Olivia has a points card for a movie theater. She receives 80 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 105 points for a free movie ticket. Write and solve an inequality which can be used to determine xx, the number of visits Olivia can make to earn her first free movie ticket.

Answer:

\(\frac{2x}{5} - \frac{3}{5}\)

The volume of given triangular prism is 24,000 cubic yards.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Here, the dimensions of base are 30 yards and 20 yards.

Here, area = 1/2×30×20

= 300 yd²

Volume of a triangular prism = Area of base triangle × Length of the prism.

= 300×80

= 24,000 yd³

Therefore, the volume is 24,000 yd³.

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Answer:

x ≤ 9

Step-by-step explanation:

The probability that a randomly chosen young adult has at least a high school education can be found using the rule of probability called the "complement rule".

To find the answer, we need to subtract the probability that a randomly chosen young adult does not have at least a high school education from 1. In other words:

Probability of having at least a high school education = 1 - Probability of not having at least a high school education.

By using this rule, we can calculate the probability.

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Answer:

\(a=7,\\b=3\)

Step-by-step explanation:

The area of a rectangle is equal to \(A=l\cdot w\), where \(l\) is the length of the rectangle and \(w\) is the width of the rectangle. In a rectangle, opposite sides are equal.

Therefore, we can write the following system of equations:

\(\begin{cases}a\cdot (9+b)=84,\\a\cdot b=21\end{cases}\)

Expand the first equation:

\(9a+ab=84\)

Substitute the second equation into the first (\(ab=21\)):

\(9a+21=84,\\9a=63,\\a=\boxed{7}\)

Solving for \(b\):

\(7b=21,\\b=\frac{21}{7}=\boxed{3}\)

Answer:

Step-by-step explanation:

Hope this helps u!!

a) The table of given values suggest that the exponential function represents exponential decay.

b) The table of given values suggest that the exponential function represents exponential growth.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

We can determine whether a exponential function is exponential growth or decay by examining the values of y as x increases.

If y increases as x increases, the function is exponential growth.

If y decreases as x increases, the function is exponential decay.

a) Using this criteria, we can observe that for the given table -

When x increases from 2 to 3, y decreases from 20 to 10. This indicates that the function is a decay function.

Similarly, as x increases from 3 to 4, 4 to 5 and 5 to 6, y decreases indicating the function is a decay function.

Therefore, the function is an exponential decay function.

b) Using this criteria, we can observe that for the given table -

When x increases from 2 to 3, y increases from 17.3 to 26.7. This indicates that the function is a growth function.

Similarly, as x increases from 3 to 4, 4 to 5 and 5 to 6, y increases indicating the function is a growth function.

Therefore, the function is an exponential growth function.

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Answer:

\(d \approx 2.8\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point A (-3, 1)

Point B (-1, -1)

Step 2: Find distance d

Answer:  d = 2.83

Step-by-step explanation: The distance between AB rounded to the nearest tenth is 2.83

Answer:

(0, -2)

Step-by-step explanation:

a point on the y-axis. that means x=0.

so, the distance of (5, -2) to (0, y) is the same as the distance from (-3, 2) to (0, y).

the distance between (5, -2) and (0, y) is based on Pythagoras (the differences in x and y directions are the sides of a right-angled triangle, and the distance is its Hypotenuse, its baseline) :

distance² = (5-0)² + (-2 - y)² = 25 + 4 + 4y + y² = 29+4y+y²

but it is also

distance² = (-3-0)² + (2 - y)² = 9 + 4 - 4y + y² = 13 - 4y + y²

so, we get

29 + 4y + y² = 13 - 4y + y²

29 + 4y = 13 - 4y

16 = -8y

y = -16/8 = -2

their, the point on the y-axis being equidistant to both points is (0, -2)

Answer:

5 containers high

Step-by-step explanation:

Given that :

Given :

Width = 20 containers

Length = 50 containers

Total containers = 5000

Hence,

Total containers = width * length * height

5000 = 20 * 50 * height

5000 = 1000 * height

Height = 5000 / 1000

Height = 5 containers

The amount that will accumulate by the end of the sixth and final payment is approximately $41,666.60.

To calculate the accumulated amount by the end of the sixth and final payment, we can use the future value of an ordinary annuity formula:

Future Value = Payment × Future Value of an Ordinary Annuity Factor

The payment is $5,800, and the interest rate is 9%. Since the payments are made at the end of each year, we can use the future value table for an ordinary annuity at 9%.

Looking up the factor for 6 years at 9% in the future value table, we find it to be 7.169858.

Now we can calculate the accumulated amount:

Future Value = $5,800 × 7.169858 = $41,666.60

Therefore, the amount that will accumulate by the end of the sixth and final payment is approximately $41,666.60. The correct answer is not among the options provided.

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To find the area of the region bounded by the curves y = x^4 - x^3 - 2x and y = x^3 - 4x^2 - 2x^3, we need to determine the points of intersection between the two curves.

First, we set the two equations equal to each other and solve for x:

x^4 - x^3 - 2x = x^3 - 4x^2 - 2x^3

Rearranging the terms:

x^4 - 2x^3 + 4x^2 = 0

Factoring out an x^2:

x^2(x^2 - 2x + 4) = 0

Setting each factor equal to zero:

x^2 = 0 or (x^2 - 2x + 4) = 0

Solving the second equation using the quadratic formula:

x = (-(-2) ± √((-2)^2 - 4(1)(4))) / (2(1))

x = (2 ± √(4 - 16)) / 2

x = (2 ± √(-12)) / 2

x = (2 ± 2√3i) / 2

x = 1 ± √3i

Since the problem asks for the area, which is a real value, we can disregard the imaginary solutions. Therefore, there are no points of intersection between the two curves.

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Answer: 8.4 meters

Step-by-step explanation:

From the question, we are informed that a roll of ribbon was 12 meters long and that Diego cut 9 pieces of ribbon that were 0.4 meter each to tie some presents. The length of ribbon used by Diego for the present would be:

= 9 × 0.4meter

= 3.6 meter.

Therefore, the meters of ribbon that were available for making wreaths would be:

= 12 meters - 3.6 meters

= 8.4 meters

Answer:

5.4

Step-by-step explanation:

We have 12 meters total,Diego: 9 pieces × 0.4 meters= 3.6 meters

So Diego used up 3.6 meters of ribbon

Part A: 9-3.6=5.4 meters left

The value of width 'w' of rectangular prism with l = n/a, h = n/a, v = n/a is given by, w = a/n.

We know that the volume of rectangular prism with length L and width W and Height H is given by,

V = L*W*H

Given that the Height of the rectangular prism, h = n/a

Length of the rectangular prism, l = n/a

Volume of the rectangular prism, v = n/a

let the width of the rectangular prism be 'w'.

So from the volume formula we get,

v = lwh

n/a = (n/a)*w*(n/a)

n/a = (n/a)²*w

w = (n/a)/(n/a)² = (n/a)*(a/n)² = a/n

Hence the value of w is a/n.

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Answer:

Right scalene

Step-by-step explanation:

The triangle has a right angle, but no sides are equal.

Answer:

The triangle is a right scalene triangle.

Step-by-step explanation:

If any angle is marked by a little square like in the triangle's bottom left corner, that means the angle is 90° or a right angle. Since none of the angles in the triangle are equivalent, that means the right triangle is a scalene triangle. So the correct choice is a right scalene triangle.

From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

As given in the question,

From the given figure:

line l is parallel to line m.

t is the transversal of line l and m

Relationship between angles for the parallel lines

∠1 and ∠2  are straight angles and are supplementary

∠3 and ∠2 are interior angles and are supplementary

⇒m(∠1 + ∠2) = m(∠3+∠2)

⇒m∠1= m∠3

Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

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The distribution that is often used to approximate the sampling distribution of the sample mean is the normal distribution. The central limit theorem states that the distribution of sample means taken from a population with a mean and standard deviation will be normally distributed if the sample size is sufficiently large.

This theorem is very important in statistics since it justifies the use of the normal distribution to approximate the sampling distribution of the sample mean. A sampling distribution refers to a probability distribution that shows the means of all possible samples of a particular size taken from a population. The concept of a sampling distribution is essential since it allows us to make conclusions about a population using the information obtained from a sample. Even though the sampling distribution of the sample mean cannot be known precisely in general, it can be approximated by a normal distribution. The normal distribution is an important probability distribution in statistics since many variables, such as the sample mean, tend to follow a normal distribution. The normal distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is characterized by two parameters, the mean and the standard deviation. The mean of a normal distribution is the center of the distribution, while the standard deviation is a measure of the dispersion of the data around the mean.

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Given:

The weight of 10 aluminum cans is 0.16 kilograms.

The aluminum in 10 cans that are recycled has a value of $0.14.

To find:

An equation to represent the number of cans c given their weight w.

Solution:

We have,

10 aluminum cans = 0.16 kilograms.

Divide both sides by 0.16.

\(\dfrac{10}{0.16}\) aluminum cans = 1 kilograms.

62.5 aluminum cans = 1 kilograms.

Let c be the number of cans and w be their weight.

1 kilograms = 62.5 aluminum cans

w kilograms = 62.5w aluminum cans

So, c = 62.5w.

Therefore, the required equation is c = 62.5w.

Answer:

150

Step-by-step explanation:

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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Answer:

Step-by-step explanation:

Sandra, Deacon, and Breanna read a total of 5 + 6 + 7 = 18 books. Since one book was read by all three children, we need to subtract it once from the total. Therefore, they read 18 - 1 = 17 different books.

Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes, leaving 8 - 2 = 6 test tubes for the other two experiments. Since the two experiments required the same number of test tubes, each one required 6/2 = 3 test tubes.

It is unclear what the question is asking. Please provide more information or a specific question.

Branson and his sister Beatrice combined their allowance of $7 each to buy a movie for $12. They spent a total of 7 x 2 = $14 on the movie. Therefore, they had 14 - 12 = $2 left to buy fruit salad. They bought 2 containers of fruit salad for $1 each, leaving them with $0. They split the containers evenly between them, so each of them got 2/2 = 1 container of fruit salad.

Before Cam broke his right arm, he could type 9 words per minute on his phone. After he broke his arm, he could only type 6 words per minute. The difference between the number of words he could type in 5 minutes before and after he broke his arm is 5 x (9 - 6) = 5 x 3 = 15 words.

Gisselle saved $6 every week for 8 weeks, so she saved a total of 6 x 8 = $48. She found a used bicycle for $50, so she did not have exactly enough for the bicycle. She was $50 - $48 = $2 short.

Answer:

well it stilll be best method

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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For a sample of rating of an automobile manufacturer's van regarding rating of 28.3 miles/gallon (mpg), the Z-test statistic value is equals to the -1.631.

Z-test is a parametric test. When the sample size is sufficiently large, it is mostly used. This test statistic is computed a standard normal distribution. It is then compared with the critical value (obtained from z-table). If the test statistic value is greater than it, there is evidence to reject the null hypothesis. We have an automobile manufacturer with its van rating. A sample of 200 vans is randomly considered. Sample size, n = 200

Mean of rating = 28

Standard deviations = 2.6

Lavel of significance= 0.01

To test the firm'claim we have to consider hypothesis testing here. Since it is claimed by an automobile manufacturer that its car has a 28.3 miles/gallon (MPG) rating, therefore, the null hypothesis and alternative can be stated as:

\(H_0 :μ = 28.3\)

\(H_a :μ≠28.3\)

Now, to determine the value of the test statistic, consider the Z-test : \( z = \dfrac{{M - \mu }}{{\dfrac{\sigma }{{\sqrt n }}}}\)

where, M -> mean

n --> sample size

Substitute all known values in above formula, \(= \dfrac{{28 - 28.3}}{{\dfrac{{2.6 }}{{\sqrt {200} }}}}\\\)

\(= \dfrac{{-0.3}}{{\dfrac{{0.26 }}{{\sqrt {2} }}}}\\\)

=> z = - 1.631

Hence, required test statistic value is -1.631.

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The volume of the solid can be found by using the general slicing method which involves slicing the solid into multiple thin slices, computing the volume of each slice.

The general slicing method can be used to find the volume of the solid with a semicircular base of radius 9 whose cross section is a triangle. This method involves slicing the solid into multiple thin slices, computing the volume of each slice, and then summing up the volumes of all the slices. To find the volume of each slice, we first need to determine the area of the cross-section for each slice. The area of the cross-section can be found by multiplying the base of the triangle by its height. For each slice, the base of the triangle is equal to 2πr/N, where r is the radius of the semicircle and N is the number of slices. The height of the triangle is equal to the thickness of each slice. Once the area of the cross-section is calculated, we can find the volume of each slice by multiplying the area by the thickness of the slice. Finally, the volume of the solid is equal to the sum of the volumes of all the slices.

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Answer:

382=380

Step-by-step explanation:

l don't know the answer but just trying

Rounding to one significant figure is to round the given number into a number where the first digit is a number and the remaining digits are all zeroes.

The number after rounding 382 to 1 significant figure is 400.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

382

We will round to 1 significant figure.

This means the hundred place value must be the only number remaining while keeping all the place values as zero.

Since the tens place value is more than 4.

We can round the hundred place value 3 into 4.

Now,

382 will be 400 when rounded to 1 significant figure.

Thus,

The number after rounding 382 to 1 significant figure is 400.

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The following equations are organized for P as a function of Q

1) P = 20-8Q

2) p = \(\dfrac{12-Q}{3}\)

3) p = 9 - 4Q

A function in mathematics is, technically speaking, a relation between a set of inputs and a set of potential outputs, where each input is related to exactly one output. Examples of functions in mathematics typically range from integers to integers or from real numbers to real numbers.

Additionally, it is a relation or a process that links each element x of a set X to the codomain of the function and to a single element y of a different set Y (typically the same set).

1) Q = 20-P

Q + P = 20

P = 20-Q

2) Q=12-3P

Q +3P = 12

3P = 12-Q

p = \(\dfrac{12-Q}{3}\)

P = 4 - 1/3Q

3) 8Q = 18 -2p

8Q + 2p = 18

2p = 18 - 8Q

p =  \(\dfrac{18-8Q}{2}\)

p = 9 - 4Q

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Complete question:

These parametric equations represent the x and y coordinates of points on the line as the parameter t varies.

To write the vector equation and parametric equations of a line that contains the point (2,7), we need an additional piece of information: either another point on the line or the direction vector of the line.

Let's say we have another point on the line, such as (4,9). With this information, we can proceed to write the vector equation and parametric equations.

Vector Equation: The vector equation of a line passing through points P(2,7) and Q(4,9) can be written as: r = p + t⋅d

Here, r represents the position vector of any point on the line, p represents the position vector of point P(2,7), t is a parameter that varies along the line, and d represents the direction vector of the line, which can be obtained by subtracting the position vectors of points P and Q:

d = Q - P = (4,9) - (2,7) = (2,2)

Therefore, the vector equation becomes:

r = (2,7) + t⋅(2,2)

Parametric Equations: The parametric equations express the x, y, and z coordinates of a point on the line in terms of the parameter t. In this case, since we are dealing with a 2D line, there will be only x and y coordinates.

x = 2 + 2t

y = 7 + 2t

These parametric equations represent the x and y coordinates of points on the line as the parameter t varies.

Please note that if you have a different point or specific direction vector in mind, the equations would be modified accordingly.

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For part a, the vector x can be expressed as a linear combination of a1 and a2 as x = -a1 - 2a2. For parts b, c, d, no linear combination of the given vectors can express x. For part e, x = a1 - 2a2 + 2a3 with constants k1=1, k2=-2, and k3=2.

To express x=(-3,-6) as a linear combination of a1=[1,4] and a2=[-2,3], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

-3 = k1 * 1 + k2 * (-2)

-6 = k1 * 4 + k2 * 3

Solving this system of equations, we get k1=-6 and k2=1. Therefore, x can be expressed as:

x = -6 * [1,4] + [ -2,3] = [-8, 9]

x = -a1 - 2a2

To express x=[5,9,5) as a linear combination of a1=[2,1,4), a2=[1,-1,3), and a3=[3,2,5), we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

5 = k1 * 2 + k2 * 1 + k3 * 3

9 = k1 * 1 - k2 * 1 + k3 * 2

5 = k1 * 4 + k2 * 3 + k3 * 5

Solving this system of equations, we get k1=1, k2=0, and k3=1. Therefore, x can be expressed as:

x = 1 * [2,1,4] + 0 * [1,-1,3] + 1 * [3,2,5] = [5,3,9]

To express x=[2,-1,4) as a linear combination of a1=[3,6,2] and a2=[2,10,-4], we need to find constants k1 and k2 such that x = k1 * a1 + k2 * a2. Solving for k1 and k2, we get:

2 = k1 * 3 + k2 * 2

-1 = k1 * 6 + k2 * 10

4 = k1 * 2 + k2 * (-4)

This system of equations has no solution, since the second equation implies that k2 is negative, but the third equation implies that k2 is positive. Therefore, x cannot be expressed as a linear combination of a1 and a2.

To express x=(2,2,3] as a linear combination of a1=[6,-2,3), a2=[0,-5,-1), and a3=[-2,1,2], we need to find constants k1, k2, and k3 such that x = k1 * a1 + k2 * a2 + k3 * a3. Solving for k1, k2, and k3, we get:

2 = k1 * 6 + k2 * 0 + k3 * (-2)

2 = k1 * (-2) + k2 * (-5) + k3 * 1

3 = k1 * 3 + k2 * (-1) + k3 * 2

Solving this system of equations, we get k1=1, k2=1, and k3=1. Therefore, x can be expressed as:

x = 1 * [6,-2,3] + 1 * [0,-5,-1] + 1 *[-2,1,2]

To express x = [17,2,3], as linear combination of a1 = [1, -2,3), a2 = [5, -2,6], a3 = [4,0,3], We need to find constants k1, k2, and k3 such that:

x = k1a1 + k2a2 + k3*a3

Substituting the given values:

[17, 2, 3] = k1[1, -2, 3] + k2[5, -2, 6] + k3[4, 0, 3]

This gives us the following system of linear equations:

k1 + 5k2 + 4k3 = 17

-2k1 - 2k2 = 2

3k1 + 6k2 + 3k3 = 3

Solving for k1, k2, and k3, we get:

k1 = 1, k2 = -2, k3 = 2

Therefore, we can express x as a linear combination of a1, a2, and a3 as:

x = a1 - 2a2 + 2a3

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Answer:

0.075 is less

Step-by-step explanation:

It is 0.075 because 0.96 is closer to 1 and so is greater

Answer:

6845.86

Step-by-step explanation: