The ages of residents of a small town are given in the following frequency distribution, approximate the

mean age

The expression for one fifth the difference of a number and 17 is B. 1/5( n - 17).

It should be noted that an expression is used to show the relationship between the variables.

In this case, the information is to find the expression for one fifth the difference of a number and 17.

Let the number be n. The expression will be:

1/5( n - 17).

In conclusion, the correct option is B.

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Answer:

F=10, S=26

Step-by-step explanation:

We know that the base is 24. Using that information, 10^2+24^2=26^2 which is a pythagorean triple

The height of the tree in the mural should be 22.5 feet.To determine the height of the tree in the mural, we can set up a proportion using the given information:

Devon's height in the mural: 4.5 feet

Devon's actual height: 6 feet

Tree's height in the mural: Unknown (let's denote it as x)

Tree's actual height: 30 feet

The proportion can be set up as follows:

(Devon's height in the mural) / (Devon's actual height) = (Tree's height in the mural) / (Tree's actual height)

(4.5 feet) / (6 feet) = x / (30 feet)

Now, let's solve for x by cross-multiplying:

4.5 feet * 30 feet = 6 feet * x

135 feet = 6x

Now, divide both sides of the equation by 6 to find x:

x = 135 feet / 6

x = 22.5 feet

So, the height of the tree in the mural should be 22.5 feet.

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The slope of the line is 1/2.

The slope is a measure of the steepness of a line, or a section of a line, connecting two points.

Slope tells you how steep a line is, or how much y increases as x increases. The slope is constant (the same) anywhere on the line.

For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

Given:

x=-5,0,4,8,13 and y=-7,3,11,19,29

To find the slope

m= (0-(-5))/(3-(-7))

m=0+5/ 3+7

m=5/10

m= 1/2

Hence, the slope is 1/2.

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The correct option is B) Collect variables terms on one side because there is one value for the variable.

The given equation in this case is,

18 = 2(4+x)

By using the Distributive property on the right side,

18 = 8 + 2x

After subtracting 8 from both sides ( Isolating variable x )

18 - 8 = 8 + 2x - 8

Compile similar terms,

10 = 2x

By dividing both sides by two ( Isolating variable x )

x = 5

As a result of the preceding explanation, it is completely obvious that we utilized all options but apart from option B.

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The complete question is-

Which would not be a step in solving 18=2(4+x)?

A) Use the distributive property.

B) Collect variables terms on one side.

C) Collect like terms.

D) Isolate the variable.

Answer:

c = 6

Total: 114

Step-by-step explanation:

The ratio of the number of cans Jordan recycles to the number Ellen recycles is 7:12.

The ratio of the number of cans Ellen recycles to the number of cans Jordan recycles is 12:7.

Jordan recycled 42 cans.

Ellen recycled 42 × 12/7 = 6 × 12

c × 12 = 6 × 12

c = 6

Total: 42 + 72 = 114

Answer: y= -2/3 x + 1/3

Step-by-step explanation:

The first thing you need to do is but it into standard y = mx + b form, where m is the slope of the line and b is the y-intercept. Using algebra, we can turn 3y + 2x = 1 into y = -2/3x + 1/3. the slope is -2/3 which means you start at the y-intercept (0,1/3) and go down 2 and to the right 3. Putting it on paper or in a graphing simulator will give you this line. The point on the y-axis is the y-intercept and the point on the x-axis is the x-intercept.

Answer:

make 3y subjet of the fomulae then subtract 2x then divide by 3 both sides then the ans will be y= -2x+1/3

Classical economics emphasizes that unfastened markets provide efficient results and are self-regulating.

Classical economics means that the long time mixture deliver curve is inelastic, therefore any divergence from complete employment is most effective transitory. The Classical version emphasizes the want of minimizing authorities interference and operating to preserve markets freed from any impediments to effective functioning.

Keynesians declare that because of imperfect markets, the economic system can function at less than full potential for an extended period of time.

Keynesians consider that expansionary economic policy (authorities intervention) has a larger role in overcoming recession.

The Keynesian angle on lengthy-run mixture deliver differs.

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The probability that she selects all 4 blue disks is 0.0317.

The probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Now, according to the question;

There is a total of 2 green disks.

There is a total of 4 blue disks.

There is a total of 3 yellow disks.

The formula for selecting the combination of 4 blue disks are

Probability = (combination for 4 blue)/ Total combination for 9.

The combination is given by the relation;

ⁿCₓ = n!/{x!(n-x)!}

The combination for getting 4 blues is-

n is the total blue disks = 9

x is the selected blue disks = 4

⁹C₄ = 9!/{4!(9-4)!} = 126

The required probability = 4/126

The required probability = 0.0317

Thus, the probability that she selects all 4 blue disks is 0.0317.

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The slope of the line parallel to the line  –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

The equation of the line:

–x + 3y = 6

Write the equation in standard form:

y = x/3 + 6/3

y = x/3 + 2

m = 1/3

The slope of the line parallel to the line  –x + 3y = 6

M = 1/3

Thus, the slope of the line parallel to the line  –x + 3y = 6 is a 1/3 option (A) 1/3 is correct.

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Answer:

Step-by-step explanation:

Let the perimeter of the square with length of n be Pₙ.

According to given table we have:

We can put this as a sequence:

Common difference is:

The recursive formula for this sequence is:

Answer:

80

Step-by-step explanation:

Simply reverse the steps.

In the end he has 60, before that he got 20 dollars for cutting grass, so subtract 20.

Now he has 40, which is after he spent half of his money on games, so multiply it by 2.

This is where he started, and he has 80 dollars saved.

The real-world description of the expression could be: John's age is one-fifth of his sister's age

The expression is given as:

2x/10

To determine the real-world description of the expression, we simply represent the variable x with a real-world expression

Take for instance:

x represents the age of a boy

So, the real-world description of the expression could be:

John's age is one-fifth of his sister's age

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11:35 will be the omitted number in the supplied sequence.

A list of components that have been arranged in a sequential fashion, with members coming either before or after, is referred to as a sequence.

The order will be provided as

9:47, 10:21, 10:57, ?, 12:15

The two increases the gap between the two numbers.

Consequently, there will be a 36-second gap between 10:57 and 10:21.

The distance between the following number and 10:57 will then be 38. The following number will be

→ 10: 57 + 00:38

→ 11: 35

Thus, 11:35 will be the following number.

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B. Neither, because it is within two standard deviations of the mean.

Given; A certain group of test subjects had pulse rates with a mean of 78.9 beats per minutes.

Standard deviation of 11.7 beats per minute.

Range Rule of Thumb:

Standard deviation = Range/4.

Range = 4×SD.

           = 4×11.7

           = 46.8

The "usual" range for this situation is,

78.9-2(11.7) to 78.9+2(11.7) = 55.5 to 102.3

Significantly low will be less than 55.5

Sig high will be greater than 102.3

Pulse rate - Mean = 92.3 - 78.9 = 13.4                              

This value below mean

Then check 2×Standard deviation = 2×11.7= 23.4                              

This value is also below the mean value.

Significantly low values are 55.5 beats per minute or lower.

Significantly high values are 102.3 beats per minute or higher.

Hence it is within two standard deviations of the mean.

Therefore, the answer is B Neither, because it is within two standard deviations of the mean.

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Answer:

f(x) = 4x³ - 7x + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Check

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula above

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) =

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above,

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318

f(x) = 4x³ - 7x + 5(a). f(0) = 5 Checkif x=0,using the formula abovef(0) = 4(0)³ - 7(0) + 5 = 0 - 0 + 5 = 5. ✓(b). f(7) = Using the formula above, f(7) = 4(7)³ - 7(7) + 5 = 4(343) - 49 + 5 =1372 - 54 = 1318

(c). f(-5) =

Using the formula above

f(-5) = 4(-5)³ - 7(-5) + 5

= 4(-125) + 35 + 5

= -500 + 40

= -460

*remember to use a calculator to check the answers

Hope this helps xoxo....

Answer: 1328

Step-by-step explanation:

4*7^3 - 7*7 + 5 = 1328

The conditions on m and b such that the linear function y = mx + b is its own inverse is 1 and 0 respectively.

A linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. It's look like the slope-intercept form of a line which is expressed as y = mx + b.

Or, it is a function that represents a straight line on the coordinate plane.

It is given that the linear is b,

y = mx + b

So, inverse of this function will be :

x = my + b

my = x - b

y = (1/m)x - b/m

Then, for both functions equal

m = 1/m and -b = b

So, m must be 1 and b must be 0.

Therefore, the value is of the m and b of the given equation y = mx + b is its own inverse will be 1 and 0 respectively.

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If the two angles are supplementary then the value of x is 33°.

Two angles that sum to a straight angle or 180° are called supplementary angles.

If the two given angles are supplementary then we can create a linear equation in x of the form:

m∠1+m∠2=180°

Substituting the values we get:

3x°+(x+48)°=180°

or, 4x°+48°=180°

or, 4x°=180°-48°

or,4x°=132°

or, x°=33°

Hence the value of x is 33°.

Disclaimer: The complete question should be: if m< 1=3x° and m2 = (x+48)° are supplementary find the value of x.

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Answer:

4 lemons per pitcher basically by looking at the graph you can determine each pitcher increased by a steady pattern of 4 lemons per pitcher.

Example: 2x=8, x=4, 2(4)=8, 8=8 true, the x and y value is cannot be 0 for this equation since no workers means no lemons. If I subtract back by -4 the graph would look like: 1 4, 0 0. Proving this. Also another example I can do is 3x=12, divide 3 by both side x=4, plug them in, 12=12 which is true. Keep in mind X means Pitcher so 4 is correct.

Oh yea less compilcated way is to just look a graph I did all those step to prove to you. Good luck!

Step-by-step explanation:

Answer:

Divide one number by the other, your quotient is the answer.

the first trip takes 3 hours

and the second one takes 3 hours and 30 minute

All sets that √7 belong to irrational numbers

The number √7 is a number inside a square root. Also, note that the number 7 is a whole number, but not a perfect square. Therefore, by our rule, we have that √7 belongs to the set of real numbers and to the set of irrational numbers.

In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the important numbers that are not rational numbers.

That is, irrational numbers can't be expressed as the ratio of two integers. When the ratio of lengths of two line segments is a real number,  the road segments are also described as being incommensurable, meaning that they share no "measure" in common, that is,  there's no length ("the measure"),  regardless of how short,  that would be used to express the lengths of both of the two given segments as integer multiples of itself.

Among irrational numbers are the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ,  and therefore the square root of two. In fact, all square roots of natural numbers,  aside from perfect squares, are irrational.

Like all real numbers, irrational numbers are often expressed in positional notation, notably as decimal numbers.  within the case of irrational numbers, the decimal expansion doesn't terminate, nor end with a repeating sequence.  

for instance, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.

Conversely, a decimal expansion that terminates or repeats must be a  real number. These are provable properties of rational numbers and positional number systems and aren't used as definitions in mathematics.

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Answer:

( x + y + z )( x^2 + y^2 + z^2 - xy - yz - zx )

Step-by-step explanation:

Use Identity to factor this long expression.

Hope this helps.

If Yumi takes 5/12 hour to complete 50 math problems Eric is able to complete 48 math problems in 2/5 hour the student that can complete math problems at a greater rate of problems per hour is: They solve the same number of problems per hour.

Calculation for the rate of Yumi

Yumi=5/12×60

Yumi=25 minutes

Rate=50/25

Rate=2

Calculation for the rate of Eric

Eric=2/5×60

Eric=24 minutes

Rate=48/24

Rate=2

Hence, Both Yumi and Eric has the same rate which is 2.

Therefore If Yumi takes 5/12 hour to complete 50 math problems Eric is able to complete 48 math problems in 2/5 hour the student that can complete math problems at a greater rate of problems per hour is: They solve the same number of problems per hour.

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After simplifying the algebraic expression 9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }, we get the result as 324 b - 153.

We are given the algebraic expression:

9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }

We need to simplify the expression.

For this, we will use the BODMAS rule.

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

So, simplifying the expression, we get that:

9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }

= 9 { 9 b - [ 2 - 27 b + 15 ] }

= 9 { 9 b - 2 + 27 b - 15 }

= 9 { 9 b - 2 + 27 b - 15 }

= 81 b - 18 + 243 b - 135

= 324 b - 153

Therefore, after simplifying the algebraic expression 9 { 9 b - [ 2 - 3 ( 9 b - 5 ) ] }, we get the result as 324 b - 153.

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Answer:

ii-7i

Step-by-step explanation:

These can be multiplied in a manner similar to expanding brackets:

(

2

+

i

)

(

3

−

5

i

)

=

6

+

3

i

−

10

i

−

5

i

2

Remember that

i

=

√

−

1

so

i

2

=

−

1

This will in turn allow us to gather the like terms like so:

6

+

5

+

3

i

−

10

i

=

11

−

7

i

If 2 and 6 were both negative, their combined value would be -2 + (-6) = -8. The arithmetic outcome of adding the magnitudes of the numbers, but with the opposite sign, yields the sum of negative integers. In this instance, the product of -2 and -6 is -8, which symbolises the joining of two negative values that produces a negative outcome.

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