What is the probability of rolling a number less than or equal to 8 with the
sum of two dice, given that at least one of the dice must show a 6?

Comparing the square root of 18 and twenty three fifths using an inequality is ✓18 < 23/5.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

The square root of 18 will be 4.25

23/5 will be 4.6

Therefore, we can see that 4.6 is greater than 4.25.

In this case, ✓18 is less than 23/5.

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The value of [tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex]) in radians is [tex]-\frac{\pi }{4}[/tex]

The value of  [tex]sin^{-1}[/tex](1) in radians is [tex]\frac{\pi }{2}[/tex]

The value of  [tex]sin^{-1}[/tex](- 1/2) is [tex]-\frac{\pi }{6}[/tex]

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

[tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex])  is -45 in degress

but [tex]\pi[/tex] rad = 180°

so that - 45° in rad is [tex]\pi[/tex] x - 45/180 which is - [tex]\frac{\pi }{4}[/tex]

[tex]sin^{-1}[/tex](1)  = 90°

but [tex]\pi[/tex] rad = 180°

so that -90° in rad is [tex]\pi[/tex] x 90/180 which is  [tex]\frac{\pi }{2}[/tex]

[tex]sin^{-1}[/tex](- 1/2) = -30°

but [tex]\pi[/tex] rad = 180°

so that - 30° in rad is [tex]\pi[/tex] x - 30/180 which is - [tex]\frac{\pi }{6}[/tex]

In conclusion then values of the sine inverse of the functions are - [tex]\frac{\pi }{4}[/tex],  [tex]\frac{\pi }{2}[/tex], and - [tex]\frac{\pi }{6}[/tex]

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There are 125 participants in this sample. Thus, the margin of error = (1.96) x (0.5/√125) = 0.089

Margin of Error = (Critical value) x (Standard Deviation/Square root of Sample Size)

Critical value = 1.96

Standard Deviation = (30% x 70%)^0.5 = 0.5

Sample Size = 125

Therefore, Margin of Error = (1.96) x (0.5/√125) = 0.089

The margin of error for the survey results described can be calculated using the formula (Critical value) x (Standard Deviation/Square root of Sample Size). A 95% confidence interval's critical value is 1.96.The standard deviation is calculated by taking the square root of the product of the sample proportion (30%) and its complement (70%). There are 125 participants in this sample. Thus, the margin of error = (1.96) x (0.5/√125) = 0.089

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The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.

As given in the question,

Cost of brick wall is equal to $40/ft

Cost of metal fencing is equal to $20/ft

Let 'x' and 'y' are the dimensions of the rectangular garden

Area of the rectangular garden = 142 square feet

⇒ 142 = xy

⇒x = 142/y

Costing of four side fencing 'C' = 40x + 20x + 20y + 20y

⇒ C = 60x + 40y

⇒C = 60(142/y) + 40y

⇒C = 8520/y + 40y

Differentiate with respect to y

dC/dy = -8520/ y² + 40

Put dC/dy = 0

-8520/ y² + 40 = 0

⇒y² = 8520/40

⇒y = √213

⇒ y= 14.6 ft

⇒ x= 142/14.6

     = 9.7 ft

Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.

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From the given information, Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.

The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.

The formula for an exponential function is where b is a positive integer that is not equal to 1.

Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b<  1, an exponential function exhibits exponential growth and exponential decline, respectively.

given,

[tex]= > y = 4(\frac{5}{6} )^x[/tex]

[tex]= > b = \frac{5}{6} < 1[/tex]

Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.

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Step-by-step explanation:

7x+8xy-72y

Since x=-2 and y=4

Then u just input it

7(-2)+8(-2)(4)-72(4)

-14-64-288

-366

Option (e) SE(u(x)) = 1 is incorrect about the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi )

The examination of the relationship between two variables is possible using bivariate analysis, which also has many real-world applications. It seeks to determine whether there is a link between the variables and how strong it is.

You can examine an association or causality hypothesis using bivariate analysis. It also aids in the prediction of dependent variable values based on changes in an independent variable.

The correlation coefficient (R) is a numerical value that ranges from -1 to 1. It reveals the strength of the linear relationship between the two specified variables.

The coefficient is referred to as Pearson's correlation coefficient when used to describe a linear regression.

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Answer:

Perimeter 34 cm

Area 42 [tex]cm^{2}[/tex]

Step-by-step explanation:

Perimeter:

Perimeter is the measurement of the distance around the figure.  I started on the far left of the rectangle and then went around counter clockwise.

3 + 3 + 3 + 5 + 3 + 3 (this is not labeled, but I see that the other sides is 3)

+3 + 5 + 3 + 3

8(3) + 2( 5) = 24 + 10 = 34

The perimeter is 34 cm

Area:

Area of the rectangle

a = l x w

a = 10(3) = 30

Area of the triangle

a = 1/2 (l x w)

a = 1/2(4 x 3) = 1/2(12) = 6

There are 2 triangles so the area of both is 12

Total area: 30 + 12 = 42

The area is 42 [tex]cm^{2}[/tex]

Answer:

y = -  [tex]\frac{1}{4}[/tex] x - 1

Step-by-step explanation:

y = mx + b  

Slope:

The m is the slope in the equation.  Look at the two points given.  If you start at the point on the left, you go down 1 and 4 to the right.  1/4

Y-intercept:

The y intercept is the b.  It is where the line crosses the y axis.  It crosses at -1

Answer:

----------------------------------------

Slope- intercept form:

Use two points on the graph:

The first point is a y-intercept, b = - 1

Find the slope:

The line is:

Answer:

Step-by-step explanation:

First: You do PEMDAS.

Second: you do what in your parentheses

Answer: Two dimensions.

Straight sides.

Congruent (equal-length) sides.

An interior and exterior.

Equal interior angles.

Equal exterior angles.

Step-by-step explanation:

The equation of the verticallly-oriented ellipse is x²/4 + y²/25 = 1

The equation of a vertically-oriented ellipse centered at the origin with major axis y axis is given by

x²/b² + y²/a² = 1 where a > b

Given that the vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full minor x-axis length of 4 units.

We have that the length of major axis 2a = 10

⇒ a = 10/2

⇒ a = 5

Also, the length of minor axis 2b = 4

⇒ a = 4/2

⇒ a = 2

So, given the equation of the vertically-oriented ellipse,

x²/b² + y²/a² = 1 where a > b

Substituting the values of the variables into the equation, we have that

x²/b² + y²/a² = 1 where a > b

x²/2² + y²/5² = 1

x²/4 + y²/25 = 1

So, the equation is x²/4 + y²/25 = 1

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Answer:

game is free. Is the total cost to bowl a function of the

Step-by-step explanation:

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes n key comparisons, in unsuccessful case.

The BST (Binary Search Tree) is a tree where all nodes on the left and right sides of a given node are larger and less than each other.

The nodes of the BST are not kept in a continuous location because it is a non-linear data structure. The element is absent from the list in the best-case scenario, making it a worst-case scenario.

The worst-case temporal complexity for linear structures is O. (n).

In the worst scenario, there will be n key comparisons.

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The right question is:

Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes.......................... key comparisons, in unsuccessful case.

Answer: 32% probability of going to the beach given the information provided in the weather forecast.

Step-by-step explanation:

The probability of going to the beach is equal to the probability of it not raining times the probability of going to the beach if it does not rain. Therefore, the probability of going to the beach is equal to (1 - 0.6) * 0.8 = 0.4 * 0.8 = 0.32.

Liam can conclude that the price and monthly rate of both the gyms are equal.

Given, Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.

Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75.

we have to mention that what Lian can conclude,

As, substituting the first equation in the second one Liam got the price which is same in both the gyms.

So, Liam can conclude that the price and monthly rate of both the gyms are equal.

Hence, Liam can conclude that the price and monthly rate of both the gyms are equal.

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Simplifying an exponential equation can be done by using different laws of exponents.

In this case, we can use the power rule and negative exponent rule

Power rule:

[tex](a^x)^y=a^x^y[/tex]

Negative exponent rule:

[tex]a^-^y=\frac{1}{a^y}[/tex]

1. Use the negative exponent rule

[tex](10x^2)^-^3=\frac{1}{(10x^2)^3}[/tex]

2. Use the power rule and simplify

[tex]10^3=1000[/tex] and [tex](x^2)^3=x^6[/tex]

∴[tex]\frac{1}{1000x^6}[/tex]

Answer:

= 10x⁻⁶

Step-by-step explanation:

2*-3 = -6

then:

[tex]10x^{2^{-3}} = 10x^{-6}[/tex]

= 10x⁻⁶

Answer: 11

Step-by-step explanation:

plug in x where eligible

4(11)-10 and 2(11)+12

both equal 34 and since a triangle's interior angles always equal 180 you can solve for the 3rd angle 32*2= 64 then 180-64= 116

The best course grade your friend can earn is 73.8% the minimum score would your friend would need on the final to earn a 75% for the course is 108%.

Given that,

Before the course's final exam, a friend had an 84% course average. Except for the final, which accounts for 15% of the course grade, everything else is included in that score.

We have to find what is your friend's best possible course grade and What grade on the final must your friend obtain in order to receive a 75% for the course.

We know that,

Best grade = (84%)(0.7) + (100%)(0.15)

Best grade=0.588+0.15

Best grade=0.738 or 73.8%

Now,

Let final = 15% of the grade

Let class work = (110%-15%)=95%

Let your friend minimum score =f

So,

70%(0.84) + 15%(final) = 75%

0.7(0.84) + 0.15f = 0.75

0.588 + 0.15f = 0.75

Collect like terms

0.15f=0.75-0.588

0.15f = 0.162

Divide both side by 0.15f

f=0.162/0.15

f =1.08 or 108%

Therefore, the best course grade your friend can earn is 73.8% the minimum score would your friend would need on the final to earn a 75% for the course is 108%.

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Answer:

To find the weight of the plane with 77 gallons of fuel in its tank, we can use the linear equation for the weight of the plane in terms of the amount of fuel in its tank. The equation has the form:Weight = m * Fuel + bWhere m is the slope of the line, which is 5.9, and b is the y-intercept, which is the weight of the plane when the amount of fuel is 0. We know that the weight of the plane with 48 gallons of fuel is 2383.2 pounds, so we can use this information to solve for b:2383.2 = 5.9 * 48 + b

b = 2383.2 - 5.9 * 48

b = 2383.2 - 280.8

b = 2102.4Now that we have the value of b, we can plug it back into the equation to find the weight of the plane with 77 gallons of fuel:Weight = 5.9 * 77 + 2102.4

Weight = 456.3 + 2102.4

Weight = 2558.7 poundsSo the weight of the plane with 77 gallons of fuel in its tank is 2558.7 pounds.

Step-by-step explanation:

The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 324.

The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 326.   This is calculated using the 1/2-value correction (de Moivre-Laplace Approximation). The 1/2-value correction assumes the normal distribution is symmetric, with the mean in the middle of the distribution. This means that the probability of being above the mean is equal to the probability of being below the mean.  Since the airline wants to be 99% confident that all ticket holders who do show up will be able to board the plane, this means that the airline needs to sell enough tickets such that the probability of being above the mean (300 tickets sold) is 99%.   Using the 1/2-value correction, the airline needs to sell 326 tickets to achieve this confidence level.

This is calculated as follows:   P(x > 300) = 0.99  P(x < 300) = 0.01  Using the 1/2-value-correction:

P(x = 300 + 0.5) = 0.99

Therefore,   x = 300 + 0.5=>  x = 300.5 => x = 326

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The number of roots the polynomial equation 2x⁴ + 5x³ -3x² - 5 have is 4

From the question, we have the following parameters that can be used in our computation:

2x^4+5x^3-3x^2-5

Express the polynomial expression properly using proper superscripts

So, we have the following representation

2x⁴ + 5x³ -3x² - 5

The degree of a polynomial is the number of roots in it

This means that

Degree = 4

So, we can conclude that the polynomial equation 2x⁴ + 5x³ -3x² - 5 has 4 roots

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a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows:

(747, 853).

b) The sampling error at the 95% confidence level is of: 35.8.

We have the standard deviation for the population is known, hence the z-distribution is used to calculate the confidence interval.

The equation that gives the bounds of the confidence interval is presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The remaining parameters are given as follows:

[tex]\overline{x} = 800, \sigma = 200, n = 55[/tex]

Then the lower bound of the interval is calculated as follows:

800 - 1.96 x 200/square root of 55 = 747.

The upper bound of the interval is calculated as follows:

800 + 1.96 x 200/square root of 55 = 853.

For a sample size of n = 120, the sampling error is obtained as follows:

Sampling error = 1.96 x 200/square root of 120 = 35.8.

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The sum of the two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8 is 11x³-2x²+3x+11.

Algebraic expressions called polynomials include coefficients and variables. For polynomial expressions, we can perform mathematical operations like addition, subtraction, multiplication, and positive integer exponents. Polynomial addition is the process of adding like terms from two or more algebraic equations while maintaining the sign of each term.

Here, given two polynomials 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

First, arrange the given polynomials. The polynomials were already arranged from the increasing to decreasing order of degree. Then,

(4x³+2x²-4x+3)+ (7x³-4x² +7x+8)

Second, group the like terms from both polynomials.

(4x³+7x³)+(2x²-4x²)+(-4x+7x)+(3+8)

Now, simplifying the combining terms, we get,

11x³-2x²+3x+11

The answer is 11x³-2x²+3x+11.

The complete question is -

Add the following polynomials, then place the answer in the proper location on the grid. write the answer in descending powers of x. Find the sum of 4x³+2x²-4x+3 and 7x³-4x² +7x+8.

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Nicole and Jared are both accurate. To generate an equation with just one variable, you can solve for either variable and then use the equivalent expression.

In the given question, when solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation.

Nicole found x = y - 10 for the same equation and substituted y - 10 for x in the other equation.

We have to check who is correct.

Nicole and Jared are both accurate. To generate an equation with just one variable, you can solve for either variable and then use the equivalent expression. You can then resolve. In contrast to Nicole, who would have produced a one-variable equation that can be used to solve for y, Jared would have produced an equation with just one variable that can be used to get the value of x.

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The right question is:

When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation. Nicole found x = y - 10 for the same equation and substituted y - 10 for x in the other equation. Who is correct? Explain.

Answer:

4√3

Step-by-step explanation:

 √48

If we factor it out we will get

√4^2 ⋅ 3

Then we pull terms out from under the radical

4√3

So, the answer is 4√3

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Answer:

A. 2.3

Step-by-step explanation:

because it become 23/10 when you turn it into a fraction

49 is the smallest possible value of x.

Given: x, y, and z are three perfect square numbers.

What is the least x that can be?

Currently, we have three numbers by the stipulation:

x > y > z > 0

and AP has these figures.

Let's now list every perfect square from 1 to 10 in the following order: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

As a result, we can observe that 25 is equal to the product of 1 plus 49.

The possible outcomes are 1, 25, and 49.

If x = 49 and z = 1, then

x + z / 2 = y

49 + 1 / 2 = y

y = 50 / 2

y = 25

Y is therefore 25 and X is 49.

As a result, 49 is the lowest value of x that can exist.

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Answer:

as you can see on the picture, they both have same rectangle

1st figure is i divide it by 2 and shade 1 to get 1/2

2nd figure is I divide it by 5 and shade 2 to get 2/5

if we use LCD:

1/2 will become 5/10

2/5 will become 4/10