Find the median of the test scores. 56, 52, 49, 52, 43, 57, 48, 52, 44, 57, 55, 45, 49, 40, 49, 53 show work

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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The equations that are true for x = -2 and x = 2 are x^2 - 4 = 0 and 2(x - 2)^2 = 0.

For x = -2, the equation x^2 - 4 = 0 becomes (-2)^2 - 4 = 0, which simplifies to 4 - 4 = 0, and therefore this equation is true when x = -2.

Similarly, for x = 2, the equation 2(x - 2)^2 = 0 becomes 2((2 - 2)^2) = 0, which simplifies to 2(0)^2 = 0, and therefore this equation is also true when x = 2.

The other equations, x^2 = -4, 3x^2 + 12 = 0, and 4x^2 = 16, are not true for x = -2 or x = 2. For example, for x = -2, the equation 3x^2 + 12 = 0 becomes 3(-2)^2 + 12 = 0, which simplifies to -24 + 12 = -12, and therefore this equation is not true when x = -2. Similarly, for x = 2, the equation 4x^2 = 16 becomes 4(2)^2 = 16, which simplifies to 16 = 16, and therefore this equation is true when x = 2. However, since the problem asks for equations that are true for both x = -2 and x = 2, the equation 4x^2 = 16 is not a correct answer because it is only true when x = 2.

Answer:

the percentage of change is 300%

Step-by-step explanation:

30 times 300% equals 90 more dollars which equals $120

The limit of the function [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)] when x tends to 1 is - 3 / 2.

In this problem we must determine the limit of a function, that is, the value to which the function goes when x tends to 1. This can be done by means of limit properties for polynomial and trigonometric limits.

First, write the limit:

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 · x] / (2 · x - 2)]

Second, use limit properties and algebra properties:

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3 + 3 - 3 · x] / (2 · x - 2)]

[tex]\lim_{x \to 1}[/tex] [[3 · cos (2 - 2x) - 3] / (2 · x - 2)] + [tex]\lim_{x \to 1}[/tex] [(3 - 3 · x) / (2 · x - 2)]

(3 / 2) · [tex]\lim_{x \to 1}[/tex] [[1 - cos (1 - x)] / (1 - x)] + (3 / 2) · [tex]\lim_{x \to 1}[/tex] [(1 - x) / (x - 1)]

Third, use polynomial and trigonometric limits:

(3 / 2) · 0 + (3 / 2) · (- 1)

Fourth, simplify the result:

- 3 / 2

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Answer:  Yes to all 3 questions

==================================================

Explanation:

VLT = vertical line test

HLT = horizontal line test

The given curve passes the VLT since it's not possible to draw a single vertical line through more than one point on the blue curve. Therefore, we have a function. Any input (x) leads to exactly one output (y).

The curve also passes the HLT through similar reasoning (use a horizontal line this time of course). This tells us the function is one-to-one. Each input leads to a unique output.

The keyword "unique" is important in the previous paragraph. It's needed to help set up the inverse. Since this curve passes the HLT, we know the inverse exists and it is a function. The inverse itself will pass the VLT.

Note: recall you reflect the given curve over the line y = x to form the inverse curve.

The true option regarding the relationship between a catalyst and a chemical reaction is D. Each reaction has its own unique catalyst.

A catalyst is a substance that accelerates the rate of a chemical reaction without affecting the end product. They only have an effect on the rate of the reaction, not the yield.

Catalysts offer an alternative reaction pathway with lower activation energy than uncatalyzed reactions. It raises the frequency of collision and, as a result of the increased collision, lowers the activation energy of the reaction.

A chemical reaction is a process that converts one or more substances, known as reactants, to one or more different substances, known as products. Chemical elements or compounds are examples of substances.

A chemical reaction rearranges the constituent atoms of the reactants to produce various products. The properties of the products differ from the properties of the reactants. It is distinct from physical changes, which include state changes such as ice melting to water and water evaporating to vapor.

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Answer: 2/ Points

Step-by-step explanation:

The points can't make up the answer to the equation, so it can't be 3!

I don't think it is the solution, because on a table points are just points of an equation!

Answer:

(x+9)(x+9)

Step-by-step explanation:

Let's factor x2+18x+81

x2+18x+81

hope this help xxx

7/15 is the probability of drawing a red bean .

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be expressed as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total beans = 7 + 2 + 6 = 15

Now out of these 15 only 7 are red.

Probability is normally written as a fraction.

                                  =      7/15

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Answer:

32 Packs

Step-by-step explanation:

Ms Hoblin will need to buy 452/14 = <<452/14=32>>32 packs of prizes.

Alternatively, you could divide 452 by 14 and then round up to the nearest whole number to determine the number of packs that she needs to buy. In this case, 452/14 = 32.64, so she would need to buy 33 packs of prizes.

After solving the equation the greatest rate is y=x. therefore, the correct option is D

What does rate in math mean?

In mathematics, the term 'rate' usually refers to a ratio or a comparison between two different values. It is defined as the amount of one quantity with respect to another, and is most commonly expressed as a fraction, with one value being the numerator and the other being the denominator. For example, "the rate of increase" is a comparison between the amount of increase in an item over time, such as the rate of inflation over a period of time. Additionally, the term 'rate' can also be used to describe a rate of change, such as the rate of growth of a population. In this case, the rate of change describes how quickly the population is changing over time.

Given that:

For rate we have to differentiate all the function first

A) y = 3/4x + 1

dy/dx = 3/4

B) y = -x

dy/dx = -1

C) y = 1/2x +2

dy/dx = 1/2

D) y = x

dy/dx = 1

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you can either graph it or solve it algebraically

move the parts of the equation to fit the sctructure of y = mx + b

2x + 4y = 20

4y = -2x + 20

divide by 4 on both sides to get 'y' by itself

y = -2/4x + 20/4

y = -1/2x + 5

this equation tells you the 'y intercept' and the slope

slope; -1/2

y intercept; 5

Answer:

2x+y=-4

Step-by-step explanation:

y-2=-2(x+3) is in point-slope form.

Ax+By=C is standard form.

We have to bring x and y to the same side of the equation.

First, let's distribute.

y-2=-2(x)-2(3)

y-2=-2x-6

Next, we will add 2 to both sides to get rid of the -2 on the left side of the equation.

y=-2x-6+2

Then, we will add 2x to both sides to get rid of the -2x on the right side of the equation.

2x+y=-6+2

Now x and y are on the same side of the equation. We just need to simplify the right side.

2x+y=-4

This is the answer in standard form.

Answer:

2x + y = -4

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Given equation:

[tex]y-2=-2(x+3)[/tex]

To write the given equation in standard form, collect the terms with variables on the one side of the equation (ensuring the term in x is positive), and collect the constants on the other side of the equation.

Distribute the right side of the equation:

[tex]\implies y-2=-2 \cdot x+(-2) \cdot 3[/tex]

[tex]\implies y-2=-2x-6[/tex]

Add 2x to both sides of the equation:

[tex]\implies y-2+2x=-2x-6+2x[/tex]

[tex]\implies y-2+2x=-6[/tex]

Add 2 to both sides of the equation:

[tex]\implies y-2+2x+2=-6+2[/tex]

[tex]\implies y+2x=-4[/tex]

Rearrange the left side to standard form:

[tex]\implies 2x+y=-4[/tex]

The values of x and y after solving the equations by using elimination method are :- 3 and 1

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

There are three ways to solve systems of linear equations in two variables: graphing. substitution method. elimination method

In the above equations

Multiplying equation 1 with 2 and adding it to equation 2 we get

X= 3

Y=1

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The probability of at most one team making a Type II error is 0.3651.

1. The probability of a Type II error for a single team is 0.2 (since the power of the test is 0.8).

2. The probability of all 10 teams making a Type II error is 0.2^10. This is because the probability of each individual team making a Type II error is 0.2 and the probability of all 10 teams making a Type II error is the product of the individual probabilities (0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 * 0.2 = 0.2^10).

3. The probability of at least one team making a Type II error is 1 - 0.2^10. This is because the probability of at least one team making a Type II error is the complement of the probability of all 10 teams making a Type II error (1 - 0.2^10).

4. The probability of at most one team making a Type II error is 1 - (1 - 0.2^10). This is because the probability of at most one team making a Type II error is the complement of the probability of at least one team making a Type II error (1 - (1 - 0.2^10)).

5. The probability of at most one team making a Type II error is 0.3651.

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Answer:

y ≥ 2x + 4

hope this may help!

Answer:

C) 21

Explanation:

The middle column represents the tens place, while the column on the left is the ones place. Range is the difference between the highest number and the lowest number.

The lowest number for road A is 29, the 2 from the middle column and 9 from the left. The largest number is 50, the 5 from the middle column and 0 from the left column.

50 - 29 = 21

Answer:

the answer is d

Step-by-step explanation:

x is -2 and y is

Answer:

Step-by-step explanation:

The standard form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept.  Let's rewirite the given equation to match this format:

 y = 6 - 6x

 y = -6x + 6

The slope is -6 and the y-intercept is 6.  The slope tells us the angle the line is taking.  A negative slope such as this means that the line is angled down as it goes from left to right.  The size of the number tells us just how steep the line is.  

All parallel lines have the same slope.  Any line with the format of y = -6 + b will be parallel.  See the attached graph for proof.  The graph shows several parallel lines to y=-6+b, including the three top lines, all with the same slope, but with three different values for b:  +6, 0, and +10.

Perpendicular lines have a slope that is the negative inverse  of the reference line, in this case y = -6x + 6.  A perpendicular line will have a slope of -(1/-6) or 1/6 [the negative inverse of -6].  Perpendicular lines will have the form y = (1/6)x + b.  See the attached graph.  The three bottom equations are all perpendicular to y=-6x+6.  All have the same slope (1/6), but differnt y-intercepts (b = 0, 6, and 10).  The y-intercept numbers for both the parallel and perpendicular lines were randomly chosen, simply to illustrate the possibilities.

In summary,

"Slope of a parallel line" is -6, and

"Slope of  perpendicular line" is (1/6)

Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.

What is Null hypothesis?

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.

from given outpout

Null hypothesis

H0:u1=u2=u3=u4

Alternative Hypothesis

H1: not all means are equal

Test statistic =F=0.49

P value=0.691

Pvalue>0.05 alpha level of significance

We fail to reject null hypothesis

Conclusion =

Do not reject H0 there is not sufficient evidence at a 0.05 significance level to warrant rejection of the claim that the four vehicle size categories have the same mean force on the left femur in crash tests.

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A 31.2 foot ladder is required to access an electrical box that is 28 feet up.

Which ratios in trigonometry are there?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle.

A right-angled triangle is formed by the ladder, the distance from the wall to the ladder's base, and the distance from the ground to the electrical box.

The link between the sides and angles of a right-angled triangle is demonstrated through trigonometric ratios.

If x stands for the ladder's length, then:

28 feet/x for sin(64).

28 feet/sin x = (64)

x = 31.2 ft

Therefore, a 31.2-foot ladder is required to reach an electrical box that is 28 feet up.

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Answer:

0

Step-by-step explanation:

4(8x–1) = 2(2x–2)

32x–4 = 4x–4

32x–4x = –4+4

28x = 0

x=0/28

x= 0

Answer:

x=0

Step-by-step explanation:

4(8x-1)=2(2x-2)

Step 1)  32x-4=4x-4

Step 2) 28x=0

Step 3) x=[tex]\frac{0}{28\\}[/tex]

Step 4) x=0

Answer:

Step-by-step explanation:

the adjacent angles are congruent

angle 1 = 51°

the sum of the angles is 360°

51 · 2 + 2 · angle (2) = 360

102 + 2angle(2) = 360

2angle (2) = 360 - 102

2 angle (2) = 258

angle (2) = 258/2

angle (2) = 129°

angle (3) = 129°

Answer: the first one

Step-by-step explanation:

...

According to the given statement 16% is the probability that the person is age 48 or older.

A metric of a data set's deviation from the mean is referred to as "standard deviation" (or ""). While a high standard deviation indicates that the numbers are more spread, a smaller standard deviation suggests that the data are clustered around the mean.

After calculating the z-score, we will look up the value in the table on page (718–719).

We will employ the equation, to determine the z-score.

z= x−μ / σ

How is x=48

μ=41

σ=7 the z-score is,

z = 48 - 47 /7

z = 7 / 7

z = 1

The value for z=1 in the table is 0.84130, meaning that the region below the curve represents people who are 48 years of age and older. However, we are looking at the area that represents people who are 48 years of age and older, hence,

1−0.8413

=0.1587≈0.16

=16%

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The complete question is-

The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?

Answer:

11.8 m

Step-by-step explanation:

this makes up a right triangle so we can use the Pythagorean theorem

a^2+b^2=c^2

a- height/leg a

b- length/ leg b

c- hypotheneus

since we are tying to find b we can isolate b^2 on one side of the equation

a^2+b^2=c^2

-a^2.       -a^2

b^2=c^2-a^2

And now we can plug in values

b^2=36^2-34^2

b^2=1296-1156

b^2=140

Square root both sides

b=11.8

Hopes this helps please mark brainliest

When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.

One can calculate the percentage by dividing the value by the total value and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.

To convert a decimal number, such as 0.57, to a percentage, just multiply it by 100. Therefore, 0.57 times 100 equals 57. Therefore, 0.57 is a percentage that equals 57%. Another example is 0.03 x 100 = 3%. Percentages are just fractions with a denominator of 100. To show that a number is a percentage, we place the percent sign (%) next to it.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

Here,

Item cost is $18.

Price to Sell = 18 + 11% ×18

= $19.98

= $20

The store manager is displaying an item that cost $18 for a selling price of $2 when the true selling price is $20.

So,

When the actual selling price is $20, the store manager is showing a $18 item with a $2 price tag.

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The domain and range of the equations for the three cars using the hypothetical condition that x represents additional gas added to the tank are;

Car #1

Domain; 0 ≤ x < ∞

Range; 607.8 ≤ y < ∞

Car #2

Domain; 0 ≤ x < ∞

Range; 568 ≤ y < 0

Car #3

Domain; 0 ≤ x < x

Range; 528.4 ≤ y < ∞

An equation is a statement that indicates that two expressions be equivalent by joining them with an equals sign.

The specified equations for three cars are;

Car #1: y = 28·x + 607.6

Car #2: y = 80·x + 568

Car #3: y = 20·x + 528.4

The domain of a function is the set of possible input values (x-values) of the function

The range is the set of possible output values (y-values) of the function

Let y represent the number of miles driven and let x represent the additional gas added to the car, we get;

The domain of car #1

The additional number of gallons of gas car #1 can drive receive has a domain of 0 ≤ x < ∞

The range for car #1

The total number of miles car #1 can drive = 607.6 ≤ y < ∞

The domain for car #2

The additional amount of gas car #2 receives is; 0 ≤ x < ∞

The range for car #2

The distance car #2 can drive is; 568 ≤ y < ∞

The domain for car #3

The additional volume of gas car #3 receives is; 0 ≤ x < ∞

The range of the function for car #3

The number of miles car #3 can drive is; 528.4 ≤ y < ∞

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Answer:

smallest angle = 35

Step-by-step explanation:

the 3 angles lying on the straight line AOB sum to 180° , then

3a + 8 + 60 - a + 4a - 38 = 180 , that is

6a + 30 = 180 ( subtract 30 from both sides )

6a = 150 ( divide both sides by 6 )

a = 25

Then

3a + 8 = 3(25) + 8 = 75 + 8 = 83°

60 - a = 60 - 25 = 35°

4a - 38 = 4(25) - 38 = 100 - 38 = 62°

the smallest angle is 35°

Answer:

Step-by-step explanation:

Given a set of parallel lines with a transversal and angles marked, you want to find the values for x and y consistent with the markings.

Alternate interior angles are congruent, so the marked acute angles have the same measure:

  3x +2y = 52

Corresponding angles are congruent, so the marked obtuse angles have the same measure:

  18x +2y = 142

Subtracting the first equation from the second gives ...

  (18x +2y) -(3x +2y) = (142) -(52)

  15x = 90

  x = 6

The value of y can be found from either equation. We choose to use the first:

  3(6) +2y = 52

  9 +y = 26 . . . . . . . . divide by 2

  y = 17 . . . . . . . . . subtract 9