complete the description of the piecewise function graphed below

After simplification, the value of x is 6.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 3x + 30 + x = 10 + 2x + 5x + 2

Now, We can solve as;

⇒ 3x + 30 + x = 10 + 2x + 5x + 2

Combine like terms;

⇒ 4x + 30 = 12 + 7x

Subtract 4x both side,

⇒ 4x + 30 - 4x = 12 + 7x - 4x

⇒ 30 = 12 + 3x

Subtract 12 both side,

⇒ 30 - 12 = 3x

⇒ 18 = 3x

⇒ 3x = 18

Divide by 3;

⇒ x = 6

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The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

AB = 6

BC = 6

CG = 6

Then the length of diagonal AC is given as,

AC² = AB² + BC²

AC² = 6² + 6²

AC = 6√2

Then the length of diagonal AG is given as,

AG² = AC² + CG²

AG² = (6√2)² + 6²

AG = 6√3

The length of the line segment AC and AG will be 6√2 units and 6√3 units, respectively.

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The median of a sample will always equal the 50th percentile.

The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. The statistical median is the number in the middle of a series of numbers. To find the median, sort each number by size; the number in the middle is the median. The median is the value in the middle of a set of data. First, organize and sort the data in ascending order from smallest to largest. Divide the number of observations by two to find the midpoint value. If there are an odd number of observations, round that number up to the nearest whole number, and the value in that position is the median.

Here,

A sample's median will always equal the 50th percentile.

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The next time that they have an appointment start at the same time is at  10:50 a.m.

Now, According to the question:

Ist Step

For the same time, take LCM of 20 and 35.

20 = 2 × 2 × 5

35 = 5 × 7

IInd Step

HCF (20, 35) = 2 × 2 × 5 × 7

HCF (20, 35) = 140

Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.

Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m. which is the next time that they have an appointment start at the same time.

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Click It or Ticket is a nationwide campaign to enforce seat belt laws and increase seat belt use, supported by major organizations.

Click It or Ticket is a nationwide mobilization campaign to enforce seat belt laws and increase seat belt use. It is a joint effort of state and local law enforcement, highway safety offices, and the National Highway Traffic Safety Administration and is supported by national and state-level organizations, including:

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a) The binomial expansion of (1+12x)^1/2 is given by:

(1+12x)^1/2 = 1^1/2 + (1/2)(1^-1/2)(12x) + (1/2)(1^-1/2)(-1/2)*(12x)^2 + ...

Binomial expression: what is it?

A polynomial with only terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct terms. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic expression that contains a constant, exponents, a variable, and a coefficient.

The first four terms, in ascending powers of x, are:

1, (1/2)(12x), (1/8)(12x)^2, (1/16)*(12x)^3

b) To use x=1/36 in the expansion, you would substitute x=1/36 into the expansion, and keep only the terms up to x^3 (the fourth term in the expansion). This will give an approximation of the value of (1+12x)^1/2 when x=1/36.

This will be an approximation of √12 because x=1/36 corresponds to 12x = 1 and the initial value of the expansion is 1 + 12x .

We can use this approximation to approximate square root of 12 and also for other square roots by using appropriate x values.

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The frequency Asked in the problem are listed below in order:

To make the information easier to understand, frequency distributions are visual displays that organise and present frequency counts. Absolute frequencies as well as relative frequencies, such as percentages or ratios, can be displayed in frequency distributions.

Given, a partial relative frequency distribution is given. class relative frequency a 0.22 b 0.18 c 0.40 d

Since all relative frequencies add up to be 1.

So,

0.22 + 0.18 + 0.40 + x = 1

x = 0.20

For b)

total sample size * relative frequency = frequency of a class

200*0.2 = 40

For c)

Frequency distribution is calculated as the frequency of a class = total sample size * relative freq.

A = 44

B = 36

C = 80

D = 40

TOTAL = 200

For d)

Percent frequency is calculated as Percent frequency of a class = 100 * relative freq.

A = 22

B = 18

C = 40

D = 20

TOTAL = 100

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Complete question:

The length of PQ in terms of MO if ∠POQ = 120° is PQ = -x * √3/3.

Let MO = x.

Since MO is perpendicular to plane α, MP and MQ form right angles with MO.

Using the Pythagorean Theorem, we have:

MP = x * tan(30°) = x * √3/3

MQ = x * tan(60°) = x * √3

Since ∠POQ = 120°, we have:

PQ = MP * 2 * cos(120°)

= 2 * x * √3/3 * -1/2

= -x * √3/3

Therefore, the length of PQ in terms of MO is PQ = -x * √3/3.

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Answer:

8 square units

Step-by-step explanation:

For a triangle,

area = base × height / 2

We need to identify a base and a height for this triangle, and then use them in the area formula above.

Use BC as the base.

A height of a triangle is usually inside the triangle, but not always.

The height of a triangle is a segment that is perpendicular to the a side, or the line containing a side, and intersects the opposite vertex.

In this case, for base BC, the height is a segment from point (-2, 2) to point A.  The length of the height is 4.

area = 4 × 4 / 2

area = 8 square units

Here we would like to find out the value of given trigonometric ratio . A right angled triangle is given to us with perpendicular= 8 and hypotenuse= 11 . Firstly let's calculate the base using Pythagoras theorem as ,

[tex]\longrightarrow h^2=p^2+b^2\\[/tex]

[tex]\longrightarrow 11^2 = 8^2+b^2\\ [/tex]

[tex]\longrightarrow 121 = 64 + b^2\\ [/tex]

[tex]\longrightarrow b^2=121-64=57\\ [/tex]

[tex]\longrightarrow b =\sqrt{57}=7.54 \\ [/tex]

Now we know that,

[tex]\longrightarrow \tan\theta =\dfrac{p}{b}\\ [/tex]

so substitute the respective values,

[tex]\longrightarrow \tan\theta =\dfrac{8}{7.54}\\ [/tex]

[tex]\longrightarrow\underline{\underline{ \tan\theta = 1.06 \approx \boxed{1}}} [/tex]

and we are done!

Answer: About 31%

Step-by-step explanation:

1. Divide 114 to 361

Answer: To find r'(1), we need to use the chain rule of differentiation, which states that:

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

In this case, we know that:

h(1) = 2, g(2) = 4, h'(1) = 4, g'(2) = 4, and f '(4) = 7

Therefore:

r'(1) = f'(g(h(1))) * g'(h(1)) * h'(1) = f'(g(2)) * g'(2) * h'(1) = 7 * 4 * 4 = 112

So, the derivative of r(x) with respect to x at x = 1 is 112

Step-by-step explanation:

Answer: the second, third and fifth options.

Step-by-step explanation:

When an equation is set up in a y=mx+b format, the slope is always equal to the value m.

The area of the trapezoid is 42.5 m².

A trapezium is a quadrilateral with four sides where two sides are parallel to each other.

We have,

Trapezoid:

Short base = 3 m

Height = 5 m

Large base.

= 4 + 3 + 7

= 14 m

Now,

Area of a trapezoid.

= 1/2 x (Short base + Large base) x h

= 1/2 x (3 + 14) x 5

= 1/2 x 17 x 5

= 42.5 m²

Thus,

Trapezoid area is 42.5 m².

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The inflation rate is 16.71 %

As we know the inflation rate is given by the percentage error.

We know that the formula for the percentage error:

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100

Let us assume that A represents the inflation rate of percentage error.

Here, the cost of the Jolly Peanut butter is = $ 3.59

So , the original cost = $ 3.59

The increased cost of Jolly Peanut butter is = $ 4.19

So , the new rate = $ 4.19

Now , the inflation rate is given by the formula of percentage error,

Percentage Error = [ ( | Measured Value - True Value | ) / True Value ] x 100

A = [ ( 4.19 - 3.59 ) / 3.59 ] x 100

A =  ( 0.6 / 3.59 ) x 100

A = 0.16713 x 100

A = 16.71 %

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Answer:

Slope:3/4

y-int: (0,5)

Step-by-step explanation:

Slope:

3x-4y=20

-3x        -3x

-4y=-3x+20

/-4     /-4

y=3/4x+5

So 5 would be y-int

A plausible lurking variable that could explain the cause and effect in the headline "Is Gluten the Culprit in Our Fight Against Obesity?" is overall diet.

It's possible that individuals who consume a diet high in gluten also consume a diet high in overall calories and processed foods, leading to weight gain and obesity. This would mean that it is not specifically gluten causing the obesity, but rather a combination of factors in the individual's diet.

A lurking variable is a variable that has a connection (e.g., may be correlated) with the response and the explanatory variable but is neither the explanatory variable nor the response variable.

Although it is not taken into account in the study, it might affect how the variables are related.

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Answer: The distance between the points (-4,7) and (-4,-5) is 12.

Step-by-step explanation:

To calculate the distance between two points, we apply the following formula:

[tex]\huge \boxed{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }}[/tex]

The points are:

To solve the process is:

We substitute the points in the previous formula given, then

[tex]\huge \boxed{\sf{d=\sqrt{(-4-(-4))^2+(-5-7)^2 } }}[/tex]

[tex]\huge \boxed{\sf{d=\sqrt{0^2+(-12)^2 }=\sqrt{0+144} }}[/tex]

[tex]\huge \boxed{\sf{d=\sqrt{144}=12 }}[/tex]

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The expression using brackets is (3x)(x⁴) + (2)(2) = 26

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

7x5-4x5+16÷4=26

Express the superscripts in the expression properly

So, we have the following representation

7x⁵ - 4x⁵ + 16 ÷ 4 = 26

Evaluate the like terms

3x⁵ + 16 ÷ 4 = 26

Divide 16 by 4

3x⁵ + 4 = 26

Factorize and use brackets

(3x)(x⁴) + (2)(2) = 26

Hence, the expression is (3x)(x⁴) + (2)(2) = 26

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[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100000\\ r=rate\to 4.2\%\to \frac{4.2}{100}\dotfill &0.042\\ t=years\dotfill &6 \end{cases} \\\\\\ A = 100000e^{0.042\cdot 6} \implies A = 100000e^{0.252}\implies A \approx 128659.60[/tex]

a. The party that won the highest percentage of votes and seats in 1982 is democrat.

b. A change between the percentage of seats won by republicans in 1982 and 2012 is 4%

c. The difference between votes percentage and seats percentage for democrat is 4% and 26% respectively. The difference between votes percentage and seats percentage for republican is 3% and 26% respectively.

The pie chart is given below:

a. We have to identify the party that won the highest percentage of votes and seats in 1982.

We can see that in diagram that gray part of circle shows the vote percentage of democrat and white part of circle shows the vote percentage of republican.

Republican gain votes in 1982 = 52%

Democrat gain votes in 1982 = 49%

So the democrats get the maximum votes in 1982.

b. We have to describe a change between the percentage of seats won by republicans in 1982 and 2012.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So the change between 1982 and 2012 = (52 - 48)% = 4%

c. We have to draw a conclusion about the difference in percentage of votes won and seats.

In 2012 republican get votes percentage = 48%

In 1982 republican get votes percentage = 52%

So, the difference between vote percentage is 4%.

In 2012 republican get seats percentage = 25%

In 1982 republican get seats percentage = 51%

So, the difference between seats percentage is 26%.

In 1982 democrat get votes percentage = 49%

In 2012 democrat get votes percentage = 52%

So, the difference between vote percentage is 3%.

In 2012 democrat get seats percentage = 75%

In 1982 democrat get seats percentage = 49%

So, the difference between seats percentage is 26%.

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If the image of point (x,5) is (-6, y) when it is translated by the vector t(6 -2), then the values of x = -12 and y = 3.

Vector translation is a mathematical concept that describes how an object is moved in space. It involves the use of a vector, which is a quantity that has both magnitude and direction. A vector can represent a displacement, a velocity, an acceleration, or any other physical quantity that has both magnitude and direction.

When an object is translated by a vector, it moves a certain distance in a specific direction. This is usually done by adding the vector to the current position of the object. The magnitude of the vector determines the distance of the translation, while the direction of the vector determines the direction of the translation.

Additionally, the vector can be used to rotate the object. This is done by multiplying the vector by the object’s rotation matrix. The result is the object's new orientation in space, which can be used to orient the object in a different direction.

Vector translation is used in a variety of applications, including computer graphics, robotics, and navigation systems. It i also used in mathematics and physics to represent physical phenomena, such as forces, velocities, or accelerations.

Let the point P(x,5) be translated by the vector t(6,-2).

The image of point P is (x',y') = (x+6,5-2) = (-6,y)

Therefore, x+6 = -6

=> x = -6-6 = -12

Similarly, 5-2 = y

=> y = 5-2 = 3

So the value of x is -12 and y is 3.

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Answer:

7/18.

Step-by-step explanation:

We know that the result is the same because multiplication is Commutative.

The order of the operation does not matter.

The two mathematical expressions can be written as:-

2) . [ 23 + ( 14 ÷ 2 ) - 20 ] = 5

3) . [ 9² - ( 8 x 4 ) + 26 ] = 75

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The two expressions will be solved as:-

For the first problem, the numbers are 23,2,14, and 20. The expression will be written as:-

[ 23 + ( 14 ÷ 2 ) - 20 ] = 5

[ 23 + 2- 20 ] = 5

[ 25 - 20 ] = 5

5 = 5

The numbers for the second expression are 8,26,9 and 4. The expression can be written as:-

[ 9² - ( 8 x 4 ) + 26 ] = 75

[ 81 - 32 + 26 ] = 75

[ 49 + 26 ] = 75

75 = 75

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As per the unitary method, Gordon is correct because the Gordon would charge more than Ironing Palace

In math the term unitary method is defined as the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

Here we have given that the total weight of these shirts is 9. 5 kg.

And here we have also given that each shirt weighs 190 g.

And Gordon charges £38 to iron these shirts.

And the charges in the Ironing Palace is 90p for each.

Here we have to use the unitary method to calculate the values for each of them,

The Total cost for Gordon is calculated as,

=> 38 x (9.5 / 0.19)

=> 1900

And the total cost for Ironing Palace is calculated as,

=> 90 x 9.5

=> 855

Therefore, while we looking into the values we have identified that Gordon is correct.

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The probability that exactly 14 adults have been vaccinated 0.49

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event

the national center for health statistics (nchs) reports that 70% of us adults aged 65 and over have ever  vaccination

the pneumococcal vaccination rate applies to an independent random sample of 20 us adults aged 65

the probability that exactly 14 adults have been vaccinated

(14/20)*(70/100)

0.49

The probability that exactly 14 adults have been vaccinated 0.49

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288 m³ is The Volume Of The Pyramid.

The space occupied inside an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Given, The base of the pyramid shown has a length of 9m and a width of 8m. The height of the pyramid is 12m.

Since, The Formula for the volume, V , of a pyramid is V = 1/3Bh ,

where B is the area of the base of the pyramid and h is the pyramid's height.

Since, Area of rectangle = Width *height

Thus, Area of the base = 9 * 8

Area of the base = 72 m²

So, the volume of pyramid (V) =  1/3Bh

the volume of pyramid (V) = 1/3 * 72 * 12

the volume of pyramid (V) =  288 m³

therefore, The Volume Of The Pyramid is 288 m³.

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According to Bernoulli's theorem, the success rate for the situation is 0.7173.

In math Bernoulli's theorem is states that that random experiment with exactly two possible outcomes, "success" and "failure" in which the probability of success is the same every time the experiment is conducted.

In order to calculate p we must sum the possible permutations of getting 0 success of 10 trials, 1 success of 10 trials, and 2 successes of 10 trials, and divide this sum by the total possible subsets from 10 elements, then it can be written as,

=> P = (10 1) (10 2) (10 1) / 2¹⁰

When we simplify this one, then we get,

=> P = 56/1024

=> P = 0.0547

When we apply the value on Bernoulli's theorem, then we get,

=> B(340, 0.0547, 0) = ( 340 0 ) x (1/1024) x (1023/1024)³⁴⁰

When we simplify this one then we get,

=> B = 0.7173

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The percent discount is 18%.

Now, According to the question:

Based on the given condition:

Formulate:

(34 - 27.88) ÷ 34

Calculate the sum or difference:

= 6.12/34

Convert decimal into fraction:

[tex]=\frac{612}{\frac{100}{34} }[/tex]

Divide a fraction by multiplying its reciprocal:

[tex]\frac{612}{100}[/tex] × [tex]\frac{1}{34}[/tex]

Write as a single fraction:

= 612/ (100 × 34)

Cross out the common factor:

= 18/100

= 9/50

Multiply a number to both numerator and denominator:

[tex]\frac{9}{50}[/tex] × [tex]\frac{2}{2}[/tex]

= 18/100

Rewrite a fraction with denominator equals 100 to a percentage: 18%

Hence,  the percent discount is 18%.

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