Identify the graph of the solution set of 13 > 5 + 4x.

Zelma is 28 years old and her son is 10 years old. We brought this conclusion with the help of algebra.

Let x = son's age now

Then, x+18 = Zelma's age now

x-1 = son's age one year ago

x+17 = Zelma's age one year ago

x+17 = 3(x-1)

x+17 = 3x-3

   2x = 20

     x = 10

Algebra is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables as if they were numbers and is therefore essential in all applications of mathematics.

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To correctly label the boxes, you need to perform two operations. In the first operation, you can choose to open any of the three boxes. Regardless of which box you open, you will be able to determine the color of one ball.

Then, you can use that information to deduce which of the other two boxes must contain two balls of the same color and which must contain one ball of each color. In the second operation, you can choose to open the box which contains two balls of the same color. The color of the ball you take out will tell you the correct label of the box. By performing these two operations, you can correctly label the boxes with only two ball selections.

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An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 19 - 6(n - 1).

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 19

Second term, a₂ = 13

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 13 - 19

Common difference, d = -6

Substituting the parameters into the mathematical expression, we have;

aₙ = 19 + (n - 1)(-6)

aₙ = 19 - 6(n - 1).

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A possible equation for F(x) is given as follows:

A. F(x) = 0.4x² + 1.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

From this graph, function f(x) is moved up one unit, hence:

F(x) = ax² + 1.

The function f(x) was also vertically compressed, meaning that a < 1, hence:

F(x) = 0.4x² + 1.

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The number of new cases of a disorder in a population that emerge in a particular time interval is called the incidence.

Incidence refers to the rate at which a new event occurs in a population. Incidence takes into account the variable time period during which a disease-free individual becomes at risk of spreading the disease.

In incident calculations, the quantifier is the number of events that have occurred in a given time. Then the quantifier of the denominator is the population that is at risk of experiencing the event during this period.

Simply put, incidence refers to new cases and is used to determine the etiology of the disease. While prevalence is more widely used to refer to health status in certain populations.

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The Equation of parabola is .y = a(x + 9)² + 7

The general equation of a parabola is: y = a(x – h)² + k where (h,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Given:

The general equation of a parabola is given by

y = a(x – h)² + k

Here (h, k) denotes the vertex.

We have 9 units to the left which is represented by '+9' and 7 units up which is represented by '+7'

So, the Equation of parabola is

y = a(x – h)²

y = a(x + 9)² + 7

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Answer:

tan(64)= x/11

Step-by-step explanation:

if we make 64 degrees are central angle then that means the side along the right angle is the adjacent and side x is the opposite

since tan∅ = opposite/adjacent

we know angle is 64 and adjacent is 11

thus,

tan 64 = x/11

Writing x^4 + 5x^2 - 8 in quadratic form will result to

Quadratic equation involves having the variables to be in exponents of 2 as the maximum. That is making the equation degree 2

The equation x^4 + 5x^2 - 8 is rewritten by say

x² = y

then we have

y² + 5y - 8

The  equation in quadratic form is  y² + 5y - 8

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Answer:

y[tex]\geq[/tex]2x-3

Step-by-step explanation:

y intersect is -3

slop is 2, which eliminates option 2 and 4

when plugging in the point 2,2 in the equation- its a true solution for option 3.

y[tex]\geq[/tex]2x-3

2[tex]\geq[/tex]4-3

2[tex]\geq[/tex]1     True.

Answer:

$24

Step-by-step explanation:

30 times .80=24

The unit of measurement for coding the length of lacerations d)centimeters.

Centimeters are the most common unit of measurement used to code the length of lacerations. This is because they are a small enough unit of measurement that they can accurately describe even the smallest of lacerations.

Centimeters are also the most commonly used metric unit of length, making them the most useful when coding lacerations for medical records. In addition, centimeters are a more precise unit of measurement than inches and are accepted internationally as a unit of measurement, making them the best choice when coding lacerations.

Finally, centimeters are consistent units of measurement, making it easy to compare laceration lengths between different patients and different medical records.

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Answer:

6.0 min

Step-by-step explanation:

20/3=6 remain 2 = 2 x 1min commercial

6 mins long

Answer:

The first one is largest volume: 27

Step-by-step explanation:

1) 3*3*3=27

2)4*4*1=16

3)2*4*2=16

4)1*6*2=12

The dependent variable is the variable that responds to or depends on the treatment and is measured by the researchers.

The dependent variable is also known as the outcome variable, response variable, or dependent measure. The dependent variable is the result that the researchers are interested in observing and understanding the relationship with the independent variable, which is the variable that the researchers manipulate or control in the study. The dependent variable is what the researchers are trying to explain or predict based on the independent variable.

In other words, the value of the dependent variable is dependent on the independent variable.

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The following is most likely a parameter as opposed to a statistic is registered voters in a county.

A parameter in statistics is any measurable number of a statistical population that summarises or describes some aspect of the population, as opposed to its typical application in mathematics, such as a mean or a standard deviation. A limited collection of factors that perfectly characterise a population and may be used to create a probability distribution for the purposes of taking samples from that population can be assessed if it exactly follows a known and defined distribution, such as the normal distribution.

The family is a parameterized family if the index is also a parameter of its members. The normal distributions, Poisson distributions, binomial distributions, and exponential family of distributions are examples of parameterized families of distributions.

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The time when the two companies would cost the same amount is after 3 hours.

Based on the information provided above, beach bikes company charges $10 bike fee and $8 per hour. Therefore, the total cost, y, can be represented by this equation:

y = 8x + 10    .......equation 1.

where:

x represents the number of hours.

For the second option, bikes unlimited charges $5 per hour and a $19 bike fee. Therefore, the total cost, y, can be represented by this equation:

y = 5x + 19    ....equation 1.

By equating equation 1 and equation 2, we have the following:

8x + 10 = 5x + 19

8x - 5x = 19 - 10

3x = 9

x = 9/3

x = 3 hours.

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Answer:

72⁰

Step-by-step explanation:

180-36= 144 (angles in a triangle=180)

144/2=72 (parallel lines are equal)

The value of x is 7.

Collinear points are the points which are formed on a straight line, whether they are close or far away.

Figure representing the question is given below.

From the figure, we have,

AB + BC = AC

(-1 + 2x) + (11) = 3x + 3

2x + 10 = 3x + 3

Like terms adding together,

2x - 3x = 3 - 10

-x = -7

x = 7

Hence the value of x is 7.

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The lengths form a right triangle are Triangle 2,3 and 4.

Side lengths a , b , c form a right triangle if, and only if, they satisfy a² + b² = c² . We say these numbers form a Pythagorean triple.

The Pythagorean theorem reads:

"In a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides."

Thus the three sides of a right triangle have an interrelated relationship.

This theorem has two mandatory properties, namely it only applies to right triangles and you must know at least two sides first to be able to determine the other side.

While the purpose of this theory is basically to determine the length of one side of a right triangle. Whereas for a right triangle it is actually very easy because one of the characteristics of a right triangle is that it has one of the 90° angles.

However, this theory can also be used to calculate the length of the diagonal of a square or beam and cube which also looks like a right triangle.

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Answer:

c = 25 * 5^t

Step-by-step explanation:

c = 25 * 5^t

This equation best suits N on the scale as it follows the pattern of the number of colonies being 5 times the previous year.

The percentage of preference of tennis or football is, 13.6%

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

Given that,

The total number of students who prefer tennis is 20.

And the total number who prefer football is 14,

so the total number who prefer either tennis or football is

⇒ 20 + 14

⇒ 34

To find the percentage of students who prefer either tennis or football, we can divide the number of students who prefer either by the total number of students and multiply by 100:

(34 / 250) x 100 = 13.6%

So, approximately 13.6% of the 8th grade class prefer either tennis or football.

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Answer: The probability of the spinner stopping at a green section and then rolling a 3 is 1/22

Step-by-step explanation: A spinner stopping at a green section

B: rolling a 3

the spinner is divided into 11 parts, 3 of them are green, then:

P(A) = 3/11

the number cube has 6 numbers, then:

P(B) = 1/6

The two events are independent, then:

P(A∩B) = P(A)*P(B) = 3/11 * 1/6 = 1/22

The perimeter of the polygon is 250m

A polygon is a closed, straight-sided two-dimensional plane shape in geometry. There are no curves on the polygon's surface. The polygon can be divided into two different types, such as regular polygons and irregular polygons, depending on its sides and angles.

The total of a polygon's sides is referred to as the polygon's perimeter. If a polygon has regular sides, its perimeter may be calculated using the formula Perimeter of Regular Polygon = (Number of Sides) x (Polygonal Side Length) units.

Given the sides of the polygon are 10 m, 55 m, 60 m, 90 m, 20 m and 15 m.

The perimeter of the polygon = sum of all sides

The perimeter of the polygon = 10m + 55m + 60m + 90m + 20m + 15 m.

The perimeter of the polygon = 250m

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The distance of Main Street is given by the equation D = 319.25 feet

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the distance of Main Street be D

Now , let the triangle be represented as ΔABC

The base of the triangle BC = 300 feet

The hypotenuse of the triangle AC = distance between First avenue and Canal street

The measure of angle ∠BAC = 70°

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

Substituting the values in the equation , we get

sin 70° = 300 / D

Multiply by D on both sides of the equation , we get

D ( sin 70° ) = 300

Divide by sin 70° on both sides , we get

D = 300 / ( sin 70° )

On further simplification , we get

D = 300 / 0.939692

D = 319.2535

D = 319.25 feet

Hence , the distance is 319.25 feet

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The upper bound is 1842 and lower bound is 1692. By using these boundaries and t-table, the sample mean is 1767 and sample standard deviation = 133.98.

Here, the two boundaries are 1692 and 1842.

Mean = (1692+1842) /2 = 1767

Here the degree of freedom, df = (n-1) = 25-1 =24

Margin of error = (1842-1692)/2 = 75

Confidence level = 99%

From the t table, value of T with confidence level 99% and df= 24 is 2.80

The equation for margin of error is M = Ts/√n

            M= 75 , T= 2.80, n =25

75 = (2.80 × s) / √25

75 = 2.80s/ 5

s = (75×5)/2.80 = 133.928 = 133.93

So the sample mean is 1767 and the standard deviation is 133.93.

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Answer:

The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side.

Step-by-step explanation:

The area of figure ABCDE is 26.5 square units.

Three angles, three sides, and three vertices make up the closed shape of a triangle. It is one of the most fundamental geometric shapes, and the symbol for it is.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape

Given:

Area of triangle ABC = 7.95 square units

Area of triangle ACD = 9.8 square units

Area of triangle AED = 8.75 square units

To calculate the area of the figure we have to add the area of the individual triangles together.

So, Area of figure ABCDE

= Area of triangle ABC + Area of triangle ACD + Area of triangle AED

= 7.95 + 9.8 + 8.75

= 26.5 square units

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Answer: (38, 25) or x = 38 and y = 25

Step-by-step explanation:

      We will use the measurement of a straight line and vertical angles to help us solve.

      First, vertical angles are congruent. We will set up an equation and use inverse operations to isolate the x variable.

  Given:

(3x - 33) = (2x + 5)

  Add 33 and subtract 2x from both sides of the equation:

x = 38

      Next, we know a straight line is equal to 180 degrees. We can substitute the value we found above for x. Then we will simplify and use inverse operations to isolate the y variable.

  Given:

(2x + 5) + (4y - 1) = 180

  Substitute for x:

(2(38) + 5) + (4y - 1) = 180

  Simplify:

81 + (4y - 1) = 180

  Subtract 80 (81 - 1) from both sides of the equation:

4y = 100

  Divide both sides of the equation by 4:

y = 25

0.3814  is the probability that a standard normal random variable .

What is the probability equation?

The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.

                      P(E) = positive outcomes/total outcomes is how it's expressed mathematically. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula. Mathematically speaking, it seems as follows: P(E) stands for positive outcomes/total outcomes.

P(0.3 < z < 3.2)

= P(z < 3.2) - P(z < 0.3)

= 0.9993 - 0.6179

 = 0.3814

Probability = 0.3814

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