) in a dinner party 5 different appetizers and 6 different desserts are served. in how many different ways 3 appetizers and 2 desserts can be selected?

The estimated age of the tomb of Sneferu is 8,330 years.

The age of the tomb can be estimated using the carbon-14 decay equation, which states that the amount of carbon-14 remaining after time t (in years) is equal to the initial amount of carbon-14 multiplied by 0.5^(t/5730).The decay equation for carbon-14 is A = A₀e⁻kt, where A₀ is the original amount of carbon-14, A is the amount of carbon-14 at time t, k is the decay constant, and t is the amount of time that has passed.

We can rearrange the equation to solve for t: t = -ln(A/A₀)/k. In this equation, A is the amount of carbon-14 found in the cypress beam, and A₀ is the amount of carbon-14 found in living cypress wood.

In this case, the initial amount of carbon-14 was 100%, and the remaining amount was 55%. Solving for t, we get t = (ln(55%)/ln(0.5))*5730 = 8,330 years.

Therefore, the estimated age of the tomb of Sneferu is 8,330 years.

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If a delivery truck is transporting boxes of two sizes: large and small. The number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.

Let L represent the number of Large boxes.

Let S represent the number of Small boxes.

Total number of boxes = 120

L + S = 120

The two equations are:

L + S = 120

55×L + 15×S = 3800

L + S = 120 eliminate L by multiplying this equation by -55

-55×(L + S = 120)      

The equations are:

55 ×L + ×15S = 3800

-55×L -55×S = -6600

0 - 40×S = - 2800

S = -2800/(-40)

S = 70

Plug S back into one of our equations.

L + S = 120

L + (70) = 120

L = 120 - 70

L = 50

So ,

L = 50 and S = 70

Therefore the number of each type of box it carrying is: Large boxes is 50 and small boxes is 70.

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[tex]6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}[/tex]

If one addend of x is c, the other addend is x-c.

An addend is a term that is added to another term to form a sum. In the equation x = c + (x-c) , c and (x-c) are the two addends that make up the sum x.

The reason why x-c is the other addend is that the sum of the two addends (c and x-c) must equal x.

In other words x = c + (x-c) can be simplified to x = c + x - c which is x = x

Therefore, If one addend of x is c, the other addend is x-c.

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A graph of the inequality is shown in the image attached below.

In this scenario, we would solve the given inequality by making m the subject of formula as follows;

-2 > m/6 - 7

By collecting like terms, we have the following:

-2 + 7 > m/6

5 > m/6

Cross-multiplying, we have:

30 > m

By re-writing the inequality, we have:

m < 30

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Also, the circle is open because of the greater than (>) symbol.

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The function is not linear because the rate of change in not constant.

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

Given:

      x                   y

      10                -6

      11                  1

       12                6

       13                12

So, the rate of Change

= 10/ (-6)

= -5/2

and, again = 11/1 = 11

As, the rate of change is not constant.

But, in linear function the rate of change is same.

Hence, the function is not linear.

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The cups of each items needed will be 9 cups of peanuts, 1.8 cups of chocolate and 7.2 cups of raisins.

From the information, 18 0ne-cup bags of tail mix is needed for the class tripThe recipe includes chocolate, chips and raisins in the ratio of 5:1:4

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number.

5x- peanuts

1x- chocolate chips

4x- raisins

5x + 1x + 4x= 18

10x= 18

x= 18/10

x = 1.8

Chocolate = 1.8 cups

Raisins = 4x

= 4 × 1.8

= 7.2 cups.

Peanut = 5x

= 5 × 1.8

= 9 cups

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The expression that shows the number of bagels Shane has left is 12-b.

Expression in math is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given;

Shane bought a package of 12 bagels

He gave b of them to his friends

Now;

Shane bought 12 bagels

Expression= 12

Shane gave b

Expression=12-b

Therefore, the expression will be 12-b.

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a) The circumference of the tire is 7.85 ft

b) About 673 times the tire will have to rotate to travel 1 mile.

The diameter of a tire is 2. 5 ft.

Let r represents the radius of the tire.

r = diameter/2

r = 2.5 / 2

r = 1.25 ft

a)  the circumference of the tire:

We know that the formula for the circumference of circle:

C = 2πr

So, the circumference of the tire would be,

C = 2 × π × r

C =  2 × π × 1.25

C = 7.85 ft

b) Let the tire will have to rotate n times in order to travel 1 mile.

We know that 1 mile = 5,280 ft

So, n = 5280 / 7.85

n = 672.6

n ≈ 673

Thus, the tire will have to rotate 673 times in order to travel 1 mile.

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The line of linear equation y = 8x - 48 is much steeper than the line of linear equation y = -x - 4-.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The table of input and output values are given for the function.

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[16 - 32]/[8 - 10]

(-16)/(-2)

8

So, the slope point is obtained as m = 8.

The equation becomes - y = 8x + b

To find the value of b substitute the values of x and y in the equation -

32 = 8(10) + b

32 = 80 + b

b = 32 - 80

b = -48

So, the value for b is -48.

Now, the equation becomes -

y = 8x - 48

A graph has been plotted for the equation.

Similarly, the points for a line is given as (-6,2) and (-9,5).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[5 - 2]/[-9 - (-6)]

(3)/(-9 + 6)

3/-3

-1

So, the slope point is obtained as m = -1.

The equation becomes - y = -x + b

To find the value of b substitute the values of x and y in the equation -

2 = -(-6) + b

2 = 6 + b

b = 2 - 6

b = -4

So, the value for b is -4.

Now, the equation becomes -

y = -x - 4

A graph has been plotted for the equation.

It is known that the larger the slope the steeper the line.

In the graph also it can be seen that the graph of line y = 8x - 48 is much steeper.

Therefore, the slope of line y = 8x - 48 is more steeper.

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King usually becomes the most emotional during moments of reflection or when he is expressing his views on civil rights and justice. King's message of hope, courage, and resilience encourages individuals to stand up for what is right and to never give up in the face of injustice.

Dr. King utilises passion in his lectures to accentuate his message and to connect with his audience on an emotional level. He frequently speaks about the sorrow and injustice that his people have endured, eliciting an emotional response from his audience. He also inspires his audience to believe in the prospect of a brighter future, which instills hope and motivation. Furthermore, he frequently employs metaphors and analogies to underline his ideas, which may be extremely effective.

King is generally the most emotional when he is reflecting or expressing his ideas on civil rights and justice. In these times, he sends a message of hope, strength, and endurance. King usually uses compelling metaphors and parables to highlight the necessity of equality and justice. He highlights the power of our actions to effect change and the importance of never losing hope in the face of hardship. He frequently urges for unity among all races and sexes and opposes all types of prejudice. He also discusses the power of love, understanding, and mutual respect in bridging gaps and creating a better society.

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The solution for the expression given above would be = 31/40. That is option B.

A fraction is defined as the part of a whole value which is written in the form of a numerator and a denominator.

The given fractions from the question;

2/5 + 3/8

Find the lowest common multiple of the figures below ( denominator) = 40

= 16 + 15/40

= 31/40

Therefore the correct fraction for the given expression = 31/40.

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Length of side of the rhombus is 5cm.

A rhombus can be thought of as a special parallelogram since it satisfies the requirements for one (a quadrilateral with two pairs of parallel sides). Another characteristic of a rhombus is that it has four equal sides, just like a square. It is also known as a tilted square for this reason.

step1

Diagonals of a rhombus bisect each other at right angles.

Let point of intersection of diagonals be O

So, OD = 3cm , OA = 4cm

From Right angled triangle △ AOD,

⇒ AD²  = OA²  + OD²   (Pythagoras theorem)

⇒ AD² =4² + 3²

⇒ AD² = 16+9

⇒AD² =25

step2

⇒ AD² =25

⇒ AD=5 cm

AD is side of the rhombus.

So, length of side of the rhombus is 5cm

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We are given that quadrilateral EFGH is a rectangle. If EF=4x−6 and HG=x+3 , then the side EF= -34.

What is a quadrilateral?

A quadrilateral is a four-sided polygon, or a shape with four straight sides. It is a type of closed, two-dimensional shape. The four sides of a quadrilateral can be of equal or varying lengths and angles. Examples of quadrilaterals include squares, rectangles, rhombuses, parallelograms, and trapezoids.

Since quadrilateral EFGH is a rectangle, the opposite sides are congruent and parallel.

Therefore, if EF = 4x - 6 and HG = x + 3, then HG=EF

so, x+3=4x-6

then, x=-9

Therefore, EF=4x-6=4(-9)-6= -34

Hence, EF= -34

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If u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), the derivative of cross product d/dt [u (t) x v (t)] is (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t)).

Formula 5 of the cross product theorem states that the derivative of the cross product of two vectors u and v is equal to the cross product of the derivatives of u and v:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt)

Where u(t) = (sin 3t, cos 3t, t) and v(t) = (t, cos 3t, sin 3t), we can find the derivatives as follows:

du/dt = (d(sin 3t)/dt, d(cos 3t)/dt, dt/dt)

= (3 cos 3t, -3 sin 3t, 1)

dv/dt = (dt/dt, d( cos 3t) /dt, d( sin 3t)/dt)

= (1, -3 sin 3t, 3 cos 3t)

Now, we can substitute these derivatives into the formula to find d/dt [u (t) x v (t)]:

d/dt [u(t) x v(t)] = (du/dt) x v(t) + u(t) x (dv/dt) = (3 cos 3t, -3 sin 3t, 1) x (t, cos 3t, sin 3t) + (sin 3t, cos 3t, t) x (1, -3 sin 3t, 3 cos 3t)

= (-3sin²3t - cos3t, t - 3cos3tsin3t, 3cos²3t + 3tsin3t) + (3cos²3t + 3tsin3t, t - 3cos3tsin3t, -3sin²3t - cos3t)

= (3cos²3t + 3tsin3t - 3sin²3t - cos3t, 2t - 6cos3tsin3t, 3cos²3t + 3tsin3t - 3sin²3t - cos3t)

= (3cos(6t) + 3tsin(3t), 2t - 3sin(6t), 3cos(6t) + 3tsin(3t))

The cross product of two vectors is a vector, and the result of the above calculation will be a vector that describes the rate of change of the cross product u(t) x v(t).

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Answer:

The degree is 4 because the term shown has TWO variables, while y has an exponent of 3, x has an exponent of 1, add the exponents of the variables to find the degree

Step-by-step explanation:

As per the given equation, the domain is [0, 3000] and the range is [0, 600].

In the term domain is defined as the set of values that we are allowed to plug into our function where as the range of a function is the set of values that the function assumes.

Here we know that the amount of sand left in a 600 mL vase can be modeled by the equation that is written as,

=> s = – 1/5 t + 600

here s refers the amount of sand left in the vase and t refers time in minutes since the sand started leaking out

Here we also know that the vase is full of sand and sand leaks out of the vase until the vase is empty.

Then in order to find the domain we have to put the value of s as 0, then we get the domain as,

=> 0 = -1/5t + 600

=>1/5t = 600

=> t = 3000

Then the domain is [0, 3000].

Similarly, in order to find the value of range we have to put the value of t as zero, then we get

=> s = -1/5(0) + 600

=> s = 600

Then the range is [0, 600]

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It's a fact that the sum of the angles of a triangle add up to 180º.

So, 55º + 85º + (3x+4)º = 180º.

That's the equation you need to solve:

     55 + 85 + 3x+4 = 180    (combine like terms)

                 144 + 3x = 180   (subtract 144 from both sides)

                           3x = 36     (divide both sides by 3)

                             x = 12      (you've got x)

Answer:

a) The two side lengths of the tenth rectangle in the sequence are 8 + (10 - 1)4 = 32 and 8 + (10 - 2)4 = 28.

b) The area of 576in2 is not possible in the given sequence because it would require a side length of 24, which does not follow the sequence given.

Step-by-step explanation:

The given sequence is represented by the equation an=8+(n−1)4, which means that for each successive rectangle in the sequence, the length of one of the sides will increase by 4. Therefore, in order for the area of a rectangle to be 576in2, the length of one of the sides must be 24, which does not follow the sequence given.

Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bottles   Glue   Glitter

1              3.8       1.9

This means,

1 bottle = 3.8 oz of glue and 1.9 oz of glitter

Now,

1 bottle = 3.8 oz of glue

Multiply 4 on both sides.

4 bottle = 4 x 3.8 oz

4 bottle = 15.2 oz

1 bottle = 1.9 oz of glitter

Multiply 4 on both sides.

4 bottle = 7.6 oz

Thus,

15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

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The percentage of games that Mamadou scores between 136 and 214 is given as follows:

99.7%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

For this problem, we have that

Hence the percentage is of 99.7%, as the measures are within three standard deviations of the mean.

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The value of the variable , k is -385/13

A function can be described an expression, equation, law or rule explaining the relationship between two variables.

These variables are known as;

From the information given, we have the function;

f(x)=-(13)/(5)x+k

Also, for the value of f(30), the function is equivalent to -1

Now, substitute the value of x as 30 and equate the function to -1. we have;

-1 = -13/(5)30 + k

Divide both sides by the cofficient of 30 + k

30 + k = -1 × -5/13

Multiply the values

30 + k = 5/13

Now, collect like terms

k = 5/13 - 30

k = -385 /13

Thus, the value is -385/13

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The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is  x² - 3x.

The solution of (x³ - 5x² -24x) / (x + 8) using synthetic division is given below:

(x³ + 5x² -24x) / (x + 8)

The divisor is -8

The coefficients are:

  1    5    -24

Using synthetic division

the first coefficient is 1

the second coefficient = 1 * (-8) + 5

the second coefficient = -3

the third coefficient = -3 * (-8) + (-24)

the third coefficient = 0

Therefore, the solution =  1(x³/x) -3(x²/x) + 0(x/x)

The solution = x² - 3x

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Answer:

She was given 1 free apple and paid for 15 apples.

Step-by-step explanation:

0.55x2=1.1

1.1x8=8.8

8.8/.55=16

16-1=15

And you know she paid for 15 apples and got 1 free.

The better buy for the shrimp based on the information will be the A. 2.24 pound bag.

From the information, Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store and the following week, he paid $17.24 for a 3.12 -pound bag at another store.

The unit price when Josh paid $11.96 for a 2.24 -pound bag of shrimp will be:

= $11.96 / 2.24

= $5.34

The unit price when he paid $17.24 for a 3.12 -pound bag at another store will be:

= $17.24 / 3.12

= $5 53

Therefore, A is cheaper.

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Complete question

Josh paid $11.96 for a 2.24 -pound bag of shrimp at one store. The following week, he paid $17.24 for a 3.12 -pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.

The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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Answer:

let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work.  Then repeat for B and C.  Then you extend the perpendicular lines (altitude) and make them intersect.  The intersect point is the orthocenter.

Step-by-step explanation:

Then you extend the perpendicular lines (altitude) and make them intersect.  The intersect point is the orthocenter.

Answer:

  see attached

Step-by-step explanation:

You want to construct the orthocenter of the given triangle.

The orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.

A perpendicular to a line through a point not on the line is constructed in a few simple steps:

The attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.

Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.

__

Additional comment

The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.

It may appear that point Z is a reflection of point C in line AB, but it is not.

Based on the information provided, it can be concluded that for each meal the restaurant used 0.4166 kilograms of potato.

To calculate the quantity of potatoes used, you can use the following formula shown below:

Total of potatoes used / number of meals

2 1/2 kilograms of potatoes/ 6 meals

2 1/2 kilograms of potatoes is equivalent to 2.5 (1/2 = 0.5)

2.5 kilograms of potatoes/ 6 meals

0.4166

Therefore for each meal, the restaurant used 0.4166 kilograms of potatoes.

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