When June went to a grocery store, 10% of the total amount she paid was spent on ice cream. Her total bill was40. How much money did June spend on ice cream?

The number of three-letter code can be formed using 12 Greek alphabets is 1320.

For the given question.

There are 12 Greek alphabet used for making the three-letter code with out repetition.

You have 12 symbols from which to choose for the first letter, 11 for the second (because you're already using one), and 10 for the third.

Using the permutation;

Number of code formed = 12×11×10

Number of code formed = 1320.

Thus, the number of three-letter code can be formed using 12 Greek alphabets is 1320.

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Answer:

Negative! -5/2

Step-by-step explanation:

.......

Answer:

y = -11

Step-by-step explanation:

23 + 18y = -21 + 14y

Combine like terms

18y - 14y = -21 -23

Do the math

4y = -44

Divide both sides by 4

y = -11

The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.

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The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

For an angle \(\theta\) the unit circle is a circle with radius 1 containing the following set of points: \((\cos{\theta}, \sin{\theta})\).

The angle for this problem is given as follows:

-4pi/3.

Hence the sine and the cosine are given as follows:

Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

(the equation of the unit circle is x² + y² = 1).

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The data should be analyzed as a paired difference experiment because each participant's laugh episodes are measured in different roles. The target parameter is the mean difference in laugh episodes.

To determine if the population means are different, a paired t-test can be conducted using the provided sample means.

a. The data should be analyzed as a paired difference experiment because the laugh episodes of each participant are measured both as a speaker and as an audience member. This pairing allows for a direct comparison of the differences in laughter episodes between the two roles.

c. To determine if there is sufficient evidence to conclude that the population means of laughter episodes for speakers and audience members are different, we need to conduct a hypothesis test. The appropriate test for paired data is the paired t-test.

Using the provided sample means of 3.5 laughter episodes for speakers and 1.4 laughter episodes for audience members, we can calculate the difference in means as 3.5 - 1.4 = 2.1.

We can then perform a paired t-test using the paired differences to test the null hypothesis that the population means are equal. If the resulting p-value is less than the chosen significance level (e.g., 0.05), we can conclude that there is sufficient evidence to suggest that the population means of laughter episodes for speakers and audience members are different.

The explanation paragraph would provide a step-by-step guide on how to conduct a paired t-test with the given data, including the calculation of the test statistic and the comparison of the p-value to the significance level.

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Answer:

$17.08

Step-by-step explanation:

Ok, so we know it takes 61-23 = 38 minutes of call to change the credit from $22.24 to $17.68.

Basically, it takes 43 minutes to lose 22.24 - 17.68 = $4.56

38 minutes - $4.56

5 minutes - $4.56 x 5 /38 = 0.6

I took 5 minutes because 5 + 61 = 66

Now, we know it takes 61 minutes for the person to have $17.68 remaining.

So, if we had 5 minutes, it becomes 17.68 - 0.6 = $17.08 remaining.

Pls mark as brainliest if possible. Cheers

The answer is: Logan's rope is longer than Sam's rope.

A number that represents a part of a whole or a ratio between two quantities, written as a numerator over a denominator. It consists of a numerator (top) and a denominator (bottom) separated by a fraction bar. For example, 1/2 represents one-half of a whole or the ratio of one to two.

Part A:

Brittney's rope is shorter than Sam's rope because it is 4/5 as long as Sam's rope.

Logan's rope is longer than Sam's rope because it is 1 1/4 times as long as Sam's rope.

Holly's rope is equal to Sam's rope because it is 8/8 (which simplifies to 1) as long as Sam's rope.

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Answer:

Choice A

Step-by-step explanation:

Base = 10

Perpendicular = 10

Hypotenuse = x

On applying Pythagoras theorem:

\( \rm \: B^2+P^2 = H^2\)

On substituting,

Simplifying,

Hence,the value of x using Pythagoras theorem is 10√2.

Choice A

The measure of length of x of the triangle is x = 10√2

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AB = 10

The measure of side BC = 10

And , For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

On simplifying , we get

The measure of side AC = x

x = √ ( 10 )² + ( 10 )²

x = √200

x = 10√2

Hence , the measure of x of triangle is x = 10√2

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Answer:

The answer is -72/5.... also as 14.4

Answer:

Step-by-step explanation: first put in the value for x, 8(-6) -5y=24

Then solve from there, 8x-6= -48

-48-5y=24

-5y=24+48 ( becomes pos when transferred to this side, since it turns to the opposite direction )

Now, -5y=72

Decide both sides by -5 and then

Y = -14.4 or -14 2/5

Answer:

a reflection over the line y= -x

The two cars are 10.5 kilometers apart, measured in a straight line.

This is calculated by taking the square root of the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km). The square root of (3.1² + 8.3²) is 10.47, which can be rounded up to 10.5.

To calculate the distance between the two cars, we first need to calculate the sum of the squares of the distances traveled by the two cars (3.1 km and 8.3 km).

3.1² + 8.3² = 68.49

Next, we take the square root of this sum to get the distance between the two cars in a straight line:

√68.49 = 8.25

Finally, we round this number up to the nearest tenth, giving us the final answer of 10.5 kilometers.

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The measure of angle BCA is 81 degrees.                                            

Answer:Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.

There are several ways to do this...here's one

Let (0, 4) be a point on the first line

Then.......a line with a negative reciprocal slope going through this point will have the equation :

y = -x + 4........so......we can find the intersection of this line with y = x - 6....set both equations equal

-x + 4  = x - 6   add x, 6 to both sides

10 = 2x     divide both sides by 2

5  = x

So...using -x + 4, the y value  at intersection  = -1.......

So...we just need to find the distance from  (0,4)  to ( 5, -1)  =

√[ (5)^2 + (4 + 1)^2 ] =  5√2  ≈  7.07 units

Here's a pic....AB is the distance  with A = (0,4)  and B = (5, -1)

Step-by-step explanation:

To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.

Taking the partial derivatives with respect to x, y, and z, we have:

fx = 2x - 2y - 1

fy = -2x + 2y + 3

fz = -1

Evaluating these partial derivatives at the point P(2, -3, 18), we find:

fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9

fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7

fz(2, -3, 18) = -1

The equation of the tangent plane at P is given by:

9(x - 2) - 7(y + 3) - 1(z - 18) = 0

Simplifying the equation, we get:

9x - 7y - z - 3 = 0

To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:

x = 2 + 9t

y = -3 - 7t

z = 18 - t

where t is a parameter representing the distance along the normal line from the point P.

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The required inequality expression is 8x + 6.50y ≤ 200

Maximum amount he can spend = $200

Cost of doll, = $6.50

Cost of car = $ 8.00

Mathematically, the maximum amount he can spend on restocking is cars and doll is :

(Cost of cars × number of cars) + (cost of doll × number of dolls) ≤ maximum amount

8x + 6.50y ≤ 200

Hence, the required inequality expression is : 8x + 6.50y ≤ 200

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Answer:

They are on the 0 yard line

Step-by-step explanation:

15yards - 7yds + 3yds = 4 yards

4 yards - 7yds + 3yds = 0 yards

0 yards

(sorry if I misunderstood)

Answer:

To find out how many points Nicky needs to score in her next game, we can use the formula for the mean (also known as the average) of a set of numbers:

mean = (sum of all numbers) / (number of numbers)

We know that Nicky has played three games and scored, and points in them. So the sum of all her points is:

sum=18+22+28

sum=68

We also know that Nicky wants to have a mean of 25 points per game, and she has played three games already. If we add the score from her next game to the sum, we will have the total number of points she has scored in four games.

An equation of the line that is a perpendicular bisector of AB with A(-6,8) and B (-1,3) is y = -x + 2.

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

For line segment AB, we have:

Midpoint of AB = [(-6 - 1)/2, (8 + 3)/2]

Midpoint of AB = [-7/2, 11/2]

Midpoint of AB = [-3.5, 5.5].

Next, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3 - 8)/(-1 + 6)

Slope (m) = -5/5

Slope (m) = -1.

At data point (-3.5, 5.5) and a slope of -1, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5.5 = -1(x + 3.5)

y = -x - 3.5 + 5.5

y = -x + 2

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Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.

Given:

Sample mean (x') = 30 km per litre

Sample standard deviation (s) = 3.5 km per litre

Sample size (n) = 50

Significance level (α) = 0.05 (5%)

Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.

Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.

We'll calculate the test statistic (t-value) and compare it with the critical t-value.

The formula for the t-value is:

t = (x' - μ) / (s / √n)

where μ is the population mean (mean petrol consumption of the existing car).

First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.

Now, let's calculate the t-value:

t = (30 - μ) / (3.5 / √50)

To reject the null hypothesis, the t-value should be less than the critical t-value.

Simplifying the equation:

t = (30 - μ) / (0.495)

To find the critical value, we compare it with the calculated t-value:

-1.677 > (30 - μ) / (0.495)

Multiplying both sides of the inequality by 0.495:

-0.8294 > 30 - μ

Rearranging the inequality:

μ > 30 + 0.8294

μ > 30.8294

Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.

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Using the profit concept, it is found that the expression is given by:

P(d) = -0.00008d² + 11.6d - 12000.

When d = 29,000, P(d) = 257,120.

The profit is the subtraction of the revenues by the cost.

In this problem, we have that the revenues and the cost are given, respectively, by:

Hence the expression for the profit is given by:

P(d) = R(d) - C(d)

P(d) = -0.00008d² + 11.6d - 12000.

When d = 29000, the value of the expression is given by:

P(29000) = -0.00008(29000)² + 11.6(29000) - 12000 = 257,120.

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Part (a): Equation 1: Pa = P[Accept lot | % nonconforming = AQL] = P[X <= c | p = 0.03], where X ~ Binomial(n, p) and Pa = 0.95.

Equation 2: P[Reject lot | % nonconforming = LTPD] = P[X > c | p = 0.06], where X ~ Binomial(n, p) and P[Reject lot] = 0.05.

Part (b):

Based on the given information, we want to find a sampling plan such that Pa = 0.95 and P[Reject lot] = 0.05. Using the nomograph provided, we can find the values of n and c that satisfy these requirements. The intersection of the two lines - one representing Pa = 0.95 and the other representing P[Reject lot] = 0.05 - gives us the values of n and c. According to the nomograph, for Pa = 0.95 and P[Reject lot] = 0.05, a sample size of n = 108 and a acceptance number of c = 2 can be used.

Part (c):

When the lot size N is not very large compared to the sample size n, the binomial distribution used in part (a) is justified. This is because the sampling distribution of the proportion of defective items in a sample from a large lot approximates a normal distribution, and the binomial distribution is a good approximation of the normal distribution for large n.

Part (d):

Returning lots to the vendor may lead to a strain on the relationship between the vendor and the company, which could negatively impact future business dealings. Additionally, it may result in delayed or reduced supply of products, causing production delays or lost sales for the company.

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Answer:

\(y=-x+1\)

Step-by-step explanation:

Slope can be represented as rise over run (change y-values over change in x-values). Since the y-value is changing by -2 every time the x-value is changing by 2, the slope of the line must be \(\frac{-2}{2}=-1\).

In slope-intercept form \(y=mx+b\), \(m\) represents the slope of the line, \(b\) represents the y-intercept, and \((x, y)\) represent the coordinates of any point the line passes through.

To find \(b\), substitute \(m=-1\) and any point the line passes through.

Using (1, 0) from the table:

\(0=-1(1)+b,\\0=-1+b,\\b=1\)

Thus, the equation of this line is \(\boxed{y=-x+1}\)

A directional hypothesis is a hypothesis that reflects the difference between groups and specifies the direction of the difference.

In contrast to a null hypothesis, which suggests there is no significant relationship between the variables being studied, a directional hypothesis makes a specific prediction about the direction of the relationship. A nondirectional hypothesis, on the other hand, predicts a relationship between the variables but does not specify the direction of that relationship.

Directional hypotheses are useful in research when there is a theoretical or empirical basis to expect a particular outcome. They can help researchers to better focus their investigation and narrow down possible outcomes, thus allowing for more robust statistical analyses. However, directional hypotheses also carry the risk of confirmation bias, as researchers might be more likely to interpret data in a way that supports their hypothesis.

In summary, a directional hypothesis predicts the difference between groups and specifies the direction of that difference, providing a more focused approach to analyzing research data compared to a null hypothesis or a nondirectional hypothesis.

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To calculate Mr. Jones' pay for the week, we need to consider his regular pay for 40 hours and his overtime pay for the additional 5 hours he worked.

His regular pay for the week would be:

$26.50/hour x 40 hours = $1,060

To calculate his overtime pay, we need to first determine his overtime rate. His overtime rate is time-and-a-half, which means he earns one and a half times his regular pay rate for each hour of overtime. So, his overtime rate is:

1.5 x $26.50/hour = $39.75/hour

Now we can calculate his overtime pay for the week:

$39.75/hour x 5 hours = $198.75

To find his total pay for the week, we just need to add his regular pay and overtime pay:

$1,060 + $198.75 = $1,258.75

Therefore, Mr. Jones' total pay for the week in which he works 45 hours is $1,258.75.

We have a transformation for the triangle EFG. In this case is a translation.

We can verify with one of the points which one of the graphs correspond to this transformation.

The transformation is:

(x,y) --> (x-3, y + 1)

We look at point E = (-0.5, 0).

We apply the transformation and get:

(-0.5, 0) --> (-0.5-3, 0+1) = (-3.5, 1)

Then, the graph that has E located in the point (-3.5, 1) is the right one.

Answer:

2x+3y= -1

Step-by-step explanation:

2x+3y=5

3y= -2x+5

y= -2/3x + 5/3

m= -2/3

put the points( -2,1) in this equation to get b

1= -2(-2/3)+b

b= 1-4/3

=-1/3

so the equation is

y = -2/3x -1/3

3y= - 2x-1

2x+3y= -1

Using geometric sequence, a) The fine on day n is $2^n (2 to the power of n). b) It would take log_2(D/2) + 1 days for the fine to reach D dollars.

In this court case, the fine on each subsequent day is equal to the square of the previous day's fine. This means that the fine follows a geometric sequence, where the common ratio is the square of the previous term.

a) To find the fine on day n, we can use the formula for the nth term of a geometric sequence:

a_n = a_1 * r^(n-1)

Where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.

In this case, a_1 = 2 (the fine on the first day), r = 2 (the common ratio), and n is the day number. Plugging these values into the formula, we get:

a_n = 2 * 2^(n-1)

So the fine on day n would be 2 * 2^(n-1) dollars.

b) To find how many days it would take the fine to reach D dollars, we can use the formula for the nth term of a geometric sequence and solve for n:

D = 2 * 2^(n-1)

Dividing both sides by 2, we get:

D/2 = 2^(n-1)

Taking the logarithm of both sides with base 2, we get:

log_2(D/2) = n - 1

Adding 1 to both sides, we get:

n = log_2(D/2) + 1

So it would take log_2(D/2) + 1 days for the fine to reach D dollars.

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Answer:

7x⁵ + 3x⁴ - 2x³ + 2x² - 5x + 6

7x⁵ - 6x⁴ + 4x² - 2x + 6

Further explanation

Given:

A polynomial of the 5th degree

A leading coefficient of 7

A constant term of 6

Problem-solving:

Let us prepare the leading terms, constant terms, and the coefficients of the polynomial are being asked.

Now we make the first polynomial, for example:

b = 3

c = -2

d = 2

e = -5

Thus, the result is

Then we make the second polynomial as an alternative. For example:

b = -6

c = 0

d = -2

e = 0

Thus, the polynomial is

Of course, you can form another polynomial using the procedure above. Try to vary the coefficients.

Notes:

Let us rephrase the following definitions.

A monomial is an algebraic expression which comprises a single real number, or the product of a real number and one or more variables raised to whole number powers. For example,

A coefficient is each real number preceeding the variable(s) in a monomial. In the examples above  are the coefficients.

A polynomial is the sum or difference of a set of monomials. For example,

Each monomial that forms a polynomial is called a term of that polynomial. For example, the term of polynomial  are

The constant term is the term of polynomial that does not contain a variable.

The leading coefficient is the coefficient of the term containing the variable raised to the highest power.

For example, consider the polynomial

are the terms of polynomial.

are the coefficients.

- 5 is the constant term.

2 is the leading coefficient.

A polynomial is said to be in standard form if the terms are written in descending order of degree. For example:

is a polynomial in standard form.

is the polynomial, but it is not in standard form.

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Keywords: a polynomial of the 5th degree, a leading coefficient of 7, a constant term of 6, a monomial, terms, the leading coefficient, constant, in a standard form, rational function, whole number power, integer

Step-by-step explanation: