42. MODELING REAL LIFE The graphs show the weight restrictions w (in tons) for vehicles with (a) axles, (b) axles, and (c) axles traveling on state roads. For each type of vehicle, write and interpret an inequality that represents the weight restriction (in ).

All real numbers n that is less than 14 when plugged in for x will be less than 14 in inequality .

What is inequality in math?

inequality  = 4n+ 13 ≤ 69

                 = 4n ≤ 69 - 13

                 = 4n ≤ 56

                 = n ≤ 56/4

                 = n ≤  14

Thus, all real numbers n that is less than 14 when plugged in for x will be less than 14.

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The number of boxes that should be opened to find it is 98 boxes.

Probability simply means the likelihood of the occurence of an event.

When there is a 3 percent chance or finding something special in a box,the number of boxes that will be opened will be illustrated thus:

Let the number of boxes be 100.

Therefore, the number of boxes will be:

= Total boxes - Percentage given

= 100 - 3

= 97

In this case, the 98th box will give the person the chance of getting it.

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The amount of money that Carson make in a week in which he made $1575 in sales is $686.25.

From the information, Carson makes a guaranteed salary of $450 per week, but is paid a commision on top of his base salary equal to 15% of his total sales for the week.

Therefore, the amount that he will be paid when he sees $1575 will be:

Base salary + Commission

= $450 + (15% × $1575)

= $450 + $236.25

= $686.25

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Answer:

4x-5

Step-by-step explanation:

The ratio of boys to girls in the 9th grade is 7 : 9. Girls are 218

proportion of girls in total students are [tex]\frac{218}{9}[/tex] = 24.2

According to the question, given that

In class ratio of boys and girls is 7 : 9

and girls in the class are 218

Proportion of girls in total class = [tex]\frac{218}{9}[/tex]

                                                    = 24.2

Therefore, we get proportion of girls in the class is 24.2

When determining if two ratios or fractions are equivalent, the proportion formula is utilized. The proportional formula is as follows:

a : b :: c : d = a/b = c/d

Proportion Formula

a:b::c:d = a/b = c/d

where,

a, d = Extreme terms

b, c = Mean terms

The product of means equals the product of extremes is one of the various proportional formulas. You can write this as ad = bc.

Two additional proportional formulas that depend on direct or indirect variation are available. When two quantities x and y are in direct proportion, y = k x, and when x and y  are in indirect proportion, y = k/x, with k serving as the proportionality constant in both cases.

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Answer:

Step-by-step explanation:

45 degrees -67/6

The thing that P(W) represents is A. It denotes the probability of screening a driver and finding that he or she is not intoxicated.

The value is 0.99257

It should be noted that probability simply means the likelihood that something will happen or occur based on the information given.

From the information, the man observed a sobriety checkpoint conducted by a police department, he saw drivers were screened and were arrested for driving while intoxicated.

P(W) = 0.000743

Therefore, those that are not intoxicated will be:

= 1 - P(W)

= 1 - 0.000743

= 0.99257

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The required polynomial function is y=3(x+3)⁴(x-4 ) for the conditions as mentioned fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

Here the given conditions are:

Fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

Let y be the f(x) and x be the variable.

Now, x+3 is the first term and x-4 be the second term with their multiplicity 4 and 1.

y=3(x+3)⁴(x-4)

For the above-mentioned fifth-degree conditions, the necessary polynomial function is y=3(x+3)⁴(x-4); 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

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Based on the distance of the race and the length of the sections, the number of people that Heather will need to be on her team are 26 people

The entire race has a length of 5 1/5 miles and this length will be divided into sections that are 1/5 miles long.

Only one member of the team can run in each of these sections so enough people are needed on Heather's team to run the 1/5 mile sections.

The number of people to be in a team can be found by the formula:
= Length of race / Length of sections

= 5 1/5 miles / (1/5)

= 26/5 ÷ 1/5

= 26/5 x 5/1

= 26 people

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A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. As opposed to the particular examples below, a scalene trapezoid is a trapezoid without equal sides.

The Greek mathematician Euclid identified five different quadrilateral shapes, of which four had two sets of parallel sides (the square, rectangle, rhombus, and rhomboid in English) and one did not (a trapezia, meaning "a table," which comes from "four" and means "a foot; end, boundary, edge").

In his commentary on the first book of Euclid's Elements, Proclus (412–485) developed two varieties of trapezia: one pair of parallel sides, or a trapezium (v), divided into isosceles (equal legs), and scalene (unequal) Similar to how cuboid and rhomboid both mean "resembles," trapezia with no parallel sides is a trapezoid, trapezoeidé, or literally "trapezium-like."

English followed Proclus's arrangement until the late 18th century, when a prominent mathematical lexicon produced by Charles Hutton in 1795 endorsed a transposition of the terms without providing an explanation. Although this error was fixed in British English around 1875, it remained in American English till the present..

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Answer:

x = 5, y = 25

Step-by-step explanation:

I use the substitution method to solve. (I hope I got the equations correct)

6x + y = 55 ---1

10x + 3y = 125 ---2

From 1: y = 55 - 6x ---3

Substitute 3 into 2:

10x + 3(55 - 6x) = 125

10x + 165 - 18x = 125

- 8x = - 40

x = 5

Substitute x into 3

y = 55 - 6(5) = 25

Answer:

(0, 6)

(-1 , 5)

Step-by-step explanation:

A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields then the function exists described as: y = 9000 + 1500 h.

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that contains a straight line as its graph exists directed to as a linear function in calculus and related fields.

The given parameters exists:

Initial = 9000

Rate = 1500

The function exists estimated as: y = Initial + Rate × h

Where h represents the number of hours.

Let the equation be y = Initial + Rate × h

Substituting the values in the above equation, we get

y = 9000 + 1500 × h

y = 9000 + 1500 h

Therefore, the function is represented as: y = 9000 + 1500 h

The complete question is:

A 21,000-gallon swimming pool contains 9000 gallons of water when a hose is placed in the pool and begins adding water at a rate of 1500 gallons per hour. Use the Segment tool to plot a graph representing the volume of water in the pool over time from when the hose is placed in the pool until the pool is full.

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In the picture we can see there is a line with an intersection line.  

∠3=(13x+7)° and ∠6 =(9x+59)°. The angles ∠5=4°, Option A is correct.

Given that,

In the picture we can see there is a line with an intersection line.

A transversal is a line that creates angles when it crosses two parallel lines (or lines on a plane) at various points.

∠3 =(13x+7)° and

∠6 =(9x+59)°

In the parallel lines alternatives angles are always equal.

So,

∠3=∠6

13x+7=9x+59

13x-9x=59-7

4x=52

x=52/4

x=13

Now,

∠3 =(13x+7)°=(13×13+7)°=(169+7)°=176°

∠6 =(9x+59)°=(9×13+59)°=(117+59)°=176°

Now,

From the supplementary angles.

∠5+∠6=180°

∠5=180°-∠6

∠5=180°-176°

∠5=4°

Therefore, We got the angles ∠5=4°, Option A is correct.

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Answer:

3811

Step-by-step explanation:

37X100= 3700

37X3=111

so 3700+ 111= 3811

Answer: 3 5/8 hours

Step-by-step explanation:

2 + 1 = 3

1 / 4 = 2 / 8

3 / 8 + 2 / 8 = 5 / 8

The length of the missing side z would be 17 units which is determined by Pythagoras's theorem.

A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

According to Pythagoras's theorem,

⇒ a² + b² = c²

Here, a = 8  b = 15 and c = z

⇒ (8)² + (15)² = z²

⇒ 64 + 225 = z²

Apply the addition operation,

⇒ 289 = z²

⇒ z² = 289

⇒ z = √289

⇒ z = 17

Therefore, the length of the missing side z would be 17 units.

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No, the given procedure doesn't result in a binomial distribution.

We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.

1: Each observation should be independent, it must not depend on the result of previous observation.

2: The probability of success should stay same from trial to trial.

3: n is fixed (the number of observations)

4: There are only two outcomes success or failure.

Surveying 2828 people to determine which statistics courses they have taken.

3 is satisfied since n is fixed

1 is satisfied since each observation is independent

4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).

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Answer:

[2005]=25.29

Step-by-step explanation:

[tex]y = 7.41 + 2.98x[/tex]

Using the binomial distribution, it is found that the mean for the number of people with the genetic mutation in such groups of 800 is of 72

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

In this problem, we have that:

About 9% of the population has a particular genetic mutation, hence p = 0.09

800 people are randomly selected, hence n = 800.

Then, the mean is given by:

E(X) = np = 800 x 0.09= 72

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Answer:

(a) Fermat's little theorem states that for any prime p , we have

a^p-1 = 1 (mod p).

for any integer ,a. Then

999999 = 1000000 - 1 = 10^6 - 1 = 1 - 1 = 0 (mod 7)

so 7 does indeed divide 999,999.

(b) Generalizing, we have

10^12n - 1 = 999...999 (12n nines) = (10^n)^12 - 1 = 0 (mod 13)

for positive integer, n. Now, since 1 = 1001 - 1000 and -1 = (mod 1001) , it follows that 10^3 is its own inverse modulo 1001, i.e.

10^3 x = 1 (mod 1001) -----> x = 10^3

This means

10^12n = (10^3 x 10^3)^2n = 1^2n = 1 (mod 1001) ----> 10^12n - 1 = 0 (mod 1001)

Answer:

A. The perimeter of the image is 4 times as large as the perimeter of the pre-image.

Explanation:

To answer this question, we use an example.

Given the pre-image:

• A square with side length 1 cm

• Perimeter = 4 x 1 = 4cm

If the square is dilated by a scale factor of 4:

• Side length = 4cm

• Perimeter = 4 x 4 =16cm

We see therefore that 'The perimeter of the image is 4 times as large as the perimeter of the pre-image.'

The correct choice is A.

The equation y = - 2x + 4 matches the line

How to find the equation?

The line passes through two points .

[tex](x_1, y_1) = (2, 0)\\\\(x_2, y_2) = (0, 4)[/tex]

We know that slope (m) is given by,

[tex]m =\frac{y_2 -y_1}{x_2 -x_1} \\\\m =\frac{4-0}{0-2} \\\\m= -\frac{4}{2} \\\\m= -2[/tex]

We know the slope- intercept form of an equation is:

y = mx+ c    ----(1)

Let us substitute the point  [tex](x_1, y_1)[/tex]  and m in (1)

y = mx+ c

0 = -2(2) +c

c = 4

Let us substitute c and m in (1)

The slope- intercept form of the equation is:

y = -2x + 4

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The inequality expression given as 2 - |6 + 12x| > -28 has a solution of -3 < x < 2

From the question, the inequality is given as

2-|6+12x|>-28

Rewrite properly as

2 - |6 + 12x| > -28

Subtract 2 from both sides

- |6 + 12x| > -30

Divide both sides by -1

|6 + 12x| < 30

Remove the absolute bracket

So, we have the following representation

-30 < 6 + 12x < 30

Add -6 to all sides of the inequality

So, we have

-36 < 12x < 24

Multiply through by 1/12

So, we have

-3 < x < 2

Hence, the solution to the expression is -3 < x < 2

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Answer:

Point of intersection is the point where two lines or two curves meet each other. The point of intersection of two lines of two curves is a point.

Step-by-step explanation:

Hope it helps! =D

2 lines intersect at:

A point

In a plane, crossed lines square measure any 2 or a lot of lines that cross each other. The purpose of intersection, which may be found on all crossed lines, is wherever the crossed lines share a standard purpose.

Perpendicular lines square measure 2 lines that cross at associate angle of right angles.

Since the purpose of intersection is that the solely location wherever the 2 graphs meet once the lines cross, the coordinates of that location offer the solution to the equations involving the 2 variables.

There are not any solutions once the lines square measure parallel.

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The ball to rise 45 meters in 3 seconds.

How do you find the solutions of a quadratic equation?

here

Function : [tex]H= 30t-5t^{2}[/tex]

height = 45m

then [tex]30t-5t^{2} = 45[/tex]

simplify the quadratic equation ⇒ [tex]6t-t^{2} -9=0[/tex]

⇒ [tex]t^{2} -6t+9=0[/tex]

⇒ [tex](t-3) (t-3)=0\\t=3.[/tex]

 time required to  reach 45m = 3 sec.

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The  system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes is:  44 x + 43 y = 217 , 45x + 18y = 144 .  Each pound of peaches cost $2 and each pound of grapes cost $3

x = price of each pound of peaches

y = price of each pound of grapes.

Given that yesterday,  he sold 44 pounds of peaches and 43 pounds of grapes for a total revenue of $217

So 44 x + 43 y = 217 be equation 1.

Also given that today he sold 45 pounds of peaches and 18 pounds of grapes for a total revenue of $144.

So 45x + 18y = 144 equation 2.

Multiplying equation 1 with 18 gives us,

792x +774y = 3906

Multiplying equation 2 with 43 gives us,  

1935x+774y = 6192

Solving these,

792x +774y = 3906

1935x+774y = 6192

---------------------------------------------

-1143 x=- 2286

x = 2286/ 1143

x = 2

Plug this value of x in equation 1 and solve for y, to get,

44 x + 43 y = 217

44 (2) + 43 y = 217

43 y = 217 − 88

43 y =129

y = 129/43

y = 3

Therefore each pound of peaches cost $2 and each pound of grapes cost $3

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