Simplify 2/3+1/6 in the simplest form

Tara has £40 to spend on invitations for her party. She can spend the money in either shop 1 or shop 2 ,the maximum number of invitations she can buy from each shop is 40 .

The maximum number of invitations she can buy from each shop will depend on the cost of each invitation.

If the invitations at shop 1 cost £1 each, then she can buy a maximum of 40 invitations from this shop. However, if the invitations at shop 2 cost £2 each, then she can buy a maximum of 20 invitations from this shop.

It is important to consider the quality of the invitations. If the invitations at shop 1 are of higher quality than those at shop 2, then it may be worth spending more money on fewer invitations from shop 1. On the other hand, if the quality of the invitations is not important to Tara, then she may be able to purchase more invitations from shop 2.

The maximum number of invitations Tara can buy from each shop will depend on the cost of the invitations and the quality she is looking for. With her £40 budget, the maximum number of invitations she can buy from each shop is 40 from shop 1 and 20 from shop 2.

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No, You would need 68.4 liters of gasoline to fill the tank, which is equivalent to 17.8 gallons. With 19.7 miles/gallon, you would only be able to drive a maximum of 350.7 miles before running out of gas.

The Gallon Conversion Theory is a mathematical formula that can be used to convert between different units of liquid measure.

The formula is based on the fact that each gallon of liquid measure is equal to four quarts, eight pints, sixteen cups, or 32 gills. It is useful for converting between different units of liquid measure when measuring large volumes.

The theory used in this question is the conversion of liters to gallons. By converting from liters to gallons, we were able to determine how far the truck could drive before running out of gas.

To do this, we first determined that the fuel tank holds 68.4 liters of gasoline.

We then converted liters to gallons by multiplying the number of liters by 0.26. This gave us 17.8 gallons. We then multiplied 17.8 gallons by 19.7 miles/gallon to get the maximum distance that could be driven before running out of gas, which was 350.7 miles.

Since the distance from Yuma to Las Vegas is 322 miles, this means that the truck would run out of gas before reaching its destination.

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So, a 49-mile taxi ride would cost $19.60.

To find the cost of a 49-mile taxi ride, you first need to determine the unit price, which is the cost per mile of the taxi ride. To calculate the unit price, you can divide the total cost of the 18-mile ride by the distance traveled. In this case, the total cost of the 18-mile ride is $7.20, and the distance traveled is 18 miles.

$7.20 ÷ 18 miles = $0.40 per mile

This means that the unit price, or the cost per mile, is $0.40. To find the cost of a 49-mile taxi ride, you can then multiply the unit price by the distance of the desired ride.

$0.40 per mile x 49 miles = $19.60

So, a 49-mile taxi ride would cost $19.60.

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$7.20 ÷ 18 miles = $0.40 per mile

This means that the unit price, or the cost per mile, is $0.40. To find the cost of a 49-mile taxi ride, you can then multiply the unit price by the distance of the desired ride.

$0.40 per mile x 49 miles = $19.60

So, a 49-mile taxi ride would cost $19.60.

For values of k between 9 and 9, the quadratic equation's roots are real and equal.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem.

In other words, if a times the square of the expression that comes after b plus b times the same expression that wasn't squared plus c equals 0, you get an equation that has the form of a quadratic.

The supplied formula is 3x 2 + 2kx + 27=0.

Here a=3, b=2k, and c=27.

Roots being real and equal is a given.

∴ b \s2 \s −4ac=0

⇒ (2k) \s2 \s −4(3)(27)=0

⇒ 4k \s2 \s −324=0

⇒ 4k \s2 \s =324

⇒ k \s2 \s =81

∴ k=±9

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Full Question = For what value of k are the roots of the quadratic equation 3x2 +2kx+27=0 real and equal?

The words that complete the fragment correctly are money, and profit.

To identify the correct terms to complete the fragment we have to identify the term that correspond to this definition, in this case is business. So, we have to look for some definitions to get a general idea of the definition.

Also, we can find those terms by inference. For example, is easy to know that the first term is money because we interact every day with this type of economic relation. So, according to the above, the correct terms would be:

A business provides goods or services in exchange for money. The goal of a business, if it wants to survive over time, is to profit.

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The number more than 5 is 6.

Number:

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits.

Greater than Number:

Greater than or equal to in mathematics is an inequality used to compare two or more numbers, quantities, or values. Used when one quantity or number is greater than or greater than the second or remaining quantity or number. This indicates that one value is greater than or greater than or greater than the other. The above symbol is ">". This is also called greater than. We can also compare the length, weight and capacity of the compared number. For example, Bella has a red pencil that is 5 cm long and a blue pencil that is 3 cm long.

According to the Question:

The number is 1 more than 5

adding 1 to 5

5+1=6

The answer is 1 more than 5 = 6.

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Answer:

Read the entire problem several times.

Look for keywords like more, less, is, etc.

Replace the keywords with their mathematical operations and shorten the words to variables. Solve the resulting equation. Answer the problem clearly in a complete sentence.

Step-by-step explanation:

hope this helps

The value of x is 4

Given that the median of the list 2x, 3x, 5x, and 8x is 12, we can arrange the list in order to find the value of x:

2x, 3x, 5x, 8x

To find the median, we need to find the middle value of the list. Since the list has an odd number of values, the median is the middle value.

2x < 3x < 5x < 8x

The median is 3x = 12, so x = 12/3 = 4

Therefore, the value of x is 4.

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The height of the cone is sin 210° × 12 cm = 10.39 cm.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. It is typically measured in either centimeters or feet and inches, and is most commonly used to describe the stature of a person. Height is an important physical characteristic, as it affects a person's overall body proportions and can influence their physical appearance.

The curved surface area of the cone can be calculated using the formula: 2πrh. Where π is the constant pi, r is the radius of the circle, and h is the height of the cone. The height of the cone can be determined by using the trigonometric function sine, where 210° is one of the angles of the triangle. Therefore, the height of the cone is sin 210° × 12 cm = 10.39 cm.

Using the formula 2πrh, the curved surface area of the cone is 2 × π × 12 cm × 10.39 cm = 75.52 cm². As the volume of a cone is one-third the product of its curved surface area and its height, the volume of the cone is 25.17 cm³ (rounded to three significant figures).

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The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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The probability that a student passed the test given that they completed the homework is 0.8 (or 80%).

To calculate this probability, we can use the formula:

P(A|B) = P(A and B) / P(B)

Where A is the event of passing the test and B is the event of completing the homework.P(A and B) is the probability that a student both passed the test and completed the homework, which is the number of students who did both divided by the total number of students in the class.

16 students passed the test and completed the homework of 28 students in total, so:

P(A and B) = 16/28 = 0.57

P(B) is the probability that a student completed the homework, which is the number of students who completed the homework divided by the total number of students in the class.

19 students completed the homework out of 28 students in total, so:

P(B) = 19/28 = 0.68

Now we can use these values to find the probability that a student passed the test given that they completed the homework:

P(A|B) = P(A and B) / P(B) = 0.57 / 0.68 = 0.8 or 80%

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Correctly written question:

In a math class with 28 students, a test was given on the same day that an assignment was due. 20 students passed the test and 19 students completed the assignment. Out of the students who passed the test, 16 also completed the assignment. What is the probability that a student passed the test given that they completed the homework?

The y intercept of the line A is 6 and the y intercept of the line B is -2 and the equation of line B is y = x - 2

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 = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -3x + 6   be equation (1)

Now , the equation of line is is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the y intercept of the line A is b = 6

For the equation of line B , we get

Let the first point be P ( -1 , -3 )

Let the second point be Q ( 0 , -2 )

And , the slope of the line is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / 0 - ( -1 )

On simplifying the equation , we get

Slope m = 1/1 = 1

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = 1 ( x - ( -1 ) )

On simplifying the equation , we get

y + 3 = x + 1

Subtracting 3 on both sides of the equation , we get

y = x - 2

Hence , the equation of line B is y = x - 2 and the y intercept is -2

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Answer: x = 6

Step-by-step explanation:

Divide 28 by 4,  gives you 7. So the parenthesis has to equal 7, i.e 6+1 equals 7.

There are two types of logarithms i.e. natural log and common log.

Natural logarithm - A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

Common logarithm - The base-10 logarithm is the most widely used logarithm in mathematics. It is also known as the standard logarithm, the decadic logarithm (named after its basis), the decimal logarithm (named after its base), or the Briggsian logarithm (named after Henry Briggs, an English mathematician who invented its application).

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Answer:

To divide 1.7 by 8.5, you will need to move the decimal point one place to the right in the divisor and the dividend. This would result in 17 and 85 as the new divisor and dividend respectively, and the division would be performed as 17/85.

Applying the theorem of angle between intersecting tangents, m<D = 30°.

The theorem states that the angle created by the intersection of two tangent lines at a point outside of a circle is equivalent to half the difference between the measures of the arcs that the tangents intercept.

Given the following:

m<B = 75°

Measure of arc AC = 2(75) [inscribed angle theorem]

Arc AC = 150°

Arc ABC = 360 - 150 = 210°

Based on the theorem of angle between intersecting tangents, we have:

m<D = 1/2(210 - 150)

m<D = 30°

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The probability that both of Eduardo’s partners for the group project will be girls is   24/65

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Answer:

x = 34 degrees

Step-by-step explanation:

angles TWU and PSR are vertical and equal

if TSU = 4x and QSR = x then PSQ = 3x

triangle PSQ has 180 degrees

we know the three interior angles of the triangle are:

x, x, 112

we found the 112 by subtracting 68 from 180 since PQR is a straight line which has 180 degrees

to find 'x' we do the following:

x + x + 112 = 180

2x + 112 = 180

2x = 68

x = 34

The formula for the area of a triangle is A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. To solve for h, rearrange the formula to 2*A/bh = 2*28/10h = 5.6 yards.

Height is a measure of vertical distance, often measured from the ground up. Its most typical application is to express the size of a person, object, or other item. Height is often measured in inches, feet, and millimetres. It is also used to determine the elevation of a piece of land or a building.

To calculate the height of a triangle, use the area of a triangle formula, A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle. Because we know the triangle's area is 28 square yards and its base length is 10 yards, we can rearrange the formula to find h:

h = 2*A/b

h = 2*28/10

h = 5.6 yards

As a result, the triangle's height is 5.6 yards.

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The equation of line is y = -72x + 360

The time for the tank to drain 18 liters of water is t = 4.75 minutes

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 = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Let the first point be P = P ( 0 , 360 )

Let the second point be Q = Q ( 5 , 0 )

Now , the slope of the line between the points is

Slope m = ( 360 - 0 ) / ( 0 - 5 )

On simplifying the equation , we get

Slope m = ( - 360/5

Slope m = -72 liters per minute

And , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = ( -72 ) ( x - 5 )

On simplifying the equation , we get

y = -72x + 360

Now , the tub loses 72 liters every minute

So , 1 minute is = - 72 liters

So , for every 18 liters , substitute the value of y = 18 ,  we get

18 = -72x + 360

Adding 72x on both sides of the equation , we get

72x + 18 = 360

Subtracting 18 on both sides of the equation , we get

72x = 342

Divide by 72 on both sides of the equation , we get

x = 4.75 minutes

Hence , it will take 4.75 minutes for 18 liters of water to be drained

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Answer:

Yes SAS they are congurent

Negative numbers don't actually have square roots because a square can only be either positive or zero. No, we cannot find the square root of the negative value.

When two numbers of the same sign are added, the result is always positive.

Theorem: Negative Numbers' Square Roots Using the number as if it were a positive integer and adding an I in front of it as a coefficient is one way to simplify an expression that involves the square root of a negative number. Or, to put it another way, for any x, where x is a positive integer or if x is a negative number, x=ix x = I x.

The worth of root 4 is equivalent to precisely 2. In any case, the roots could be positive or negative or we can say there are dependably two roots for some random number. Subsequently, root 4 is equivalent to ±2 or +2 and - 2 (positive 2 and negative 2).

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the system of linear equations by graphing - y=-x+7,  y=x+1; values for y is (6,6).

A linear equation is an equation in which the highest power of the variable is 1. The general form of a linear equation is "ax + b = 0", where "a" and "b" are constants and "x" is the variable. For example, "2x + 3 = 0" is a linear equation. The solution to a linear equation is the value(s) of the variable that make the equation true. Linear equations can be solved using various methods such as algebraic manipulation, substitution and elimination. Linear equations can be represented graphically as a straight line, and the solution of the equation is the point where the line crosses the x-axis (or y-axis if the equation is in terms of y). Linear equations have a wide range of applications in many fields, including physics, engineering, economics, and many others.

To solve the system of linear equations by graphing, we can first graph each equation on the coordinate plane.

y = -x + 7 represents a line with a slope of -1 and y-intercept of (0,7) y = x + 1 represents a line with a slope of 1 and y-intercept of (0,1)

If we graph these two lines, we can see that they intersect at a single point, which represents the solution to the system of equations.

The x-coordinate of the point of intersection can be found by setting y equal to each other and solving for x. x = y

And the y-coordinate of the point of intersection can be found by setting x equal to each other and solving for y. y = x

Therefore the solution of the system is (x,y) = (x,x) = (6,6)

So the solution of the system is (6,6)

We can check this point by substitute x=6 and y=6 in each equation of the system and see if it makes both equations true.

y = -6 +7 = 1 y = 6 + 1 = 7

So the point (6,6) is a solution for the system of equations.

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The end behavior of a function describes the trend of graph for x approaches to infinity(Right)  and x approaches to negative infinity (Left) .

The end behavior of the graph of polynomial function is behavior of the graph of the function "f(x)" as x approaches positive infinity or negative infinity.

Consider the function , y = x² ;

we know that the graph of this function is a U shaped graph facing in upward direction ;

we see that as "x" approaches negative infinity , "y" tends to positive infinity ;

and as "x" approaches positive infinity , "y" tends to positive infinity .

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Answer:

14 batches of cookie

Step-by-step explanation:

Cora has 7/2 cup of flour

3/4 of flour= 1 batch of cookie

7/2= ?

7/2×1×4/3=14/3

14 batches

The number of integral solutions of the given equation x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5) is 136.

Suppose we wish to determine the number of integer -tuples (₁,…,[tex]x_{k}[/tex])

such that

₁ +⋯+ [tex]x_{k}[/tex] = , [tex]x_{i}[/tex] ≥ [tex]c_{i}[/tex] …(1)

The transformation [tex]y_{i}[/tex] = [tex]x_{i}[/tex] − [tex]c_{i}[/tex], 1 ≤ ≤ reduces (1) to

₁ +⋯+ [tex]y_{k}[/tex] = − (₁ +⋯+ [tex]c_{k}[/tex]), [tex]y_{i}[/tex] ≥ 0…(2)

The number of solutions to (2)

is given by the binomial coefficient [tex]\binom {(n-c_{1}- ... -c_{k})+k-1 }{k-1}[/tex].

For the given problem, = 3, = 0, and each [tex]c_{i}[/tex] = −5. Therefore, the number of solutions is

[tex]\binom {17}{2}=^{17}C_2=\frac{17!}{2!(17-2)!}[/tex]

= 136.

Thus, 136 integral solutions are there to x₁ + x₂ + x₃ = 0 with [tex]x_{i}[/tex] ≥ (-5).

--The given question is incorrect; the correct question is

"How many integral solutions does x₁ + x₂ + x₃ = 0 have if  [tex]x_{i}[/tex] ≥ (-5)?"--

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Answer:

57.4

Step-by-step explanation:

Go to point A and draw a line straight down, perpendicular to HT.  Let's label the point where your drawn line hits AT as B.  Now you have the line segments HB, BT.  

HB + BT = 100

Solve for the height of the triangle, BA.

BA = sin35(80) = 45.9

HB = cos35(80) = 65.5

BT = 100 - 65.5 = 34.5

Now you can solve for AT, which is the hypotenuse of ΔBAT:

(AT)² = 45.9² + 34.5² = 3295

AT = √3295 = 57.4

Answer:

36 lbs

Step-by-step explanation:

44lbs -> $550

X -> $450

Cross-multiplication:

X × 550 = 44 × 450

X = (44×450)/550

X =36 lbs

So the answer is 36 lbs of apples

Another way to solve it :

550/44 = 12.5 which means $12.5 for every 1lbs of apples

Now if we have $450

Divide it by 12.5

450/12.5 = 36 lbs

Answer:

0  is both a number and a numerical digit used to represent that number in numerals.

Step-by-step explanation:

For example positive and negative

The Boeing F-14 was superseded by the F/A-18E/F Super Hornet.

The F-14 is what?

The two-seat F-14 Tomcat was used by the US Navy as a shipboard air defense, intercept, strike, and reconnaissance aircraft. The new aircraft was created by Northrop Grumman to replace the F-4 Phantom fighter, and the US Navy started employing it in 1972.

Jan 12, 2023 · In 1987, the F-14B, which featured a superior engine, entered production. The F-14D Super Tomcat was developed as a result of further developments in the radar, avionics, and missile capacity, and it made its first flight in 1988.

The F/A-18E/F Super Hornet took the place of the 338 F-14s in all three versions that were in use by the US Navy.

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