Please help me to solve this question​

In total, the number of greetings will be 1159.

Mathematical symbols used to represent quantities or values include numbers. They are employed in the measurement, comparison, addition, subtraction, multiplication, and division processes in mathematics. According to their qualities and properties, numbers can be categorized into a variety of groups, including natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. There are specific properties and guidelines for mathematical operations for each group of numbers. Mathematics depends on numbers, which are also utilized in many other disciplines, including science, engineering, economics, and statistics.

The number of greetings exchanged between the host and the other mothers and daughters must be counted first. Since there is only one host, the number of mother-daughter pairs is 20 - 1 = 19. There are thus a total of 38 greetings, 19 between the host and the other moms, and 19 between the host and the other daughters.

The number of pleasantries exchanged between the guest mums and everyone else must next be tallied. The host, the other mothers, and the daughters must all be greeted, making a total of 20 - 1 = 19 guest mothers. Thus, each host mother must extend 1 + 19 + 20 = 40 greetings. There will be 760 greetings exchanged between the guest mothers and everyone, or 19 x 40.

The number of pleasantries exchanged between the mothers and the invited girls must also be tallied. Moreover, there are 20 guest girls, so 19 of them must welcome the mothers. As a result, there will be 361 pleasantries exchanged between the mothers and the guest daughters.

In total, the number of greetings will be 38 + 760 + 361 = 1159.

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-12v+6y+18

you multiply everything by -3, so -3×4v=-12v
-3×(-2y)=6y, since negative × negative=positive
-3×(-6)=18

i hope this helps :)

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

Answer:.

Step-by-step explanation im not sure

Answer:

Step-by-step explanation:

47.)  sin20 = 6/b

b = 6(sin20) = 17.5

c = √6²+17.5² = 18.5

48.)  tan61 = y/18

y = 18(tan61) = 32.5

z = √18²+32.5² = 37.1

49.)  r = √25²+23² = 34

50).  d = √30²+7² = 30.8

51.)  sin71 = j/19

j = 19(sin71) = 18

k = √19²-18² = 6.2

52.)  y = √4²-1² = √7 = 2.6

53.)  sin49 = f/26

f = 26(sin49) = 19.6

h = √26²-19.6² = 17

54.)  t = √7²+4² = 8.1

Answer:

x-1+5x+1=180, 6x=180, x=30

Step-by-step explanation:

Answer:

2 - √3

Step-by-step explanation:

Find other root. Use x as a substitute.

\(x = 2 + \sqrt{3}\\x - 2 = \sqrt{3}\\\left(x - 2\right)^2 = 3\\x^2 = 4 - 2 \times x \times 2 = 3\\x^2 - 4x + 1 = 0\)

Now, we must use the quadratic formula to find the rest of the solution.

\(x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}\\x = \frac{4\pm \sqrt{\left(-4\right)^2-4 \times 1 \times 1} }{2}\\\frac{4 \pm \sqrt{12} }{2} = 2 \pm 3\)

If one root of this polynomial [root] is 2 - √3, the other will be 2 + √3. Inversing that rule, the answer is 2 - √3.

Answer:

5000 g

Step-by-step explanation:

1 kg = 1000 g

5 kg is 5 times 1 kg

5 * 1 kg = 5 * 1000 g

5 kg = 5000 g

I do not understand what do you mean

A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:

(x, y)                                              →                 (-x, y).

\(f(x) = \frac{3}{8} (4)^x\)                               →              \(g(x) = \frac{3}{8} (4)^{-x}\)

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The number of small rooms reserved is 4.

The number of large rooms reserved is 8.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Small rooms are denoted as S.

Large rooms are denoted as L.

Now,

We will make two equations.
L = 2S _____(1)

8L + 6S = 88 ______(2)

Putting (1) in (2) we get,

8L + 6S = 88

8 x (2S) + 6S = 88

16S + 6S = 88

22S = 88

S = 88/22

S = 8/2

S = 4

Now,

Putting S = 4 in (1) we get,

L = 2 x 4

L = 8

Thus,

The number of small rooms and large rooms reserved is 4 and 8.

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when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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the coordinate of X is at 8 units of P and at 4 units to the left of Q

So the coordinate of X is: -5 + 8 = 3

We know that point X is between points P and Q, in such a way that the ratio between the lengths of the segments PX and XQ is 2:1

First, we can length of the segment PQ is equal to the difference between their coordinates, so we get:

L = 7 - (-5) = 12

Then the length of segment PQ is 12 units, if we divide that in 3 we will get:

12/3 = 4 units.

So the segment PQ can be divided into 3 segments of 4 units each.

If the ratio PX to XQ is 2:1

Then the segment PQ must be divided into 3 parts, such that PX takes two of these parts and XQ is the remaining one.

Then the coordinate of X is at 8 units of P and at 4 units to the left of Q

So the coordinate of X is: -5 + 8 = 3

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Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

Slope m = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

Answer:

y = 4x - 6

Step-by-step explanation:

Hi there!

We are given the points (3,6) and (1, -2), and that a line passes through these 2 points

We want to find the equation of said line

There are 3 ways to write the equation of the line:

The  most common way is slope-intercept form, so let's write the equation of the line this way

First, we need to find the slope

The slope (m)  can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) & \((x_2, y_2)\) are points

Before we calculate, let's label the values of the points.

\(x_1=3\\y_1=6\\x_2=1\\y_2=-2\)

Now substitute into the formula

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2-6}{1-3}\)

Subtract

m=\(\frac{-8}{-2}\)

Divide

m= 4

The slope of the line is 4

Substitute 4 as m in y=mx+b:

y = 4x + b

Now to find b

Since the equation passes through both (3,6) and (1, -2), we can use either point to help solve for b.

Taking (3,6) for example:

Substitute 3 as x and 6 as y.

6 = 4(3) + b

Multiply

6 = 12 + b

Subtract 12 from both sides

-6 = b

Substitute -6 as b into the equation

y = 4x - 6

Hope this helps!

Topic: finding the equation of the line

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Answer:

Step-by-step explanation:

-4.4 + (5-2)(-6) = -4.4 + (3)(-6) = -4.4 + (-18) = - 22.4

Answer:

the answer is (2•5x5y3)

Step-by-step explanation:

1.  (2x4 • y3) • 5x

Multiplying exponential expressions

2. x4 multiplied by x1 = x(4 + 1) = x5

Final result :

(2•5x5y3)

Sorry if I'm wrong

Answer:

10 x ^5 y^ 3

Step-by-step explanation:

Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

Answer:

8

Step-by-step explanation:

3/4 cup leaves 1/4 cup from each cup

1/4+1/4+1/4=3/4

so it would be 3/4+3/4+3/4+3/4+3/4+3/4+3/4+3/4=8 cups

In roster notation, the set can be represented as:

{Loan fraud, Bank fraud, Employment fraud, Utilities/phone fraud, Other}

To write the set of identity theft types that made up more than 50% of all reported claims, we can examine the percentages provided.

The type of identity theft fraud that made up more than 50% of all reported claims is:

Government documents/benefits fraud (49.2%)

In roster notation, the set can be represented as:

{Government documents/benefits fraud}

To list the set of types of identity fraud that made up less than 20% of all reported cases, we can examine the percentages provided for each type of identity theft fraud.

The types of identity theft fraud that made up less than 20% of all reported cases are:

Loan fraud (3.5%)

Bank fraud (5.9%)

Employment fraud (3.3%)

Utilities/phone fraud (9.9%)

Other (19.2%)

In roster notation, the set can be represented as:

{Loan fraud, Bank fraud, Employment fraud, Utilities/phone fraud, Other}

To write the set of identity theft types that made up more than 50% of all reported claims, we can examine the percentages provided.

The type of identity theft fraud that made up more than 50% of all reported claims is:

Government documents/benefits fraud (49.2%)

In roster notation, the set can be represented as:

{Government documents/benefits fraud}

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Answer:

2500

Step-by-step explanation:

Monthly total cost, C(x) = 400 + 200x dollars

Monthly total revenue, R(x) = \(350x -\dfrac{1}{100}x^2\) dollars

Profit = Revenue - Cost

\(=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400\)

To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.

\(P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500\)

Next, we check if the point x=7500 is a maxima or a minima.

To do this, we find the second derivative of P(x).

\(P''(x)=-\dfrac{1}{50} $ which is negative\)

Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.

Therefore, the company needs to produce 2500 units to maximize profit.

To graph the inequality k > 5 on a number line, mark an open circle at 5 and shade the region to the right.

To graph the solutions to the inequality k > 5 on a number line, follow these steps:

Draw a horizontal line and mark a point for the number 5 on the line.

-------------------|---|---|---|---|---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Since the inequality is k > 5, the solution includes all values greater than 5. Therefore, draw an open circle (○) at the number 5 to represent that 5 itself is not included in the solution.

-------------------|---|---|---|---○---|---|---|---|---|---|

0 1 2 3 4 5 6 7 8 9 10

Shade the region to the right of the open circle. This shading represents all values that are greater than 5 and satisfy the inequality k > 5.

-------------------|---|---|---|---○===================>

0 1 2 3 4 5 6 7 8 9 10

The resulting number line graph illustrates that any value to the right of the open circle (excluding 5 itself) satisfies the inequality k > 5.

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Answer:

72 minutes

Step-by-step explanation:

you convert the 80% to decimal form so its now 0.80.

then you multiply how long the school play was (90) times the 'percentage' of how long the main character was on the stage (0.80).

90 times .80 is 72.

hope this helped:)

Answer:

(1,1) is the answer

Explanation:

Both lines cross at (1,1)

Given:

The figure with some sides measurements.

Required:

What is missing side length and which triangle is a right triangle?

Explanation:

Converse of Pythagoras theorem:

So, take BAD right triangle,

Now,

Answer:

Answer:

Step-by-step explanation:

Angle A is marked as a right angle. Therefore, triangle ABD is a right triangle.

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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No, it is not a regular polygon.

A hexagon is a six sided polygon. And a convex hexagon means, the hexagon's vertices are pointed outwards.

And no interior angle has an angle measure more than 180°.

Given:

A polygon.

To be a regular polygon:

Given Hexagon,

should have equal sides and equal angles.

We have no information about the angles and sides.

Therefore, it is not a regular polygon.

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The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

In this question we must compare a given exponential function with a set formed by four functions. As the function is crescent and monotonous, then  we can choose the correct graph by a evaluating the function for a given x-value and find the graph that matches with such finding:

f(5) = 3⁵

f(5) = 243

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

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Answer:

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.

Step-by-step explanation:

I am going to say that:

x is the proportion of 5th graders.

y is the proportion of 6th graders.

z is the proportion of 7th graders.

The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11

This means that:

\(\frac{y}{z} = \frac{4}{11}\)

So

\(11y = 4z\)

\(y = \frac{4z}{11}\)

The number of 5th graders to that of the 6th graders was 13 to 9.

This means that:

\(\frac{x}{y} = \frac{13}{9}\)

\(9x = 13y\)

\(x = \frac{13y}{9}\)

All of them is 100%

This means that:

\(x + y + z = 1\)

We need to find z.

\(y = \frac{4z}{11}\)

\(x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}\)

Then

\(x + y + z = 1\)

\(\frac{52z}{99} + \frac{4z}{11} + z = 1\)

The lcm(least common multiple) between 11 and 99 is 99. Then

\(\frac{52z + 9*4z + 99z}{99} = 1\)

\(187z = 99\)

\(z = \frac{99}{187}\)

\(z = 0.5294\)

By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

z(7th graders) is 52.94%.

x + y(5th and 6th graders) is 100 - 52.94 = 47.06%

52.94 - 47.06 = 5.88

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.