A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of​ wheat, on the third​ square, four grains of​ wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining 30​ squares, how many grains of wheat should be placed on square ​? Also find the total number of grains of wheat on the board at this time and their total weight in pounds.​ (Assume that each grain of wheat weighs​ 1/7000 pound.)

If a bottle of perfume on sale for $30 after a discount of 25%, then the original price of the perfume is $40

The selling price of the perfume = $30

The percentage of discount on perfume = 25%

Consider the original price of the perfume = x

Then the equation will be

[ Original price - Original price × 25%] =  The selling price of the perfume

Substitute the values in the equation

[ x - x×(25/100) ] = 30

( 1 - 25/100)x = 30

( 1 - 0.25)x = 30

0.75x = 30

x = 30 / 0.75

x = $40

Hence, if a bottle of perfume on sale for $30 after a discount pf 25%, then the original price of the perfume is $40

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The solution of the given equation is 2x² - 13x +13.

What is the solution of the equation?

The collection of all values that, when substituted for unknowns, cause an equation to hold true is known as the solution. Two fundamental algebraic rules using the additive property and the multiplicative property are utilized to determine the solutions for equations needing a single unknown raised to a power of one.

What is the simplification rule?

For those sorts of reasoning that deal with conjunctions, the rule of simplification provides a strong argument. This covers natural deduction, predicate logic, and propositional logic.

Here, we have

Given equation 2(x - 2)² - 5(x - 2) - 5

By applying the simplification rule, we get

= 2(x - 2)² - 5(x - 2) - 5

= 2( x² + 4 - 4x ) - 5x +10 - 5

= 2x² + 8 - 8x - 5x + 5

= 2x² - 13x +13

Hence, the solution of the given equation is 2x² - 13x +13.

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Answer: 7

Step-by-step explanation:

To do this, we need to simplify the numerator.

This means we need to multiply 7^8 x 7^3 x 7^4

To multiply these, we add the exponents together.

This gives us 7^15.

Now, we need to simplify the denominator.

This means we need to multiply 7^9 x 7^5

This gives us 7^14.

Now that we have both the numerator and denominator simplified, we divide 7^15 and 7^14.

To divide 7^15 and 7^14, we need to subtract the exponents.

This gives us 7^1.

7^1 = 7.

The volume of cone is 324cubic inch, volume of Cuboid volume is equal to 4,080 cubic meter and cylinder Volume is 550 cubic cm

How would you define rounding?

Making a number simpler while maintaining a value that is close to what it was is known as rounding. Although less accurate, the outcome is simpler to utilize. Example: Since 73 is closer to 70 than to 80, 73, when rounded to the closest ten, equals 70. However, 76 rises to 80.

Given: A variety of solid shapes

To determine the volume and surface area of each solid

Solution:

Cone radius = 9 inch.

H height equals 12 inch

15 feet is the slant height.

Volume equals (1/3)πr²h = 324cubic inch.

Round to nearest tenth = 320 sq inch

Surface area equals πr² + πrl = π(81 + 135) sq inch = 679 sq inch

Round to nearest tenth = 680 sq inch

Cuboid volume is equal to 16 x 15 x 17 = 4,080 cubic meter.

Round to nearest tenth = 4,080 cubic meter

Surface area is equal to 2 (15 * 17 + 15 * 16 + 17 * 16) = 1,474 square meter.

Round to nearest tenth = 1,470 square meter

cylinder Volume = πr²h = π(5)²  * 7 = π 175 cubic cm = 550 cubic cm

Round to nearest tenth = 550 sq cm

cylinder Surface area is equal to  2πr(r + h ) = 10π (5+7) = 377 sq cm.

Round to nearest tenth = 380 sq cm

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Answer:

The answer is {-8, -2, 3, 4, 8}

Domain is basically the x,

while range OR image is the y,

while codomain is y values that do not have ties to any x value

There are 18 possible combinations for the model and color options.

According to the given information,

There are 3 motorbike manufacturers.

There are 6 different colors available.

Total combinations possible = Motorcycle count *color count

Total combinations possible=3*6

                                                 =18

Therefore, there are 18 possible combinations that are available.

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Answer:

[tex] x = \dfrac{\log 5}{\log 7} [/tex]

Step-by-step explanation:

[tex] 7^{2x} - 4 \times 7^x = 5 [/tex]

[tex] 7^{2x} - 4 \times 7^x - 5 = 0 [/tex]

[tex] (7^x)^2 - 4(7^x) - 5 = 0 [/tex]

This is a quadratic equation in 7^x.

Let u = 7^x.

Substitute u for 7^x to see the quadratic equation more clearly.

[tex] u^2 - 4u - 5 = 0 [/tex]

Now we have a factorable quadratic equation in u.

[tex] (u - 5)(u + 1) = 0 [/tex]

[tex] u - 5 = 0 [/tex]  or  [tex] u + 1 = 0 [/tex]

[tex] u = 5 [/tex]  or [tex] u = -1 [/tex]

Now substitute back 7^x for u.

[tex] 7^x = 5 [/tex]  or  [tex] 7^x = -1 [/tex]

[tex] 7^x = -1 [/tex] does not have a real solution.

Continue solving [tex] 7^x = 5 [/tex] for x.

Take log of both sides.

[tex] \log 7^x = \log 5 [/tex]

[tex] x \log 7 = \log 5 [/tex]

[tex] x = \dfrac{\log 5}{\log 7} [/tex]

Answer:

[tex]x=\log_75[/tex]

Step-by-step explanation:

Given equation:

[tex]7^{2x}-4 \cdot 7^x=5[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]

[tex]\implies (7^x)^2-4 \cdot 7^x=5[/tex]

Subtract 5 from both sides:

[tex]\implies (7^x)^2-4 \cdot 7^x-5=0[/tex]

[tex]\textsf{Let \; $u = 7^x$}:[/tex]

[tex]\implies u^2-4u-5=0[/tex]

Factor the quadratic:

[tex]\implies u^2+u-5u-5=0[/tex]

[tex]\implies u(u+1)-5(u+1)=0[/tex]

[tex]\implies (u-5)(u+1)=0[/tex]

Apply the zero-product property:

[tex]\implies u-5=0 \implies u=5[/tex]

[tex]\implies u+1=0 \implies u=-1[/tex]

[tex]\textsf{Substitute back in \; $u = 7^x$}:[/tex]

[tex]\implies 7^x=5[/tex]

[tex]\implies 7^x=-1 \quad \textsf{is not valid as $7^x > 0$}.[/tex]

Therefore, the only valid solution is:

[tex]\implies 7^x=5[/tex]

[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies \log_75=x[/tex]

[tex]\implies x=\log_75[/tex]

Answer: triangle, rectangle, pentagonal

Step-by-step explanation: b x h and length x width = base.

The solution to the system of equations is (7 , 10.5).

Systems of equations are collections of equations where the intersection point (s) between the equations serves as the solution. The majority of the equation systems you encounter in algebra are collections of two linear equations with the formula Ax + By = C.

y = 2x - 3.5 …. (1)

x - 2y = -14 …. (2)

Let us use the elimination method to solve the system of linear equations.

Multiply equation (1) by 2

2y = 4x - 7

- 4x + 2y = -7 …. (3)

By adding equation (2) and (3)

- 3x = - 21

Divide both sides by - 3

x = 7

Substitute the value of x in equation (1)

y = 2 (7) - 3.5

By further calculation

y = 14 - 3.5

y = 10.5

Therefore, the solution to yhe system of equations is (7, 10.5).

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The equation of line is y = -7x - 95

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 of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the two points be P1 and P2

P1 ( x₁ , y₁ ) = P1 ( -13 , -4 )

P2 ( x₂ , y₂ ) = P2 ( -9 , -32 )

Step 1 :

To calculate the slope m of the two points

m =  ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values of x₁ , y₁ , x₂ , y₂ in the equation , we get

m = ( -32 - (-4) ) / ( -9 - (-13) )

m = (-32 + 4 ) / ( -9 + 13 )

m = -28 / 4

m = -7

Therefore the slope is -7

Step 2 :

Now , the equation of the line is given by

y - y₁ = m ( x - x₁ )

Substituting the values of x₁ , y₁ and m in the equation , we get

y - (-4) = -7 ( x - (-13) )

y + 4 = -7 ( x + 13 )

y + 4 = -7x - 91

Subtracting 4 on both sides , we get

y = -7x - 95

Hence , the equation of line is y = -7x - 95

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The inverse of the conditional statement "If p then q" is, "p and not q".

What is conditional statement?

"If...then" is how a conditional statement is expressed. If we consider p and q to be the two statements, then p and q can be written under several conditions, such as;

If the "If" component (p) and the "then" part (q) of a conditional statement are both negated, this is known as a conditional statement in reverse. The conditional statement in geometry is known as p → q. Where stands for NOT or negating the statement, the inverse is written as  ~ p → ~  q.

In logic, "p and not q" is identical to the negation of "if p then q."

Therefore, the inverse of the conditional statement "If p then q" is,  

"p and not q".

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f(x) function increases faster.

From the question, we have

g(x) =5/2x-3

At x =0, g(x) = -3

At x =1, g(x) = -1

Hence, f(x) function increases faster.

Subtraction:

Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.

The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.

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The car's initial purchase price when it was brand new is 22711.89 when the vehicle Diana purchased is eight years old. It cost her $6,700.

Given that,

The vehicle Diana purchased is eight years old. It cost her $6,700. The annual rate of depreciation for this brand and model is 14.15 percent.

We have to find what was the car's initial purchase price when it was brand new.

We know that,

The formula is y=A(1-r)ˣ

Here,

y is 6700

r is 0.1415

x is 8

We get,

6700=A(1-0.1415)⁸

6700=A(0.295)

A=22711.89

Therefore, The car's initial purchase price when it was brand new is 22711.89 when the vehicle Diana purchased is eight years old. It cost her $6,700.

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Answer:$22,706.62

Step-by-step explanation: This is the correct answer.

1. The cheese production for 2006 is 7.76 billion.

2. The cheese produced in 2014 is 9.84 billion.

It should be noted that a function is simply used to show the relationship between the variables that are given.

In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:

y = 7.1(1.03)^x

y = cheese production

x = number of years after 2003.

1. Therefore, since 2006 is 3 years after 2003, this will be

y = 7.1(1.03)^x

y = 7.1(1.03)³

y = 7.1 × 1.093

y = 7.76 billion

The production is 7.76 billion.

2. The production in 2014 will be;

y = 7.1(1.03)^x

y = 7.1(1.03)^11

y = 7.1 × 1.385

y = 9.84 billion

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While dividing 7 tens into 3 groups the greatest number of tens you can put in each group = 2 tens

In this question, we need to divide 7 tens into 3 groups.

We need to find the greatest number of tens you can put in each group.

We know that 7 tens = 70

We need to divide 70 in 3 groups.

70/3 = 23.33

From given choices the greatest number of tens we can put in each group = 2

Therefore, while dividing 7 tens into 3 groups the greatest number of tens you can put in each group = 2 tens

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Dario cut 15 slices of lasagna containing 1/4 pounds of cheese.

Total amount of cheese in lasagna =

[tex] \frac{2}{3} [/tex] + [tex]1 \frac{3}{4} [/tex] + [tex]1 \frac{1}{3} [/tex]

Total amount of cheese = [tex] \frac{2}{3} [/tex] + [tex] \frac{7}{4} [/tex] + [tex] \frac{4}{3} [/tex]

Taking LCM we get 12

Total amount of cheese = (2×4) + (7×3) + (4×4)/12

Total amount of cheese = 8 + 21 + 16/12

Total amount of cheese = 45/12 pounds

Number of slices = total amount of cheese ÷ amount of cheese in each piece

Number of slices = 45/12 ÷ 1/4

Number of slices = (45×4) ÷ 12

Number of slices = 15

Thus, there are 15 slices of lasagna.

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67% of years  will have an annual rainfall of less than 43 inches.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often indicated by the percent sign '%', but the abbreviations 'pct.', 'pct', and 'pc' are also sometimes used. Percentages are dimensionless numbers. It has no units of measure.

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According to the graph transformation, the function y = |2x| is compressed than the parent function y = |x| and the function y = 1/2x is drawn as straight line.

Graph transformation:

The graph transformation refers a process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph and it also shows the modification of algebraic equations.

Given,

Here we have the function y = |2x| and y = 1/2x.

Now, we need to find the transformations do to the parent function: y=|x|.

Here we need to plot the graph for each of the function.

And we have to plot the separate graph for the parent function.

While we compare these two graph we have identify the function y = |2x| is compressed than the parent function y = |x|.

And the function y = 1/2x makes the straight line on the graph but the parent function has v shaped graph so, it is not possible to compare them.

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Answer:

Step-by-step explanation:

f⁻¹(x) = x/4    

The actual length of route of 28 cm on drawing is 84 meters.

The actual length will be calculated by firstly writing the ratio and proportion form. Then equating the product of extremes and product of mean.

Ratio and proportion form -

Let us assume the actual length be x. Ratio in actual :: Ratio of scale drawing

28 : x :: 1 : 300

1×x = 28×300

Performing multiplication on both sides of the equation

x = 8400

Now converting the actual length to metres, based on the fact that 100 cm is 1 m.

8400 cm = 84 metres

Hence, the actual length is 84 metres.

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The complete question is -

Daisy is given a scale drawing with the route to her campsite. The route to the campsite is 28 cm on the drawing. The scale on the drawing is 1 : 300. What is the actual length of the route?

The number of ways that 5 players can be selected from the 11 eligible players is; 462 ways

The number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth is; 120 Ways

Permutations and combinations are ways of representing groups of objects by selecting them  and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

We are given that In a soccer match;

A tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the penalty mark.

Each kick must be taken by a different player

Now, to find the number of ways that 5 players can be selected from the 11 eligible players, we will use combination to get;

11C5 = 11!/(5! * (11 - 5)!)

= 11!/(5! * 6!)

= 462 ways

Now, if we care about order or position, we will use permutation to get the number of ways that the 5 selected players can they be designated as first, second, third, fourth, and fifth;

5P5 = 5!/(5 - 5)

= 120 Ways

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Answer:

x<-4

Step-by-step explanation:

To solve this problem, follow these steps:

1. Subtract 5 from both sides.

13<-2x+5

13(-5)<-2x+5(-5)

2. Simplify.

(8)<-2x+5-5

3. Subtract the 5's. And bring down the new equation.

8<-2x+5-5

8<-2x

4. Divide -2x on both sides.

8/-2<-2x/-2

5. Simplify and cancel out the -2's.

-4<x

6. Move the variable to the left and flip the inequality.

x<-4

Explanation:

170%,41/25,2,168%,89/50 from least to greatest?

170% = 1.7

41/25 = 1.64

2 = 2

168% = 1.68

89/50 = 1.78

Least to greatest:

41/25 , 168% , 170% , 89/50 , 2

The function f(n) to represent the elevation after n hours is y = -665 x + 7315.

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point-slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This suggests that a linear equation in two variables can represent a line.

Let the x value represent hours and elevation is represented by y values.

So,

(x₁, y₁) = (1, 6650)

(x₂, y₂) = (2, 5985)

Find the slope by using the slope formula

m = (y₂-y₁)/ (x₂-x₁)

= (5985 - 6650) /(2 - 1)

= -665

So, the function f(n) to represent the elevation after n hours is given by

(y - 6650) = -665 (x - 1)

y - 6650 = -665x +665

y = -665 x + 7315

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9.1875 are the mean and variance of depth in random variable.

What is random variable in math?

The mean of the random variable X is

                                                E(X) =b+a/2

                                                        = 19 + 8.5/2

                                                       = 13.75

The variance of the random variable X is,

                                                       V(X) = ( b - a)²/12

                                                               = ( 19 - 8.5 )²/12

                                                             = 9.1875

If the random variable X is uniformly distributed on the interval [8.5, 19], then the mean of the random variable X is 13.75 and the variance of the random variable X is 9.1875.

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The cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

Given:

If it' 50 c outside and the temperature will drop 70 c in next 3 hour.

Temperature (cold) = present temperature - temperature in next 3 hour.

= 50 - 70

= -20 c.

Therefore the cold will it get if it' 50c outside and the temperature will drop 70c in next 3 hour is -20 c.

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Answer:

The sides of an angle are called rays and the endpoint here they meet are called vertexes

The solution of the given logarithmic function log 6 is 1.78.

For the stated function;

= log 6

= log(2 x 3)

Using the multiplication property of log;

log (m x n) = log m  + log n

= log(2) + log(3)

solve the value by calculator;

= 0.69 + 1.09

= 1.78

Thus, the solution of the given logarithmic function log 6 is 1.78.

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