Isaac has a points card for a movie theater. He receives 65 rewards points just for signing up. He earns 12. 5 points for each visit to the movie theater. He needs at least 210 points for a free movie ticket. Write and solve an inequality which can be used to determine xx, the number of visits Isaac can make to earn his first free movie ticket

Answer:

a. a=10

b. b=-300

c. c=-1

d. d= -3567

Step-by-step explanation:

a. subtract 30 from each side

b. subtract 500 from each side

c. add 1 to each side

d. subtract 3,567 from each side

since r is so widely used, it is appropriate to calculate r for nonlinear data: False.

The calculation of r (Pearson's correlation coefficient) is based on the assumption that the relationship between the two variables is linear. Therefore, it is not appropriate to calculate r for nonlinear data as it may give misleading results.

In summary, it is not appropriate to calculate r for nonlinear data as it assumes a linear relationship between the variables. Other methods such as Spearman's rank correlation or Kendall's tau may be used for nonlinear data.


n: The correlation coefficient 'r' is specifically designed to measure the strength and direction of a linear relationship between two variables. While it is widely used, calculating 'r' for nonlinear data is not appropriate, as it will not accurately capture the true nature of the relationship between the variables.

When dealing with nonlinear data, it is better to use other statistical methods designed for such data, rather than relying on the correlation coefficient 'r'.

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The first three positive values of lambda for which the problem (1 - x^2)y" - 2xy' + lambda y = 0, y(0) = 0, y(x), y'(x) bounded on [-1, 1] has nontrivial solutions are lambda = 1, 1, 9.

The power series: y = sum_(n=0)^infinity a_n x^n.

Using the Frobenius method,

First, we assume y' = sum_(n=1)^infinity n*a_n x^(n-1) and y" = sum_(n=2)^infinity n*(n-1)*a_n x^(n-2).

We then plug these into the original equation and rearrange the terms to obtain:

sum_(n=2)^infinity [(n*(n-1)*a_n - 2*n*a_n + lambda*a_n)*x^(n-2) - a_(n-2)*x^(n-2)] = 0.

By equating the coefficients of x^(n-2) to zero, we obtain the recurrence relation:

a_n = a_(n-2)/[(n-2)^2 - lambda].

Since y(0) = 0, we know that a_0 = 0. We can also assume a_1 = 1 for simplicity.

Using the recurrence relation, we can find a_2 = 0, a_3 = 1/[(1)^2 - lambda], a_4 = 0, a_5 = a_3/[(3)^2 - lambda] = 1/[(1)^2 - lambda][(3)^2 - lambda], and so on.

We can see that the even coefficients are all zero, and the odd coefficients are in the form of a product of terms in the denominator.

For the solution to be bounded on [-1, 1], the denominator must not be zero. Therefore, we need to find the first three positive values of lambda for which (n-2)^2 - lambda = 0 for some odd integer n.

Solving for lambda, we obtain lambda = (n-2)^2 for odd n.

The first three positive values of lambda are (1-2)^2 = 1, (3-2)^2 = 1, and (5-2)^2 = 9.

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Answer:

YES

Step-by-step explanation:

when you distribute the -(27 - t) you get (t  - 27) which is the same as the original

A regular solid shape is defined as a three-dimensional object that has all its faces congruent and all its vertices congruent. In other words, all faces have the same shape and size and all vertices have the same angle measures.

Among the options provided, only the cube is a regular solid shape. A cube is a three-dimensional object that has six equal square faces. Each face is a square and each vertex has the same angle measure. The edges of a cube are congruent and the shape is highly symmetrical.

The cylinder is not a regular solid shape because it has two congruent circular faces and one curved surface, which is not congruent to the other two faces. The vertices of a cylinder also have different angle measures.

The cuboid is not a regular solid shape because it has six rectangular faces, and the shape is not highly symmetrical. The vertices of a cuboid also have different angle measures.

In conclusion, a regular solid shape must have congruent faces and congruent vertices, and only a cube satisfies these conditions. It is important to note that not all regular shapes are regular solid shapes, for example, a sphere is a regular shape, but it is not a regular solid shape because it has no faces, vertices or edges.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

24

Step-by-step explanation:

\(\sf Given\:fraction:\dfrac{48}{72}\)

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 72:  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

So the greatest common factor (GCF) of 48 and 72 is 24.

Therefore, to simplify the fraction, divide the numerator and denominator by 24:

\(\sf \implies \dfrac{48}{72}=\dfrac{48 \div 24}{72 \div 24}=\dfrac{2}{3}\)

Answer:

24

Step-by-step explanation:

Factors of 48 and 72

Solving

By using the formula for area of triangle using coordinates, the following results are obtained

13) Area of triangle = \(\frac{15}{2} \ sq. units\)

14) Area of triangle = \(\frac{49}{2} \ sq. units\)

What is area of triangle?

Area of a triangle is the total space taken by the triangle. If the coordinates of triangle are \((x_1, y_1), (x_2, _2) \ and \ (x_3, y_3)\), then area of triangle is calculated by the formula

Area of triangle = \(\frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

13) The given coordinates are E (3, 1), F(3, -2) and G(-2, 2)

Area of triangle =

\(\frac{1}{2}|3(-2-2) + 3(2-1) + (-2)(1 -(-2))|\\\\\frac{1}{2}|3(-4) + 3(1) -2(3)|\\\\\frac{1}{2}|-12 + 3 - 6|\\\\\frac{1}{2}|-15|\\\\\frac{15}{2} \ sq. units\)

14) The given coordinates are E (-3, 4), F(4, 4) and G(3, -3)

Area of triangle =

\(\frac{1}{2}|(-3)(4-(-3)) + 4(-3-4) + 3(4-4)|\\\\\frac{1}{2}|(-3)(7)+4(-7)+3(0)]\\\\\frac{1}{2}|-21-28+0|\\\\\frac{1}{2}|-49|\\\\\frac{49}{2} \ sq. units\)

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The required value of y is 117°

Given AB and CD are parallel lines;

and EF is the transversal

Thus 2x + 16 = 3x - 12 { because they are corresponding angles }

On solving the above mentioned linear equation

we get,

x = 25

Thus the required angles are  2x + 16 = 50 + 16 = 66 degrees

and 3x - 12 = 75 - 12 = 63 degrees

And to find the value of y

we can use linear pair property

Thus y + 63 = 180

y = 180 - 63

y = 117 °

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Two equal-size vectors at right angles to each other have a resultant that is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

The magnitude of the resultant vector of two equal-size vectors at right angles to each other can be determined using the Pythagorean theorem.

Let's assume the magnitude of each vector is represented by "a".

According to the Pythagorean theorem, the magnitude of the resultant vector, denoted as "R", can be calculated as:

R =\(\sqrt{a^2 + a^2}\)

R = (\(\sqrt{2a^{2} )}\)

R = \(\sqrt{2}\) a

Therefore, the magnitude of the resultant vector is equal to \(\sqrt{2}\) times the magnitude of each individual vector.

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Answer:

$104,750

Step-by-step explanation:

we just add 101,00 and 3,750 together since they are both being financed

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A random sample is a representative subset of individuals selected from the larger population in such a way that each member of the population has an equal chance of being chosen.

The purpose of a random sample is to obtain a sample that is unbiased and reflects the characteristics of the entire population.

By giving every individual an equal opportunity to be included in the sample, random sampling helps minimize selection bias and ensures that the sample is more likely to be representative of the population as a whole. This allows researchers to make valid inferences and generalizations about the population based on the characteristics observed in the random sample.

Random sampling is widely used in various fields, including research, surveys, and statistical analysis, to draw reliable conclusions about a larger population based on a smaller subset of individuals.

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a)

\(B=\frac{\mu\mu_0 I}{D}=1.6\cdot 10^{-4}~T,\)

b)

\(B=\mu_0I\frac N{2\pi r}=9.6\cdot 10^{-4}~T.\)

Answer:

Step-by-step explanation:

Given the inequality expression |x| < a. The two cases for solving the expression are x<a and -x < a (or x>-a)

Note that the absolute value of a number will return both its positive and negative value. That's why the value of x i.e |x| returns both x and -x in the expression above.

The connecting word of the expression is that 'the absolute value of variable x is less than a' where a can take any value.

The slope can be calculated using the following equation:

Where (x1, y1) and (x2, y2) are two points on the line.

We know that if you buy 6 cans, x = 6, it will cost $3.00, y = 3.

We also know that if we buy zero cans, x = 0, it will cost nothing, y = 0.

So we have the points (0, 0) and (6, 3), so:

So, the slope is 1/2, fourth alternative.

Answer:

-26.25 - 15.5x = -15.5x - 11.78

collect the like term

-15.5x + 15.5x = -11.78 + 26.25

= 14.48

Answer:

no solution

Step-by-step explanation:

- 5(5.25 + 3.1x) = - 6.2(2.5x + 1.9) ← distribute parenthesis on both sides

- 26.25 - 15.5x = - 15.5x - 11.78 ( add 26.25 to both sides )

- 15.5x = - 15.5x + 14.47 ( add 15.5x to both sides )

0 = 14.47 ← False

this false statement indicates the equation has no solution

By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

To show that (0,1) and R have the same cardinality, we can apply the Schroder-Bernstein theorem, which states that if there exist injective functions from set A to set B and from set B to set A, then A and B have the same cardinality.

First, we can define a function from (0,1) to R by using a bijection. For example, we can use the function f(x) = tan[(πx - π/2)].

This function maps each value in the interval (0,1) to a unique real number in R. Since the tangent function is injective in the interval (-π/2, π/2), the function f(x) is also injective.

Next, we can define a function from R to (0,1) by using the inverse of the tangent function. For example, we can use the function g(x) = (π/2 + arctan[x])/π.

This function maps each real number to a unique value in the interval (0,1). The function g(x) is also injective since the inverse of the tangent function is injective.

By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

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The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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The range of (f+g)(x) is all real numbers.

To find the range of (f+g)(x), where f(x) = x+9 and g(x) = -6, follow these steps:

1. Combine f(x) and g(x) using the sum function: (f+g)(x) = f(x) + g(x)
2. Substitute the functions into the equation: (f+g)(x) = (x+9) + (-6)
3. Simplify the equation: (f+g)(x) = x+3

Now that we have (f+g)(x) = x+3, we can determine the range.

Since x can be any real number, the range of (f+g)(x) is also all real numbers because adding 3 to any real number still results in a real number.

Therefore, the range of (f+g)(x) is all real numbers.

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Answer:

Step-by-step explanation:

16^2= 16*16 or 256

Answer: 256

Step-by-step explanation:

Just do 16 times 16 so it would be 256

Answer:

The answer is "ab(13+15)".

Step-by-step explanation:

Please find the complete question in the attached file.

Given value:

\(\to 13ab+15ab\\\\\to ab(13+15)\\\\\)

Answer:

\(\text{A. 8}i\)

Step-by-step explanation:

The math constant \(i\) represents \(\sqrt{-1}\). Because \(\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\), we can rewrite the equation given the problem as \(\sqrt{-64}=\sqrt{64}\cdot \sqrt{-1}=\boxed{8i}\).

Answer:

Marcus spent $6.36.

Step-by-step explanation:

First off, the fact that tax is included makes it easier for you, you don't need to worry about any multiplying!

Alright, so, he bought 2 candy bars for $0.79 EACH - that's 2 * $0.79 = $1.58.

Next, a drink for $1.49 and a bag of chips for $3.29. That's $1.49 + $3.29 = $4.78.

Now you add those two numbers up: $1.58 + $4.78 = $6.36.

Therefore, Marcus spent $6.36!

Step 1:

50%= 50/100 = 0.5

Step 2:

50% of 50%= (50×0.5)/100= 0.25

Step 3:

50% of 50% of 50% = (50×0.25)/100= 0.125

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Answer:

Answer is A -  Angles that are congruent are complementary to the same angle.

Step-by-step explanation:

trust the process

The value of price per pint is $3.88.

What is the total cost?

Total cost is an economic metric that includes both the initial cash outlay and the opportunity cost of the decision-makers options when calculating the costs incurred to produce a good, buy an investment, or acquire a piece of equipment.

Here, we have

Given: A 4-cup bottle of mouthwash costs $7.44.

We have to find the price per pint.

4 cups = 1 quart

2 pints = 1 quart

So you have 1 pint of mouthwash.

But there are two in the bottle.

Therefore you divide the price by 2

7.76 / 2 = 3.88 dollars.

Hence, the value of the price per pint is $3.88.

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Answer:

The area is 8

Step-by-step explanation:

If the perimeter is 12, we can just start guessing and checking. in this case, if 4 is the length, that means 2 is its width, since 4-2=2. then you find the area(basexhight) 4x2=8!

Answer:

b = 8.485

c = 23.995 ≈ 24

Step-by-step explanation:
Part b:

\(\sqrt{(10-4)^2+(9-3)^2}\)

√(36 + 36)

= 8.485

Part c:

Base = \(\sqrt{(6-2)^2+(1-5)^2}\)

Base = 5.656

Area = Base x Height x 0.5

Area = 5.656 x 8.485 x 0.5

Area = 23.995 ≈ 24

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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