3.5% as a fraction or mixed number

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:

the first one is the correct answer

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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Answer:

Step-by-step explanation:

Answer:

11(c)-9

Step-by-step explanation:

The product is the result of multiplication, so the product of 11 and c looks like: 11*c or 11(c).

Nine less means subtract, so we simply subtract from the above to get:

11(c)-9 or I suppose another answer could be -9+(11(c))

Answer:

3.65

Step-by-step explanation:

3.78

1.30

___

2.48

3-1=2

7-3=4

8-0=8 -

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.

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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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 unknown side length x is 65 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

Perpendicular = 33

Base = 56

Using Pythagoras theorem

H² = P² + B²

H² = 56² + 33²

H²= 3136 + 1089

H² = 4225

H= √4225

H = 65

Hence, the unknown length is 65 units.

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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

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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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:

Step-by-step explan

THATS A U PROBLEM!

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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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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Answer:

f(1) = 7

Step-by-step explanation:

f(1) has x = 1 in the interval x < 2 with f(x) = - 2x + 9 , then

f(1) = - 2(1) + 9 = - 2 + 9 = 7

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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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 estimates of the area under the curve using rectangles is given as follows:

The area under a curve is approximated using the definite integral of the function that defines the curve within it's bounds.

As it is specified that the area should be approximated using rectangles, a Left Riemann Sum will be used to approximate the area.

With two rectangles, the Delta value is obtained as follows:

[tex]\Delta_x = \frac{9 - (-9)}{2}[/tex]

[tex]\Delta_x = 9[/tex]

The values of x are obtained with the rule presented as follows:

[tex]x_i = a + \Delta_x(i - 1)[/tex]

With two rectangles, the values are given as follows:

-9 and -9 + 9 = 0.

The numeric values are given as follows:

The definite integral is given as follows:

[tex]\sum_{i = 1}^n = \Delta_xf(x_i)[/tex]

Hence the result is of:

9 x 81 = 729 units squared.

With four rectangles, the Delta value is given as follows:

[tex]\Delta_x = \frac{9 - (-9)}{4} = 4.5[/tex]

Hence the values of x are:

x = -9, x = -4.5, x = 0, x = 4.5.

The numeric values are:

Hence the result of the integral is given as follows:

4.5(60.75 + 81 + 60.75) = 911.25 units squared.

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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.

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 :)

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:

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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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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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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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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Please find attached herewith the solution of your question.

Answer:

40π square inches

If you have any doubt, please comment.

The process of arriving at an approximate answer to a computation such as 0.79 × 403 is called estimation.

Having an approximate estimate of something's worth, number, size, or extent is referred to as estimation in mathematics. When we are willing to accept a response that is extremely near to the true result, we utilize estimates of numbers to make mental computations simpler and faster.

The computation is approximate, or the number is rounded to the nearest place value.

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