Use the quadratic formula to determine the exact solutions to the equation.

6x2+4x−3=0

The age that has the maximum number of arrest is 25 years

The equation of the function is given as:

[tex]f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x[/tex]

See attachment for the graph of the function.

The end behavior of the graph is

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

This means that:

As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases

From the graph, the maximum is:

Maximum = (25.388, 356.166)

Remove the y values

Maximum = 25.388

Approximate

Maximum = 25

Hence, the age that has the maximum arrest is 25

Read more about functions at:

https://brainly.com/question/23426439

#SPJ1

Steve is 1.2 times faster than Paul.

The quantitative relationship between two values indicating how frequently one value is contained within the other.

For example: Speed = Distance / Time

Total distance covered by both Steve and Paul = 100m

Total time taken by Steve = 10s

Steve's speed = 100 / 10 = 10m/s

Total time taken by Paul = 12s

Paul's speed = 100 / 12 = 8.33m/s

Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2

Hence we can say that Steve is 1.2 times faster than Paul.

Learn more about ratios on:

https://brainly.com/question/2328454

#SPJ4

Answer:

1960

Step-by-step explanation:

1960

times 56 times 7 time 5 = 1960

68% of the data lies within one standard deviation from the mean

95% of the data lies within two standard deviation from the mean

99.7% of the data lies within three standard deviation from the mean

The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean

Find out more on empirical rule at: https://brainly.com/question/10093236

#SPJ1

On the given graph, we can see that we have:

The correct option would be a in both cases.

We want to study the asymptotes of the graph

If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.

the graph has a horizontal asymptote (or two actually) at y = 3.

For the vertical asymptote we just look at the vertical dashed line, it is at x = -2

Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.

If you want to learn more about asymptotes:

https://brainly.com/question/1851758

#SPJ1

Step-by-step explanation:

So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]

Distribute the multiplication on the left side:

[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]

Distribute the multiplication on the right side:

[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]

Add like terms on the left side:

[tex]100a+10b+c+111=130a+13b+1.3c[/tex]

Subtract 100a, 10b, and c from both sides

[tex]111=30a+3b+0.3c[/tex]

So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.

So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value

111 = 30(3) + 3b + 0.3c

111 = 90 + 3b + 0.3c

Now subtract the 90 from both sides

21=3b+0.3c

Well 3 can fit into 21, 7 times!

21 = 3(7) + 0.3c

21 = 21 + 0.3c

subtract 21 from both sides

0 = 0.3c

and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant

c = 0

This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!

part b:

So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.

So let's start with the same equation except this time instead of 1.3 it's 1.4

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]

Distribute on the left side;

[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]

Distribute on the right side:

[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]

Add like terms on left side:

[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]

Subtract 100a, 10b, and c from both sides:

[tex]111 = 40a + 4b + 0.4c[/tex]

Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.

So only 2 40's can fit in 111 without going over the value

111 = 40(2) + 4b + 0.4c

Subtract 80 from both sides

[tex]31=4b+0.4c[/tex]

4 can fit into 31, 7 times

31 = 4(7) + 0.4c

31 = 28 + 0.4c

subtract 28 from both sides

3 = 0.4c

divide both sides by 0.4

7.5 = c.

Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.

Step-by-step explanation:

First, there is a vertical stretch by a factor of 3,

Next, there is a horizontal compression by a factor of 2.

Reflect about the y axis.

After, shift to the right 3 units horizontally,

Finally , shift upwards 7 units

A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.

Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

For further clarifications on parts of a circle, visit: https://brainly.com/question/15618723

#SPJ1

The measure of the ∠Q = 41°

By law of cosines:

a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Which can we stated as:

[tex]{q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)\\\\[/tex]

solving equation using normal algebra:

60cos(Q) = 36 + 25 - 16

60 cos(Q) = 45

cos(Q) = 45/60

cos(Q) = 3/4

[tex]Q = {cos}^{-1} (\frac{3}{4})\\[/tex]

Thus, Q = 41°

Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.

To learn more about Finding angles visit:

https://brainly.com/question/3067469

#SPJ4

[tex]\huge\boxed{25\%}[/tex]

We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.

We know the counts for every category except for "art but not biology", so we can use subtraction.

[tex]26-4-5-5=12[/tex]

This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.

Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).

This is simple division.

[tex]4/16=0.25=25\%[/tex]

n^3 + 6

I'll make n stand for the number

Six more means adding extra 6 onto our number cubed.

So, n x n x n = n^3

(n^3 means n cubed)

Thus, answer is n^3 + 6

Hope this helps!

Answer:

2x+7

Step-by-step explanation:

To Simplify an Expression , we combine Like-Terms

So for our Question , we have Terms with x and Constant Term

Combine Terms with x : 5x-2x-x=2x

Constant Term : 7

Then 5x-2x+7-x = 2x+7

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation: }[/tex]

[tex]\mathbf{5x - 2x + 7 - x = }[/tex] ________[tex]\mathbf{\ x \ + }[/tex]________

[tex]\huge\textbf{Simplify the left side of the equation, to}\\\huge\textbf{get the result of the right side of the}\\\huge\textbf{equation.}[/tex]

[tex]\huge\textbf{Simplifying the LEFT side:}[/tex]

[tex]\mathbf{5x - 2x + 7 - x}[/tex]

[tex]\mathbf{= 5x - 2x + 7 - 1x}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{= (5x - 2x - 1x) + (7)}[/tex]

[tex]\mathbf{= 5x - 2x - 1x + 7}[/tex]

[tex]\mathbf{= 3x - 1x + 7}[/tex]

[tex]\mathbf{= 2x + 7}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{2\mathsf{x} + 7}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints

1 pound = 16 ounces

Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces

= 13/4 × 16

= (208) / 4

= 52 ounces

1 gallon = 4 quarts

0.15 gallon = 0.6 quarts

1 quart = 2 pints

0.6 quart = 1.2 pints

Pint of water dispensed in 20 seconds = 1.2 × 20

= 24 pints of water

Learn more about weight:

https://brainly.com/question/229459

#SPJ1

By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.

Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.

We have to first plot both the equations on the graph.

For plotting we need points which can be calculated as

C=2x

when x=1 ,C or y=2

when x=3 , C or y=6

C=x+5

when x=0 ,C or y=5

when x=1 ,C or y=6

By combining both equations we get

C=(3x+5)/2

Plot this also and finding points

when x=0  , C=5/2

when x=1 , C=4

Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2

Learn more about equation at brainly.com/question/2972832

#SPJ10

Answer:

So, after

3

years, Impulse Clothing and Opal Essence will own the same number of clothing stores.

The total number of stores during that year will be 8.

Answer:

66.4 in^2

Step-by-step explanation:

Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:

16 + 50.4 = 66.4

Stratified sampling is used by Made Eyewear

Stratified sampling is is where we divide the population into groups by some characteristic such as age or occupation or gender. Then make sure our survey includes people from each group in proportion to how many there are in the whole population.

Example of this sampling is A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age and use of eyeglasses, like 18–29, 30–39, 40–49, 50–59, and 60 and above

So, Stratified sampling is used by Made Eyewear

Learn more about SAMPLING here

https://brainly.com/question/9910540

#SPJ4

The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.

In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.

It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.

Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.

Learn more about standard deviation here: https://brainly.com/question/475676

#SPJ4

500 people

200 people wearing red shirts

200x15%= 30 people

30 =6% of 500

Answer: 65

Step-by-step explanation:

By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]

So, by the Pythagorean theorem,

[tex]x=\sqrt{60^2 + 25^2}=65[/tex]

The correct answer is option D which is the side length will be (64n)¹⁸.

The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.

Given that:-

The sides of the square will be calculated as follows:-

A = (64n)³⁶

a² = (64n)³⁶    Here a = Side of the square.

a = √ (64n)³⁶

a = 64n¹⁸

Therefore the correct answer is option D which is the side length will be (64n)¹⁸.

To know more about an area of square follow

https://brainly.com/question/13389992

#SPJ1

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.

Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:

10 - 8 < s > 8 + 10

2 < s > 18

The range of values for the third side is: A. 2 < s < 18.

Learn more about the triangle inequality theorem on:

https://brainly.com/question/1909012

#SPJ1

Answer: A. 2 < s < 18.

Step-by-step explanation:

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

The statement of expressions is two terms and three factors.

According to the question, the statement that teaches us about expression is made up of two terms, each of which has three factors.

The ABC and DEF expressions define the expression of two terms, each of which comprises two elements.

As a result, the answer is two terms and three factors.

Therefore, the answer is two terms and three factors.

Know more about an expression here:

https://brainly.com/question/723406

#SPJ4

The equation [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex] has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Given function,
= [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex]
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).

Given function has x intercept at (14, 0) and y intercept at (0, 6).

Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).

Learn more about function here:

brainly.com/question/21145944

#SPJ1

Answer:20ft

Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20

20x15 equals 300 so it goes both ways

The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

Given the polynomial function below

F(x)=x³-x² + 4x-4

Group

F(x)=(x³-x²) + (4x-4)

f(x) = x²(x-1)+4(x-1)

f(x) = (x²+4)(x-1)

If f(x) = 0

x²+4 = 0 and x -1. = 0

x² = -4 and x = 1

x = ±2i and -1

Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

Learn more on zeros of polynomial here: https://brainly.com/question/11724515

#SPJ1

Answer:

22.470

Step-by-step explanation:

In this example you have to use the trigonometric function sine which is defined as [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex]

Plug in known values:

[tex]sin(64) = \frac{x}{25}[/tex]

Multiply both sides by 25

[tex]sin(64) * 25 = x[/tex]

Approximate sin(64) using a calculator:

[tex]0.89879 * 25 = x[/tex]

Simplify

[tex]22.470 \approx x[/tex]

Answer: 1 bottle, 6 bottle, 8 bottle

Answer: 1 bottle for $1.07, 8 bottles for $8.56 and 6 bottles for $6.42

Answer:

The answers are:
(i) 108.33%
(ii) 93.75%

Step-by-step explanation:

The original area and perimeter are as follow:

Perimeter = 2l + 2w
                = 2(2p) + 2(p)
                = 4p + 2p
                = 6p cm

Area = l * w
        = 2p * p
        = 2p^2 cm^2

A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm

A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm

Perimeter = 2l + 2w
                 = 2(2.5p) + 2(0.75p)
                 = 5p + 1.5p
                 = 6.5p cm

Area = l * w
        = 2.5p * 0.75p
        = 1.875p^2 cm^2

Now that we have found the changes, let's calculate the percentage changes

Percentage change of perimeter:

x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33

Percentage change of area:

x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75

Answer:

i = 8 1/3%

ii = -6 1/4%

Step-by-step explanation:

The previous answer is wrong this is the correct one:

Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm

i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm

The percentage change is

65-60/60 x 100

= 5/60 x 100

= 500/60

= 8 2/6% simplified 8 1/3%

ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2

The percentage change is

187,5-200/200x 100

= - 12,5/200 x 100

= - 1250/200 = - 6 1/4 %

That is the Correct answer. Hope that help

Answer:

x = 8

Step-by-step explanation:

Every angle in an EQUILATERAL triangle = 60°

so   9x -12 = 60

       9x = 72

         x = 8  

Step-by-step explanation:

[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]

[tex]9x = 60 + 12[/tex]

[tex]9x = 72[/tex]

[tex]x = \frac{72}{9} \\ [/tex]

[tex]x = 8[/tex]

hence the value of x is 8...