Which graph represents the function f(x) = |x + 31?
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a. The probability that all the marbles are red is calculated as follows:

(7 choose 3) / (18 choose 3) = (35 / (816)) = 0.0429

So, the probability that all the marbles are red is 0.0429, rounded to 4 decimal places.

b. The probability that none of the marbles are red is calculated as follows:

(12 choose 3) / (18 choose 3) = (220 / 816) = 0.2696

So, the probability that none of the marbles are red is 0.2696, rounded to 4 decimal places.

Answer:

do it yourself

Step-by-step explanation:

Answer:

A. The transformation preserves distances and angles between points.

B. The transformation preserves the orientation of the figure.

C. The transformation involves a sliding of the figure in a fixed direction.

D. The transformation results in a change of size or shape of the figure.

E. The transformation results in a reflection of the figure.

For the transformation to be a translation, statements A, B, C and E are not true, while statement D is true.

Step-by-step explanation:

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

g(x) = 4ˣ

The function is shifting up 2 and shifting right 5. Then the function is given as,

g(x) = 4⁽ˣ⁺⁵⁾ + 2

The function after reflecting over the x-axis is given as,

- g(x) = 4⁽ˣ⁺⁵⁾ + 2

g(x) = - 4⁽ˣ⁺⁵⁾ - 2

And then horizontally compressing by a factor of 5. Then the function is given as,

f(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2

The equation of the transformation of the function g(x) will be g(x) = - 5 · 4⁽ˣ⁺⁵⁾ - 2.

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The inverse of the given function is f(x) = 2x/(1 - x)

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is

f(x) = x/(2+x)

Assume that y = f(x) = x/(2+x)

Solve y = x/(2+x) for x:

y = x/(2+x)

Multiply (2+x) on both sides:

y(2+x) = x

2y + xy = x

Subtract xy from both sides:

2y = x - xy

2y = x(1 - y)

x = 2y/ (1 - y)

Now replace x with y and y with x:

y = 2x/(1 - x)

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Answer:

11 bat and 8 helmets.

Step-by-step explanation:

Let x = the number of bats

Let y = the number of batting helmets

x + y = 19  Rewrite as y = 19 - x

18.25x + 24.50y = 369.75  Multiply by 100

1825x + 2450y = 36975  Substitute 19 - x for y

1825x + 2450(19 -x) = 39675   Distribute the 2450

1825x + 46550 - 2450x = 39675  combine like terms

-625x + 46550 = 39675  subtract 46550 from both sides

-625x = -6875  Divide both sides by -625

x = 11

He bought 11 bats

x + y = 19  Substitute 11 for x to solve for y

11 + y = 19  Subtract 11 from both sides

y = 8

He bought 8 helmets.

Faith earned £96 in interest at the end of the 3 years.

Using the  simple interest formula:

I = P x r x t

where

I is the interest earned,

P is the principal or initial amount invested,

r is the interest rate as a decimal, and t is the time period in years.

In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:

I = £800 x 0.04 x 3

= £96

Therefore, Faith earned £96 in interest at the end of the 3 years.

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The area of the kite is 0.08 metres squared.

A kite is a quadrilateral. Therefore, the window has the shape of a kite. The square metres of glass that will be used to construct the kite can be calculated as follows:

The area of a kite is half the products of the diagonals of the kite.

Therefore,

area of the kite = 1 / 2 pq

where

Therefore,

p = 20 + 20 = 40 cm

q = 25 + 15 = 40 cm

Hence,

area of the kite = 1 / 2 × 40 × 40

area of the kite = 1600  /2

area of the kite = 800 cm²

area of the kite = 0.08 m²

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The transformation used are:

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

The graph from y = h(x) to y = h(-x)  + 1.

This is a translation of one unit to the left and one unit up.

The graph from y = g(x) to y = 2g(x)  - 4.

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

Now,

The graph of y = h(-x)  + 1 is given below.

The graph of y = 2g(x)  - 4 is given below.

Thus,

(a)

This is a translation of one unit to the left and one unit up.

(b)

- There is a vertical stretch of 2 units.

- This is a translation of four units down.

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The number of adults and children in the group were 64 and 36 respectively by using an algebraic equation.

It is given that the entry ticket to a local museum costs $12 for an adult and $8 for a child. A group of 100 people paid an entry fee of $1,056.

Let the number of adults in the group = x

number of adults in the group = y

Total number of  people paid an entry fee = 100

So the equation becomes : x + y = 100

 or x = 100 - y

Cost for adult ticket = $12

Cost for child ticket = $8

Total entry fee paid = $1,056

Second equation = 12x + 8y = 1056

putting value of x from equation 1

12(100 - y) + 8y = 1056

1200 - 12y + 8y = 1056

4y = 144

y = 36

x = 100 - 36 = 64

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The estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.

We are given that for the period 2009-2013, 7/10.3 is approximately the number of Time Warner Cable video subscribers for every Comcast video subscriber. We are also given that there were 21.7 million Comcast video subscribers in 2013.

To estimate the number of Time Warner Cable video subscribers in 2013, we can use the following proportion:

7/10.3 = x/21.7

where x is the number of Time Warner Cable video subscribers in 2013.

Solving for x, we get:

x = (7/10.3) x  21.7

x ≈ 14.8 million

Therefore, the estimated number of Time Warner Cable video subscribers in 2013 is approximately 14.8 million.

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Answer:

18x+9

Step-by-step explanation:

Answer: 18x + 9

Step-by-step explanation:

1) Combine like terms 23x -5x to get a new equation of 18x + 9.

Answer:

a.  2p + 2d + 1c + 1p + 1c + 2p + 1d

b. 5p + 3d + 2c

c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

Step-by-step explanation:

a.
From the cute diagram we see that the family bought

2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink

Using the variables provided, this becomes

2p + 2d + 1c + 1p + 1c + 2p + 1d

b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)

Adding the coefficients of each grouped term we get

(5p) + (3d) + (2c)

Opening the brackets, this becomes
5p + 3d + 2c

c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

On solving the provided question we can say that 2 decimal places =29.92 miles per hour

Integer and non-integer numbers are often expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the name for the method used to represent numbers in the decimal system. A decimal is a number with a whole and a fractional component. Decimal numbers, which are in between integers, are used to express the numerical value of full and partially whole amounts. A decimal point separates the complete number and the fractional portion of a decimal number. The dot between the whole number and the fractions is known as the decimal point. A decimal number is, for instance, 25.5. In this instance, 25 is the entire number, while 5 is the

top speed is 26 knots,

1 knot = 1.15078 miles per hour

26 knots = 26 * 1.15078

= 29.92028 miles per hour

2 decimal places

=29.92 miles per hour

boat has a  displacement of 96000 tons

1 ton = 0.907185 metric tonnes

96000 tons = 0.907185 * 96000

= 87,089.76 metric tonnes

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The ratio that is equivalent to the greatest fraction is B. 8:4.

A ratio is a relative size or value contained in another quantity.  It is computed as the quotient of the smaller and larger values.

Ratios are fractional values, which we can depict as fractions, decimals, or percentages.

Ratios are also depicted using the ratio symbol (:), describing the numerical relationship between two or more values or variables.

The sum of ratios = 8

5/8 = 0.625

The sum of ratios = 12

8/12 = 0.67

The sum of ratios = 9

2/9 = 0.22

The sum of ratios = 14

9/14 = 0.64

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Answer:B

Step-by-step explanation:

Answer:

Angle P= Angle W=2(2x-6)

=4x-12

To find the weight of 4.3 cubic feet of water, we need to first find the number of gallons of water that 4.3 cubic feet holds and then multiply that by the weight of 1 gallon of water.

1 cubic foot holds 7.48 gallons of water, so 4.3 cubic feet holds 4.3 x 7.48 = 31.964 gallons.

1 gallon of water weighs 8.33 pounds, so 31.964 gallons of water weigh 31.964 x 8.33 = 265.9012 pounds.

Therefore, 4.3 cubic feet of water weigh 265.9012 pounds.

To find the weight in tons, we need to divide the weight in pounds by 2000:

265.9012 pounds ÷ 2000 = 0.13295 tons

So 4.3 cubic feet of water weigh 0.13295 tons.

Answer:

0.13314 tons.

Step-by-step explanation:

We can start the calculation by first converting the cubic feet of water to gallons and then converting the gallons to pounds.

Conversion from cubic feet to gallons:

4.3 cubic feet = 4.3 cubic feet * 7.48 gallons/cubic foot = 32.084 gallons

Conversion from gallons to pounds:

32.084 gallons = 32.084 gallons * 8.33 pounds/gallon = 266.279 pounds

Conversion from pounds to tons:

266.279 pounds = 266.279 pounds / 2000 pounds/ton = 0.13314 tons

So, 4.3 cubic feet of water weigh 266.279 pounds or 0.13314 tons.

Answer:

0.89

Step-by-step explanation:

As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89

Answer:0.89

Step-by-step explanation:

The mean of the frequency distribution is 52 degrees. and option A is carrect  . A) The computed mean is close to the actual mean because the difference between the means is less than​ 5%

First, we calculate the class mid-points (x); This is the mean of the class intervals.

For 40 - 44, x = (40 + 44)/2 = 42. This is applied to all other classes.

40 −44 = 42

45 −49 = 47

50 −54 = 52

55 −59 =57

64 −64 = 62

So:

x  42    47     52       57     62

f    22    55    1212     77      11

mean = ∑f(x)/∑f

= (42*22+47*55+52*1212+57*77+62*11)/(22+55+1212+77+11)

= 71604/1377

=52

actual mean = 51.8

and now mean = 52

percentage difference = ((52-51.8)/51.8)*100

= 0.3861 percentage

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The value of the expression is -11/15

It is important to note that algebraic expressions are expressions having factors, constants, variables, coefficients and terms.

From the information given, we have that;

3 1/2x - 5 1/3x

turn into improper fractions

7x/2 - 16x/3

Now, let's determine the value by substituting the  value of x as 2/5 in the expression, we have;

7(2/5)/2 - 16(2/5)/3

Multiply the values

14/5/2 - 32/5 /3

Take inverse of the denominator

14/5 ×1/2 - 32/5 × 1/3

7/5 - 32/15

21 - 32/15

-11/5

Hence, the value is -11/15

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Answer:

Step-by-step explanation:

You want to order the accounts greatest to least by their value after 10 years.

The value of each account can be found using the compound interest formula:

  A = P(1 +r/n)^(nt)

Principal P earning rate r compounded n times per year for t years.

For the three accounts, the corresponding values are ...

The order, greatest to least, according to the account values is ...

__

Additional comment

The $700 account will overtake the $950 account after 11 years. It will take about 46 years for it to overtake the $800 account. Eventually, the higher interest rate with greater frequency of compounding wins out.

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Answer:

400 m walking

Step-by-step explanation:

sum the parts of the ratio , 2 + 13 = 15 parts

divide the distance covered by 15 to find the value of one part of the ratio.

3000 m ÷ 15 = 200 m

then

2 parts = 2 × 200m 400 m

400 m covered by walking

On solving the provided question, we can say that expression is - doctor’s name and address, EDG 2020

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

expression is -

doctor’s name and address

EDG 2020

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The correct question is -

Which of the following is something you would not expect to see on a basic loan application?

a. employer's name and address

b. doctor's name and address

C. annual or monthly income

d. current monthly rent or mortgage payment

Please select the best answer from the choices provided

Answer:

Step-by-step explanation:

What is the least number and greatest number of shells he would need

Check the picture below.

Make sure your calculator is in Degree mode.

a)The standard deviation is given by σ = sqrt(np(1-p)) = sqrt(24 × 0.75 × 0.25) = 2.12 . b)Significantly low: μ - 2σ = 18 - 2 × 2.12 ≈ 13.76 ,Significantly high: μ + 2σ = 18 + 2 × 2.12 ≈ 22.24 ,c)z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08.

A group of 24 peas with green pods has a binomial distribution with n = 24 and p = 0.75. The mean is calculated as = np = 24 0.75 = 18, and the standard deviation is calculated as = sqrt(np(1-p)) = sqrt(24 0.75 0.25) = 2.12 (rounded to two decimal places).

b) The range rule of thumb states that results that deviate from the mean by more than two standard deviations are considered significantly low or significantly high. In this case, the values separating significantly low and significantly high results are:

Significantly reduced: - 2 = 18 - 2 2.12 13.76

Significantly greater: + 2 = 18 + 2 2.12 22.24

c) To see if a result of three peas with green pods is significantly low, we must calculate its z-score, which is given by:

z = (x - μ) / σ = (3 - 18) / 2.12 ≈ -7.08

Because the z-score is much lower than -2, the cutoff for significantly low results, we can conclude that a result of 3 peas with green pods is significantly low.

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The boxplot without the outliers is (c)

Outliers are data points that are significantly different from the other data points in a dataset.

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

Using the definition in (a) as a guide, we have the boxplot to be (c)

This is so because it has a minimum of 15 and a maximum of 95 (just as the original boxplot)

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The exponential regression equation that best fits the data in the table is given as follows:

C. f(t) = 11.9(1.12)^t.

The standard definition of an exponential function is given as follows:

y = a(b)^x.

In which:

For this problem, we have that the parameters are estimated as follows:

This means that the correct option is given by option C.

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The Main Street is 1/12 of a mile longer than the Oak Street

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

Using the above as a guide, we have the following:

Difference = Main Street - Oak Street

substitute the known values in the above equation, so, we have the following representation

Difference = 1/3 - 1/4

Evaluate the difference

Difference = 1/12

Hence, the difference is 1/12 of a mile

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Answer:

x [tex]\geq[/tex] 19.75

Step-by-step explanation:

x ≥ 50 - 30.25

x ≥ 19.75

To get a free meal, he needs to spend 19.75 or more.