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An equation to represent the total cost (y) for any number of rides (x) is y = 4x + 10.

In order to write an equation that model this situation, we would assign variables to the number of rides at an amusement park and the total cost respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that it cost $4 per ride, plus a $10 fee to get in as follows;

y = 4x + 10.

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The dimensions of the rectangle are 8 inches as width and 13 inches as length.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The equation is given as:

x² + 5x - 104.

x² + 13x - 8x - 104

x(x + 13) - 8 (x + 13).

x - 8 = 0

x = 0 + 8

Width = 8

Length = x + 5

= 8 + 5.

= 13

The width is 8 inches and length is 13 inches.

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Determine the solutions of the equation. What solution

makes sense for the situation?

A rectangle has a length that is 5 inches greater than its

width, and its area is 104 square inches. The equation (x

+5)x = 104 represents the situation, where x represents

the width of the rectangle.

(x + 5)x = 104

x2 + 5x - 104 = 0

What are the dimensions of the rectangle?

Answer:

I think the answer is C

-3,-2

∠2 and ∠7 -Interior Alternate angles

∠1 and ∠3 -Corresponding angles

∠4 and ∠5 -Exterior Alternate angles

∠3 and ∠5 -Corresponding angles

An angle is a measure of the amount of rotation between two lines or planes. It is typically measured in degrees or radians. An angle can be formed by two rays that share a common endpoint, known as the vertex of the angle. The rays are called the sides of the angle, and the endpoint is called the vertex. Angles can be classified as acute, right, obtuse, or straight, depending on their measure.

Everyday objects contain some of the everyday examples of angles. Angles are formed by the shapes of objects like chairs, pizza, fingers, and scissors. The vertex point, a common vertex that connects the two lines that make up the angle sign, is present.

In the given figure

∠2 and ∠7 -Interior Alternate angles

∠1 and ∠3 -Corresponding angles

∠4 and ∠5 -Exterior Alternate angles

∠3 and ∠5 -Corresponding angles

Hence, the answer is:

∠2 and ∠7 -Interior Alternate angles

∠1 and ∠3 -Corresponding angles

∠4 and ∠5 -Exterior Alternate angles

∠3 and ∠5 -Corresponding angles

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Two numbers are in the ratio 8cm:1m, he greater number is 3,125.

A ratio in mathematics demonstrates how many times one number is present in another. A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. An ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or the value represented by this fraction are all examples of ratios.

Given that, Two numbers are in the ratio 8cm:1m and smaller number is 250.

let the greater number is x.

ratio = 8cm/1m

= 8cm/100cm

= 1/12.5 or 1:12.5

1/12.5 = 250/x

⇒ x = 250 * 12.5

⇒ x = 3,125

So, the greater number is 3,125.

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Answer:

33/108290 = 0.000305

Step-by-step explanation:

There are 52 cards in a deck.

There are 3 face cards of each of 4 suits in a deck, so there are 12 face cards in a deck.

Taking all cards at once is the same as taking one card at a time with no replacement.

First card: p(face card) = 12/52 = 3/13

Now there are 11 face cards and a total of 51 cards left.

Second card: p(face card) = 11/51

Now there are 10 face cards and a total of 50 cards left.

Third card: p(face card) = 10/50 = 1/5

Now there are 9 face cards and a total of 49 cards left.

Fourth card: p(face card) = 9/49

Now there are 8 face cards and a total of 48 cards left.

Fifth card: p(face card) = 8/48 = 1/6

Since each drawing of a card is an independent event, the overall probability of drawing 5 face cards is the product of the individual probabilities.

p(5 face cards) = 3/13 × 11/51 × 1/5 × 9/49 × 1/6

p(5 face cards) = 33/108290 = 0.000305

Answer:

Step-by-step explanation:

It would be 264/5 or 52^4/5

(^4 is the fourth power)

The function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1 because the limit of h(t) as t approaches 1 is equal to h(1).

First, we need to show that the limit of h(t) as t approaches 1 is equal to h(1).

Since h(t) = (2t-3t^2)/(1+t^3), we can rewrite the limit of h(t) as t approaches 1 as:

lim t->1 (2t-3t^2)/(1+t^3) = lim t->1 (2-3t)/(1+t^3)

We can now use the properties of limits to evaluate the limit.

Substituting t=1 into the expression for the limit, we have:

lim t->1 (2-3t)/(1+t^3) = (2-3(1))/(1+(1)^3) = -1/(2)

Now, we can use the definition of continuity to show that h(t) is continuous at a=1.

Since the limit of h(t) as t approaches 1 is equal to h(1), then h(t) is continuous at a=1.

Thus, we have successfully shown that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1.

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Answer:

The square root of 50 can be simplified to the radical form of 5*sqrt(2)

Step-by-step explanation:

To simplify the square root of 50, we factor the number 50, which is 50 = 510 = 552. The square root of any number that is a perfect square, such as 55, is equal to the number inside the square root, which is 5 in this case. The square root of any number that is not a perfect square, such as 2, remains under the radical sign.

Therefore, the simplified radical form of the square root of 50 is √50 = 5√2.

The square root of 50 in simplest radical form is 5√2.

To find the square root of 50 in simplest radical form, we need to determine if there are any perfect square factors in 50 that can be taken outside the square root symbol.

The prime factorization of 50 is 2 × 5².

We can see that 5² is a perfect square factor of 50.

Therefore, we can rewrite the square root of 50 as the square root of (2 × 5²).

Using the property of square roots, we can split the square root of a product into the product of the square roots of each factor:

√(2 × 5²) = √2 × √(5²)

The square root of 5² simplifies to 5, so we have:

√(2 × 5²) = √2 × 5

Therefore, the square root of 50 in simplest radical form is 5√2.

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The sampling technique being used in this scenario is simple random sampling.

It can be determined that simple random sampling is being used because individuals are selected at random from an alphabetical list of all registered voters. In simple random sampling, a random sample of individuals is selected from a larger population using a random procedure such as using a random number generator or drawing names out of a hat. The selection of individuals is completely random and every individual in the population has an equal chance of being selected.

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Answer:

C.

Step-by-step explanation:

The area of a rectangle is typically written as:

[tex]A = l x w[/tex]

where: l represents the length and w represents the width.

Since, in the given problem, we already know the value of the length which is 14.4 inches, and the value of width is one-third of the length. Thus, the width would be:

[tex]= (14.4)(\frac{1}{3})\\= \frac{24}{5} \\= 4.8 inches[/tex]

We will simply substitute this value to the formula to get the area.

[tex]A = lxw\\A = (14.4)(4.8)\\A = 69.12 in^{2}[/tex]

Answer:

its c i did this test

Step-by-step explanation:

If the denominator is having a poor integer, then we can multiply the numerator and denominator each through -1, to carry the minus signal at the top.

What is supposed through integer ?

The variety 0 (0), a tremendous natural variety (1, 2, three, and so on.), or a terrible integer denoted by way of a minus sign (1, 2, 3, and many others.) are all examples of integers.

The inverse components of the equal superb numbers are the bad numbers.

the lowest organization and ring of the natural numbers are fashioned by using the integers.

to distinguish them from the more common algebraic integers, the integers in algebraic quantity theory are every so often particular as rational integers.

In truth, (rational) integers are rational numbers which are also algebraic integers.

inside the beyond, the word was used to refer to a a couple of of 1 or the whole aspect of a blended quantity.

we will multiply and divide -five with the aid of (-1), to get;

(-five)*(-1) = five

as a result, five is a effective rational range.

1 can be expressed inside the form of ratio, such that,

1 = 1*1

wherein each numerator and denominator, i.e. 1 and 1 are high-quality integers.

therefore, 1 is a high quality rational wide variety.

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The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = - 3x + 2.5

The value of the equation at x = 1 will be given as,

y = - 3 × (1) + 2.5

y = - 3 + 2.5

y = - 0.5

The value of the equation at x = - 1.5 will be given as,

y = - 3 × (-1.5) + 2.5

y = 4.5 + 2.5

y = 7

The value of the equation at x = 8.5 will be given as,

y = - 3 × (8.5) + 2.5

y = - 22.5+ 2.5

y = - 20

The value of the equation at x = 1, x = -1.5, and x = 8.5 will be 0.5, 7, and -20, respectively.

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Complete question:

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Answer: Infinite Solutions

Step-by-step explanation:

When an equation is the exact same as the other, they have an infinite amount of solutions.

I hope I helped :D

Answer: This equation has infinite solutions.

Step-by-step explanation: There are all real numbers on both sides of the equation. I hope this helps!

The meaning of the rate of change in the context of this problem is 4/7.

P-8 / p(14)

8p / p(14) =4/7

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A: (a) The 98% confidence interval would be wider than the 95% interval. As the confidence level increases, the margin of error increases, thus making the interval wider.

(b) The width of the confidence interval would decrease as the sample size increases. This is because a larger sample size will result in a more accurate representation of the population, thus allowing for a narrower confidence interval.

(c) The manufacturer cannot adjust the confidence interval to take this nonresponse into account, as the nonresponse does not affect the accuracy of the sample. The confidence interval is based on the sample itself and not the population from which it was drawn.

Random sampling is a method of selecting a sample of individuals from a population such that each member of the population has an equal chance of being selected.

Random sampling is often used in research studies to ensure that the sample is representative of the population as a whole.

Random sampling is also used to minimize bias and ensure that the sample is not influenced by any particular group or individual.

Random sampling is important because it helps ensure that the results of the study are accurate and valid.

Random sampling helps to ensure that the sample is representative of the population and that the results are not influenced by any particular group or individual.

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Answer:

-4x^2 + x + 10

Step-by-step explanation:

see the image below for further details. Hopefully, it’s correct! :)

The expression can be simplified as follows:

2(x - y)/[y(x + y)]

The condition for the expression is given as follows:

x ≠ y, y ≠ 0.

The expression for this problem is defined as follows:

[(x - y)²]/(2xy + 6y) x (4x + 12)/(x² - y²)

The factors of the expression can be simplified as follows:

The terms that can be simplified are given as follows:

Hence the product is given as follows:

(x - y)/(x + y) x 2/y

2(x - y)/[y(x + y)]

As the expression is a fraction, the denominator cannot be zero, hence the conditions are given as follows:

x ≠ y, y ≠ 0.

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Zara extends the width of her garden by 11 feet. This can be calculated with the help of perimeter formula:

Equation used to solve the problem: P = 2L + 2W

2(12) + 2W = 46

24 + 2W = 46

2W = 22

W = 11

Zara extends the width of her garden by 11 feet.

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.

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A graph which shows this relationship is: B. graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0.

In order to determine the ordered pairs and linear function that could represent a linear relationship in the given table, we would have to determine the slope of based on the data points.

In Mathematics, the slope of a linear function can be calculated by using this this mathematical expression;

Slope = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (0 + 1)/(0 + 2)

Slope = 1/2

Slope = 0.5.

At data point (-2, -1), a linear function of this line can be calculated in point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y + 1 = 0.5(x + 2)

y = 0.5x + 1 - 1

y = 0.5x

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The length of the hypotenuse is 43.37 .

Now, According to the question:

Pythagorean triples are [tex]a^2+b^2 = c^2[/tex] where a, b and c are the three positive integers. These triples are represented as (a, b, c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).

Now, Solving the problem:

There are two sides :

a = 9

b = 40

and, to find the length of the hypotenuse.

According to the Pythagoras formula:

[tex]a^2+b^2 = c^2[/tex]

Plug the values in above formula:

[tex]9^2+40^2=c^2[/tex]

81 + 1600 = [tex]c^2[/tex]

[tex]c^2[/tex] = 1681

c = [tex]\sqrt{1681}[/tex]

c = 43.37

Hence, The length of the hypotenuse is 43.37 .

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Answer: Dr. Johnson is conducting an experimental study to test the effectiveness of a new therapy for individuals with arachnophobia, which is the fear of spiders. He is measuring the pulse rate of the participants before and after the therapy as an indicator of their fear response when confronted by an actual spider. The data collected will likely be used to determine if the therapy is effective in reducing the participants' fear of spiders as measured by their pulse rate.

It is important to note that while pulse rate is a good indicator of fear response, it is not the only indicator of fear and it is also not a definitive measure of the effectiveness of the therapy. Other factors such as self-reported fear, behavioral changes, and physiological changes should also be considered to get a comprehensive understanding of the therapy's effectiveness.

Step-by-step explanation:

The data does not take into account population increases over the two years. It is possible that there were more people in 2002, so the number of cases could have gone up without there being an actual increase in the rate of infection.

It could also be the case that better reporting and the more accurate diagnosis were responsible for the increase in numbers. The two-year period could also be too short to draw any meaningful conclusions. Diseases can have long-term cycles of increase and decrease, so it is possible that the increase in numbers was just part of a longer-term cycle that had already been in progress.

To accurately assess the situation, it would be necessary to look at longer-term data and take into account changes in population size.

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The coordinates of the image of the parallelogram are:

C = (-4, 8)

D = (-2, 4)

E = (6, 3)

F = (4, 7)

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

Parallelogram CDEF with vertices:

C = (-4, -4)

D = (-2, 0)

E = (6, 1)

F = (4, -3)

The parallelogram is reflected over the line y = 2.

This means,

The y-coordinates will change and the x-coordinate will remain the same.

Now,

C = (-4, -4)

There are 6 units between y = 2 and y = -4 so,

C' = (-4, 2 + 6) = (-4, 8)

D = (-2, 0)

There are 2 units between y = 2 and y = 0 so,

D' = (-2, 2 + 2) = (-2, 4)

E = (6, 1)

There are 1 units between y = 2 and y = 1 so,

E' = (6, 2 + 1) = (6, 3)

F = (4, -3)

There are 5 units between y = 2 and y = -3 so,

F' = (4, 2 + 5) = (4, 7)

Thus,

The coordinates of the image are:

C = (-4, 8)

D = (-2, 4)

E = (6, 3)

F = (4, 7)

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Answer: When a polygon is transformed so that the image of A′ is at (−2, 4) and the image of D′ is at (−1, 2), it means that the image of the polygon is congruent to the original polygon and has undergone a transformation of a horizontal reflection.

A horizontal reflection is a transformation in which the shape is reflected over the x-axis, resulting in a mirror image of the shape with the same size and orientation but reflected horizontally. In this case, the image of the polygon is congruent to the original polygon and has undergone a horizontal reflection with a horizontal translation of 3 units to the left.

The transformation can be described as a composition of the horizontal reflection over the x-axis and a translation of -3 units horizontally.

Step-by-step explanation:

By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets.Answer is x = 5/2, -4.

By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets.Finding the highest common factor between each term in the phrase is the simplest method of factorization.

In front of any brackets, indicate the highest common factor (HCF).The Grouping method, the difference in two squares, and the sum or difference in cubes are the four primary methods of factoring. The Greatest Common Factor (GCF) is another.

2x^2 + 3x - 20

Since 2 * -20 equals -40, we require two numbers whose total is +3 and whose product is -40.

We write this as + 8 and -5.

Factor by grouping: = 2x2 + 8x - 5x - 20

= 2x(x + 4) - 5(x + 4)

= (2x - 5)(x + 4)

So, the roots are x = 5/2 and -4.

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Matching the correct angle pair, we have;

i. Example of corresponding angles - Angle 1 and Angle 5

ii. Example of alternate interior angles - Angle 3 and Angle 6

iii. Example of alternate exterior angles - Angle 2 and Angles 7

iv. Example of Vertical angles - Angle 5 and Angle 8

A transversal is a straight line which intersect two parallel lines, thus forming a series of angles with some common properties. Some of the common properties are: alternate angles, vertically opposite angles, corresponding angles, etc.

Considering the given choices in the question, matching the correct angle pairs; we have;

i. Example of corresponding angles - Angle 1 and Angle 5

ii. Example of alternate interior angles - Angle 3 and Angle 6

iii. Example of alternate exterior angles - Angle 2 and Angles 7

iv. Example of Vertical angles - Angle 5 and Angle 8

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The value of the inequality -4(x - 6) < 22 will be x < 1/2.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

The process of solving an inequality using the Distributive Property is similar to solving an equation using the Distributive Property. Both involve simplifying expressions by distributing terms to isolate the variable. However, the only difference is that in an inequality, you have to be careful about the direction of the inequality symbol and make sure to reverse it if you multiply or divide both sides by a negative value.

The value of the inequality will be:

-4(x - 6) < 22

-4x + 24 < 22

Collect the like terms

-4x < 22 - 24

-4x < -2

Divide

x < -2/-4

x < 1/2

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