3/4 divided by 1/2 - using unit rate proportionality

Answer:

y(y-5) =750 squared-feet

Step-by-step explanation:

[tex] {y}^{2} - 5y = 750 \\ 750 - y(y - 5) = 0 \\ (y + 25)(y - 30) = 0[/tex]

Please find attached herewith the solution of your question.

Answer:

40π square inches

If you have any doubt, please comment.

Step-by-step explanation:

x = number of deluxe staterooms on Pacific.

deluxe staterooms on Caribbean = x + 16

deluxe staterooms on Mediterranean = 4x - 28

1176 = x + (x + 16) + (4x - 28) = 6x - 12

1188 = 6x

x = 1188/6 = 198

so,

Pacific has 198 luxury staterooms.

Caribbean has 198 + 16 = 214 luxury staterooms.

Mediterranean has 4×198 - 28 = 792 - 28 = 764 luxury staterooms.

Answer:

Step-by-step explanation:

Answer:

the first one is the correct answer

The values of x can be that is x = 6 or x > 6 or x < -2 .

What is algebraic expression ?

Algebraic expression can be defined as the combination of variables, constants and exponents.

Given expressions,

2x-7 < -11 or 2x-7  >= 5

So, from the first expression,

2x-7 < -11

2x < -11+7

2x < -4

x < -2 or x>2

From the second expression,

2x - 7 >= 5

2x >= 5+7

2x >= 12

x >= 6

So , in this case x = 6 or x can be greater than 6.

Hence, The values of x can be that is x = 6 or x > 6 or x < -2 .

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A vertical shift is an example of a non-rigid transformation this statement is False.

Vertical shift is the transformation of a graph in which all of its points are shifted up or down by a fixed amount. This transformation does not change the shape of the graph but only moves the graph up or down along the vertical axis. It is often used to analyze the effects of changes in parameters on the graph. For example, a vertical shift may be used to show the effect of a change in the slope of a line.

A vertical shift is an example of a rigid transformation because it preserves the angles and distances between the points of the original figure. A rigid transformation is one that preserves the shape and size of the original figure.

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Answer:

25

Step-by-step explanation:

5/9 x 45  Cross cancel the 9 and 45. 9 goes into 9 once and 9 goes into 45 5 times

5/1 x 5/1 = 25/1 = 25

Answer: No, it is not possible to have a 3/8-inch pipe with an inside diameter of 21/32 inches

Step-by-step explanation:

The inside diameter of a pipe is always smaller than the outside diameter. The outside diameter of a pipe is a measurement of the pipe's exterior, while the inside diameter is a measurement of the pipe's interior. Therefore, if the pipe is 3/8 inches in outside diameter, the inside diameter will be less than 3/8 inches.

In addition, 21/32 inches is greater than 3/8 inches, so it is not possible to have a 3/8 inches pipe with an inside diameter of 21/32 inches. This is because the inside diameter is always smaller than the outside diameter.

- C

To find out how much John should sell the games for to make a 146% profit, we can use the following formula:

selling price = cost + (cost x (profit percentage / 100))

We know that the cost is $13.80 and the profit percentage is 146%. So we can plug those values into the formula:

selling price = $13.80 + ($13.80 x (146 / 100))

Solving this equation gives us:

selling price = $13.80 + ($13.80 x 1.46) = $13.80 + $20.108 = $33.908

So, John should sell the games for $33.908 (rounding to the nearest .10, the answer is $33.90)

Out of the options you provided: the closest one is $33.00

I hope this helps :)

The height of the isosceles triangle OPQ is given as follows:

2.41.

An isosceles triangle is a triangle that has two equal side lengths, hence it also has two equal angle measures.

The top angle is of 45º, while the sum of the internal angles of the triangle is of 180º, hence the base angles are obtained as follows:

2x + 45 = 180.

2x = 135

x = 135/2

x = 67.5º.

Then the height is obtained considering a right triangle, in which the height is opposite to an angle of 67.5º, while the adjacent side has length of 1, which is half the base.

Applying the tangent of the angle of 67.5º, the height is obtained as follows:

tan(67.5º) = h/1

h = tan(67.5º)

h = 2.41.

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To find the P value using Excel, you can use the T.TEST function. The T.TEST function calculates the probability of a given test statistic, such as the T-value, assuming that the null hypothesis is true. The function takes several arguments, including the range of values for the sample data, the hypothesized mean of the population, the type of test (two-tailed or one-tailed), and the significance level.

Here is an example of how to use the T.TEST function in Excel:

Enter your sample data into a column in Excel.

In an empty cell, enter the formula =T.TEST(data range, hypothesized mean, type of test, significance level).

Replace "data range" with the range of cells containing your sample data, "hypothesized mean" with the mean of the population, "type of test" with 1 for a one-tailed test or 2 for a two-tailed test, and "significance level" with the level of significance.

Press enter, the P-value will be returned.

For example, if your sample data is in cells A1:A10, the hypothesized mean is 0, the type of test is two-tailed, and the significance level is 0.05, the formula would be =T.TEST(A1:A10, 0, 2, 0.05)

The P-value returned will be the probability that the sample data came from a population with a mean equal to the hypothesized mean, assuming that the null hypothesis is true.

Answer:

When a mixed number is written as a decimal, the whole number does not change but the fraction is changed to an equivalent decimal.

For example, if a mixed number is 2 1/4, the whole number is 2 and the fraction is 1/4. When this mixed number is written as a decimal, the whole number remains 2, but the fraction 1/4 is changed to the equivalent decimal 0.25. So the mixed number 2 1/4 is written as 2.25 in decimal form.

The amount of mulch that he put on each vegetable bed will be 1/9.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

In this situation, the gardener spread 1/3 of a bag of mulch evenly over his 3 equal-sized vegetable beds.

The amount of mulch that he put on each vegetable bed will be:

= 1/3 ÷ 3

= 1/3 × 1/3

= 1/9

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The conclusion of the test hypothesis at the significance level of 0.05 is given as follows:

The results are statistically insignificant at the significance level of 0.05, meaning that there is insufficient evidence to conclude that the mean on the day after Thanksgiving is less than the mean on the day after Christmas.

At the null hypothesis, it is tested if the mean is not greater than 135, that is:

[tex]H_0: \mu = 135[/tex]

At the alternative hypothesis, it is tested if the mean is greater than 135, hence:

[tex]H_1: \mu > 135[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 147, \mu = 135[/tex]

The standard error is obtained as follows:

[tex]s = \sqrt{\left(\frac{49}{\sqrt{57}\right)^2 + \left(\frac{32}{\sqrt{55}\right)^2}}[/tex]

s = 7.79.

Hence the test statistic is of:

t = (147 - 135)/7.79

t = 1.54.

The p-value of the test is obtained considering a right-tailed test, as we are testing if the mean is greater than a value, with 57 + 55 - 2 = 110 df and t = 1.54.

Using a t-distribution calculator, the p-value is given as follows:

0.0632.

Greater than the p-value, hence the result is not significant.

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The quadratic expression for the curves is written as

The curve opening up y = a(x + 4)² - 7

The curve opening down y = -1/8(x - 4)² + 3

The equation of the quadratic equation is written using the formula

y = a(x - h)² + k

where h and k are points of the vertex v(h, k)

The curve opening up

h = -4 and k = ?

using points C and B

-5 = a(0 + 4)² + k, -5 = 16a + k

1 = a(4 + 4)² + k, 1 = 64a + k

solving simultaneously

-5 = 16a + k

1 = 64a + k

subtraction

-6 = -48a

a = 1/8

solving for k

-5 = 16a + k

-5 = 16 * 1/8 + k

k = -7

substituting the values

y = a(x + 4)² - 7

The curve opening down

A is the vertex (4, 3)

y = a(x - 4)² + 3

using D (0, 1) to solve a

1 = a(0 - 4)² + 3

1 - 3 = 16a

a = -1/8

hence the equation is y = -1/8(x - 4)² + 3

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Answer:

A rational consumer is an economic concept that presupposes that when making a choice, consumers will always focus primarily on the maximisation of their private benefits. In decision making, rational consumers select the option that will bring the most utility and satisfaction to them.

-1

8 is bigger than 0, so according to the function, we need to use the third one so it would be -1

Salut/Hello!

Answer: a) 90 tiles ; b) 3 m

Step-by-step explanation:

a) First we need to imagine a drawing of the empty worktop. We know the width is equal to 6 tiles and the length is equal to 15 tiles. If the shorter edge fits 6 tiles then we have 6 sets of 15 tiles.
6 x 15 = 90 tiles

b) We know the length of one tile is 20 cm so the length of 15 tiles that fit in the worktop is equal to 300 cm or 3 m

I hope it was helpful!

a) To cover the workshop, he has to use 90 tiles altogether.

b) The length of the workshop is 3 meters.

We know that the area of the rectangle is

Area =  length × width

Here shorter edge is called width and the longer edge is called length.

Also given that,

The tiles required to cover the shorter edge are 6 tiles.

The tiles required to cover the longer edge are 15 tiles.

so, the total tiles required to cover the worktop are

Area = 15 tiles × 6 tiles

= 90 tiles

Therefore, 90 tiles are required to cover the worktop.

To find the length of the worktop,

Required length = length of each tile × no. of tiles

By applying the formula,

Required length = 20 cm × 15

= 300 cm

1 meter = 100 centimeteres

Therefore, the length of the worktop is 3 meters.

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Answer:28 sq mm

Step-by-step explanation:

Triangle's area: length times the height then divided by 2.

8×7÷2

=56/2

=28

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^{x-5}=9\\ \\ 3^{x-5}=3^2 \\ \\ x-5=2 \\ \\ x=7[/tex]

Answer:

-3

Step-by-step explanation:

The company should create 1 unit of production in Plant 1 in order to optimize its earnings.

The company should create 1 unit of production in Plant 1 in order to optimize its earnings.

Any extra unit above one in Plant 1 would reduce the demand for the firm's goods, which is determined by

P = 78 – 15 Q, where Q = Q1 + Q2.

For instance, the company will generate four units in Q2 if it produced two units in Q1.

The negative demand for the firm's goods will range from 33 units

(78 - 15 x 3, where Q = 3) to -12 units (78 - 15 x 6, where Q = 6),

depending on the production output.

The output of the company at Plant 1 (Q1) that maximizes its earnings is therefore 1.

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Belle's house is approximately 5.83 miles away from Cora's house.

What is a Pythagoras Theorem?

The Pythagorean theorem is a fundamental concept in mathematics, named after the ancient Greek mathematician Pythagoras. The theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as an equation: [tex]c^2 = a^2 + b^2[/tex], where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

We can use the Pythagorean theorem to solve this problem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

We can consider this problem as two right triangles with Rosa's house being the common point, and therefore the right angle.

Let x be the distance between Belle's house and Cora's house.

So, we can set up the equation as:

x^2 = 3^2 + (5)^2

x = sqrt(3^2 + (5)^2)

x = sqrt(9 + 25)

x = sqrt(34)

x = approximately 5.83 miles.

Hence, Belle's house is approximately 5.83 miles away from Cora's house.

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The division of the given polynomial would be (x^4) + 81.

What is the synthetic division?

Synthetic division is a method for dividing polynomials that allows you to divide a polynomial by a linear factor (a factor in the form of (x-c) where c is a constant) without actually performing the long division process. It is a short cut method that simplifies the process of dividing polynomials.

To divide the polynomials using polynomial division, we will use the following steps:

Write the polynomials in descending order of exponents.

(2x^3 + x^4 - 6x^2 + 11x - 10) (x^2 + 2 - x)

Create a grid with the dividend on the left and the divisor on the right.

2x^3 x^4 -6x^2 11x -10

x^2 2 -x  

Bring down the leading coefficient of the dividend, which is 2x^3 in this case. Write it in the next row of the grid.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

Multiply the divisor (x^2 + 2 - x) by the leading coefficient (2x^3) and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

Subtract the second row from the third row and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

Divide the new leading term by the leading term of the divisor, which is x^2, and write the result in the next row.

2x^3 x^4 -6x^2 11x -10

2x^3 x^2 2 -x  

2x^5 2x^4 4x^3 -2x^4  

0 -x^4 -2x^2 11x -10

-x^2

So the final answer would be (-x^2) + (x^4 + 2x^2 - 11x + 10).

Hence, the division of the given polynomial would be (x^4) + 81.

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Answer:

A, B and E

Step-by-step explanation:

As x gets very large , the function that becomes largest is y = 5x^3

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. Where a>0 and a is not equal to 1. x is any real number.

This means that the greater the power of x , the larger the function of y.

For example, If y = 5x^n , as n increases the value of x increases and the value of y will increase also.

Therefore the largest function as x becomes large is y = 5x^3

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The solution is: Correct option is 3: Equally likely and unlikely.

We have,

Equally likely indicates the likelihood that the outcomes of each experiment will occur. For instance, if you roll a fair, six-sided die, there is an equal probability of getting any of the faces (1, 2, 3, 4, 5, or 6). The likelihood of a coin landing on its head (H) or tail (T) is equal (T).

What has equal and unequal likelihood?

Equally likely suggests that the event is fair and that all possible outcomes have an equal chance of happening. If two outcomes are not equally likely to occur, then the event would be unfair and one or more of the events would be more likely to do so.

Given that, P(terriers) is 50%

i.e., P(terriers) = 1/2

So, P(not terriers) = 1 - 1/2 = 1/2

This is an equally likely and unlikely event. i.e., The likeliness and unlikeliness of the event are equal and equal to 50%.

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Answer:

Let's call the number of seats in the first aircraft "x", the number of seats in the second aircraft "y", and the number of seats in the third aircraft "z".

From the problem statement, we know that:

x = y + 88 (the first aircraft has 88 more seats than the second aircraft)

z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)

x + y + z = 1909 (the total number of seats in all three aircraft is 1909)

We can substitute the first equation into the third equation to get:

y + 88 + 2y - 103 = 1909

3y = 2000

y = 666 (the number of seats in the second aircraft)

Now that we know the number of seats in the second aircraft, we can use the first and second equations to find the number of seats in the other two aircraft:

x = y + 88 = 666 + 88 = 754 (the number of seats in the first aircraft)

z = 2y - 103 = 2(666) - 103 = 1229 (the number of seats in the third aircraft)

So, the first aircraft has 754 seats, the second aircraft has 666 seats and the third aircraft has 1229 seats.

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Answer: The first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.

Step-by-step explanation:

Let's call the number of seats for the first aircraft x, the number of seats for the second aircraft y, and the number of seats for the third aircraft z.

From the problem, we know the following:

x = y + 88 (the first aircraft has a capacity of 88 more seats than the second aircraft)

z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)

x + y + z = 1909 (the total number of seats for all three aircraft is 1909)

We can use the first equation to substitute for x in the second and third equations:

y + 88 = y + 88

2y - 103 = z

Now we have a system of equations:

y + 88 + y + 2y - 103 + z = 1909

4y + z = 2000

We can use the first equation to find y:

y = (1909 - 88 - 103) / 4 = 709 / 4 = 177

Now we can substitute this value of y back into the first equation to find x:

x = y + 88 = 177 + 88 = 265

and substitute it back into the second equation to find z:

z = 2* 177 - 103 = 248

So the first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.