁷/y¹⁰

Therefore, the simplified expression is x⁷/y¹⁰.

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Answer:

A will receive 288, B will receive 432, and C will receive 144.

Step-by-step explanation:

The total ratio of the parts is 2+3=5. This means that the whole amount represents 5 parts.

To find the size of one part, we can divide the total amount by the total number of parts:

One part = 720/5 = 144

Now that we know the size of one part, we can use the ratio to find the amounts that A, B, and C will receive:

A will receive 2 parts: 2 × 144 = 288

B will receive 3 parts: 3 × 144 = 432

C will receive 1 part: 1 × 144 = 144

Therefore, A will receive 288, B will receive 432, and C will receive 144.

Answer:

Deductive reasoning

The answer is deductive reasoning.

The correct equation in vertex form for the function is:

g(x) = 2(x-5)² + 9

What is the parabola?

The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.

Option A is the correct equation in vertex form for the function:

g(x) = 2(x-5)² + 9

The vertex form of a parabola is y=a(x-h)²+k, where (h,k) is the vertex of the parabola. We are given that the vertex is located at (5,9), so h=5 and k=9. Substituting these values into the vertex form equation, we get:

g(x) = a(x-5)² + 9

To find the value of a, we can use one of the points that the parabola passes through. Let's use point (7,1):

1 = a(7-5)² + 9

1 = 4a + 9

-8 = 4a

a = -2

Substituting this value of a into the equation, we get:

g(x) = -2(x-5)² + 9

Expanding the square and simplifying, we get:

g(x) = -2x² + 20x - 41

This is not in vertex form, but if we factor out the -2 from the first two terms, we get:

g(x) = -2(x² - 10x + 20.5)

Completing the square inside the parentheses, we get:

g(x) = -2(x-5)² + 50.5

This is also in vertex form, but the constant term is not 9 as given in the problem.

Therefore, the correct equation in vertex form for the function is:

g(x) = 2(x-5)² + 9

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Answer:

B

1 x 10^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

One mathematical sentence that relates to a real-life scenario in business is:

Profit = Revenue - Cost

This formula represents the basic accounting equation, which is used to calculate the profit or loss of a business. In this equation, "Revenue" represents the total amount of money a business earns from its sales or services, and "Cost" represents the total amount of money a business spends on producing its goods or services.

By subtracting the cost from the revenue, we can determine the amount of profit a business has made. If the resulting value is positive, the business has made a profit; if it is negative, the business has suffered a loss.

This mathematical sentence is widely used in business and finance, and is essential for determining the financial health of a business. It can be used to make important decisions, such as whether to invest in new products or services, or to expand the business. Overall, the profit equation is a crucial tool for businesses to ensure their continued success and growth

Answer:

10x

Step-by-step explanation:

Just add or subtract.

4x + 7x - 1x

4 + 7 - 1 = 10

10x

Answer: i believe its 10x

Step-by-step explanation:

Answer: -4 5/12

Step-by-step explanation: because -7 2/3+(-5 1/2)= -13 1/6

finally take -13 1/6 + 8 3/4= -4 5/12

Answer: True

Step-by-step explanation: That was a complete guess. Did you forget to include an image? Am I missing something?

So the average rate of change of the function over the interval 0 ≤ x ≤ 15 is 4.4.

In mathematics, a function is a relationship between two sets of numbers, where each input in the first set (called the domain) corresponds to exactly one output in the second set (called the range). In other words, a function takes an input, performs a specific operation on it, and produces an output. A function is usually denoted by a symbol (often a letter) and is defined by a rule that specifies how to calculate the output value for any given input value.

Here,

To find the average rate of change of the function over the interval 0 ≤ x ≤ 15, we need to calculate the change in the function value divided by the change in x over the interval.

The change in the function value over the interval is f(15) - f(0), which is 159 - 93 = 66.

The change in x over the interval is 15 - 0 = 15.

Therefore, the average rate of change of the function over the interval 0 ≤ x ≤ 15 is:

average rate of change = change in f / change in x

= 66 / 15

= 4.4

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Answer:

Given that

(5a+6 )°+90°+(7a)°=180°

(angles on a straight line sum up to 180°)

5a°+6°+90°+7a°=180°

5a°+7a°=(180-96)°

12a°=84°

Deviding both sides by 12° gives

a=84/12

a=7°

therefore the value of

a=7°

Answer:

X (minutes) Y (cost in dollars)

10 7.30

20 14.60

30 21.90

40 29.20

50 36.50

60 43.80

Answer:

Step-by-step explanation:

To construct the data set, we need to consider the given measures of central tendency:

Mean: 9

Median: 8

Mode: 5

Midrange: 11.5

We can start by finding five values that are less than or equal to the median of 8, and five values that are greater than or equal to the median. Since the mode is 5, we can include it as one of the lower values.

Let's try to find the other four lower values that satisfy the given conditions:

The sum of all values is 10 * 9 = 90 (since there are 10 values and the mean is 9).

The mode is 5, so we need at least two values that are equal to 5.

The midrange is (max + min) / 2 = 11.5, so we need a maximum value that is 3 more than the minimum value.

Here's one possible set of 10 values that satisfy these conditions, listed in ascending order:

{2, 3, 4, 5, 5, 8, 9, 10, 12, 13}

To check that this set of values satisfies the given conditions:

The mean is (2+3+4+5+5+8+9+10+12+13) / 10 = 9.

The median is 8 (the middle value when the values are listed in ascending order).

The mode is 5 (the most common value).

The midrange is (13 + 2) / 2 = 7.5 + 4 = 11.5 (the average of the maximum and minimum values).

Answer:

r = 3

Step-by-step explanation:

Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides.

AO^2 = AB^2 + BO^2

(2 + r)^2 = 4^2 + r^2

r^2 + 4r + 4 = 16 + r^2

4r = 12

r = 12/4

r = 3

Answer:

Step-by-step explanation:

its c

Answer:

(x-4)-(x+7)=8 is x = -19

Step-by-step explanation:

To solve the equation for x, we need to simplify the left-hand side by combining the like terms:

(x-4)-(x+7)=8

x - 4 - x - 7 = 8 (distribute the negative sign)

-x - 11 = 8 (combine like terms)

To isolate x, we need to get rid of the constant term on the left-hand side. We can do this by adding 11 to both sides:

-x - 11 + 11 = 8 + 11

-x = 19

Finally, we can solve for x by multiplying both sides by -1:

x = -19

Therefore, the solution for the equation (x-4)-(x+7)=8 is x = -19.

One packet of raisins costs £1.53 after buying three packets with a £5 note and receiving 41p change.

Total amount paid = £5

Change received = 41p (41 pence)

as he paid £5 note and gets 41p change

100 pence make £1, 41p is equal to £0.41

total amount paid = £5 - £0.41 = £4.59

Ben bought 3 packets of raisins for £4.59

cost of one packet = cost of 3 packets of raisin / 3

cost of one packet = £4.59 ÷ 3 = £1.53

Therefore,  one packet of raisins costs £1.53.

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Answer:

The profit (P) of a company is equal to the revenue (R) minus the cost (C): P = R - C.

Step-by-step explanation:

Option B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.

To determine whether a relation is a function, we need to check whether each input value (the first coordinate of each ordered pair) is associated with exactly one output value (the second coordinate of each ordered pair).

The input value 1 is associated with two different output values (3 and 4), so this relation is not a function.

Therefore, the relation given by set B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10) is not a function.

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The question given is incomplete, the complete question is:

Which of the relations given by the following sets of ordered pairs is not a function?

A. (-4, -4), (-3, -3), (0, 0), (3, -3), (4, -4)

B. (-4, -2), (-1, -1), (1, 3), (1, 4), (7, 10)

C. (5, 1), (4, 1), (3, 1), (2, 1), (1, 1)

D. (-5, -7), (-4, -6), (-3, -5), (-2, -4), (-1, -3)

The length of the most direct path between Ann and the pile of bottle caps is given as follows:

31 feet.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Ann's location is given by the following ordered pair:

(-4,3).

The location of the pile of bottle caps is given by the following coordinate pair:

(4, -10).

Hence the distance is given as follows:

D = sqrt((4 - (-4))^2 + (-10 -3)^2)

D = 15.5 units.

Each unit represents 2 feet, hence:

15.5 x 2 = 31 feet.

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Answer:

A.) 5.68
B.) 8.4%
C.) 99.6%

Step-by-step explanation:

Vector W is not a linear combination of the vectors v1, v2 and v3.

w is a linear combination if it is written as a system of equations of the vectors v1, v2 and v3.

Considering the first three lines, the system of equations modeling these variables is given as follows:

From the second equation, the value of y is given as follows:

2y = -1

y = -0.5.

From the third equation, the value of x is given as follows:

x - 0.5 = -1

x = -0.5.

From the first equation, the value of z is given as follows:

-0.5 + z = 2

z = 2.5.

From the fourth equation, we have that:

z = 1.

Which is false, as we found z = 2.5 solving the system of equations, hence Vector W is not a linear combination of the vectors v1, v2 and v3.

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