at an intersection, the red light light times are normally distributed with a mean time of 3 minutes and a standard deviation of 0.25 minutes. Approximately what percent of red lights last between 2.5 and 3.5 minutes

Answer:

[tex] (0, 8\sqrt{3}) [/tex]  and  [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).

Step-by-step explanation:

distance formula

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

We want the distance, d, from points (-2, 0) and (2, 0) to be 14.

Point (-2, 0):

[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

Point (2, 0):

[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]

[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]

We have a system of equations:

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]

Since the right sides of both equations are equal, we set the left sides equal.

[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]

Square both sides:

[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]

Square the binomials and combine like terms.

[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]

[tex] 4x = -4x [/tex]

[tex] 8x = 0 [/tex]

[tex] x = 0 [/tex]

Now we substitute x = 0 in the first equation of the system of equations:

[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]

[tex] \sqrt{4 + y^2} = 14 [/tex]

Square both sides.

[tex] y^2 + 4 = 196 [/tex]

[tex] y^2 = 192 [/tex]

[tex] y = \pm \sqrt{192} [/tex]

[tex] y = \pm \sqrt{64 \times 3} [/tex]

[tex] y = \pm 8\sqrt{3} [/tex]

The points are:

[tex] (0, 8\sqrt{3}) [/tex]  and  [tex] (0, -8\sqrt{3}) [/tex]

Answer:

its a! sorry im so late

Step-by-step explanation:

Answer:

? = 26 in

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

?² = 24² + 10² = 576 + 100 = 676 ( take the square root of both sides )

? = [tex]\sqrt{676}[/tex] = 26

Answer:

26 inch

Step-by-step explanation:

unknown side can be found using Pythagorean theorem

a*a+b*b=c*c

24*24+10*10=c*c

576+100=c*c

√676=c

c=26inche

Answer:

x = 66°

Step-by-step explanation:

Hello,

This question involves use of rules or theorems of angles in a right angled triangle

<DAB + <BAC = 180°

Sum of angles on a straight line = 180°

98° + <BAC = 180°

<BAC = 180° - 98°

<BAC = 82°

Now, we can use <BAC to find x because some of angles in a triangle is equal to 180°

32° + 82° + x = 180°

Sum of angles in a triangle = 180°

114° + x = 180°

x = 180° - 114°

x = 66°

Angle x = 66°

Answer:

To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic

1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation

We simplify and check the number of real roots with the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex] for quadratic equations  the form 0 = a·x² - b·x + c

Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.

Step-by-step explanation:

Answer:

Isolate one variable in the system of equations. Use substitution to create a one-variable equation. Then, set the quadratic equation equal to zero and find the discriminant. If the discriminant is negative, then there are no real number solutions. If the discriminant is zero, then there is one real number solution. If the discriminant is positive, then there are two real number solutions.

Step-by-step explanation:

I just took the test on Edge 2020

Answer:

sqroot 16/49 A

Step-by-step explanation:

The expression  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] is equivalent to expression [tex]\sqrt{\frac{16}{49}}[/tex] because by property  [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex].

The expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] can be simplified by taking the square root of 16 and the square root of 49 separately.

√16 equals 4 because the square root of 16 is the number that, when multiplied by itself, gives 16.

Similarly, √49 equals 7 because the square root of 49 is the number that, when multiplied by itself, gives 49.

So, the expression [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] simplifies to 4/7.

and we know that [tex]\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b} }[/tex]

[tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] , which simplifies to 4/7.

Therefore, [tex]\sqrt{\frac{16}{49}}[/tex] is equivalent to  [tex]\frac{\sqrt{16}}{\sqrt{49}}[/tex] .

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Answer:

Associative Property.

Step-by-step explanation:

The Associative Property is the property that says that (a + b) + c = a + (b + c).

Hope this helps!

Answer:

Associate Property

Step-by-step explanation:

I found my answer at baba com

Answer:

(-3, -11)

i needed to put more characters so here

Answer:

-x^2 +2x +8

Step-by-step explanation:

f(x) = 2x + 1

g(x) = x^2 – 7,

(f – g)(x) = 2x +1 - ( x^2 -7)

Distribute the minus sign

             = 2x+1 - x^2 +7

Combine like terms

             = -x^2 +2x +8

Answer:

its not true. Answer is (f + g)(x) = x2 + 2x - 6

Step-by-step explanation:

Trust me. Good luck.

Answer:

P((1 or 2) and Tail) = 1/6 = StartFraction 1 over 6

Step-by-step explanation:

A six-sided die and a coin.

Probability of getting <3 and tail.

P((1 or 2) and Tail)

= 2/6 * 1/2

= 1/6

Answer:

1/6

Step-by-step explanation:

We have

[tex]16=2^4\implies\sqrt[4]{16}=2[/tex]

[tex]81=3^4\implies\sqrt[4]{81}=3[/tex]

[tex]32=2^5\implies\sqrt[4]{32}=2\sqrt[4]{2}[/tex]

So

[tex]2\sqrt[4]{16x}-2\sqrt[4]{2y}+3\sqrt[4]{81x}-4\sqrt[4]{32y}[/tex]

is equivalent to

[tex]2^2\sqrt[4]{x}-2\sqrt[4]{2y}+3^2\sqrt[4]{x}-8\sqrt[4]{2y}[/tex]

which reduces to

[tex]13\sqrt[4]{x}-10\sqrt[4]{2y}[/tex]

Answer:  see graph (attached)

Step-by-step explanation:

Plot coordinates for each line. You MUST include the boundary points.

y = 3x - 5       x ≤ 1    

Choose x = -2, then y = 3(-2) - 5 = -11

Must include x = -1, then y = 3(-1) - 5 = -8

Draw a line starting at (-1, -8) and passing through (-2, -11)

y = -2x + 3      -1 < x < 4

Must include x = -1, then y = -2(-1) + 3 = 5

Must include x = 4, then y = -2(4) + 3 = -5

Draw a line segment starting at (-1, 5) and ending at (4, -5).

Note that both are strictly less than so must have open dots.

y = 2      x ≥ 4

Must include x = 4, then y = 2

Choose x = 5, then y = 2

Draw a line starting at (4, 2) and passing through (5, 2)

Answer:

Relative frequencies:

Headaches = 23.55 %

Hypertension = 8.68%

Upper respiratory tract infections =24.79%

Nasopharyngitis = 21.07

Diarrhea = 21.09%

None of these adverse reactions appear to be much more common than the others.

Step-by-step explanation:

Compute frequency:

The number of adverse reactions categories:

Headaches

Hypertension

Upper respiratory tract infections

Nasopharyngitis

Diarrhea

Frequency of each adverse reaction:

Adverse reaction                                Frequency        

Headaches                                                 57                    

Hypertension                                              21

Upper respiratory tract infections             60

Nasopharyngitis                                          51

Diarrhea                                                       53

Compute total frequency

Total frequency is compute dby taking sum of all frequencies;

Sum of frequencies = 57 + 21 + 60 + 51 + 53

                                 = 242

Compute relative frequency:

In order to find if any one of these adverse reactions appear to be much more common than the others, we have to compute relative frequency using these adverse reactions.

By calculating relative frequency we are looking at the number of times a specific adverse reaction appears to be more common, compared to the others.

To calculate relative frequency, divide the frequency of each adverse reaction by the total frequency i.e. 242.

Relative frequency for Headache = 57 / 242

                                                        = 0.2355

                                                        = 23.55 %

Relative frequency for Hypertension = 21 / 242

                                                             = 0.0868

                                                             = 8.68 %

Relative frequency for Upper respiratory tract infections = 60 / 242

                                                                                              = 0.2497

                                                                                              = 24.97 %

Relative frequency for Nasopharyngitis = 51 / 242

                                                                  = 0.2107

                                                                   = 21.07 %

Relative frequency for Diarrhea    = 53 / 242

                                                        = 0.2190

                                                         = 21.90 %

If you observe the relative frequencies of all the adverse reactions, none of them appear to be much more common than the others. Relative frequencies of headaches, upper respiratory tract infections, nasopharyngitis and diarrhea are almost equally common however, relative of hypertension appears to be very less than the other three.

Answer:

x + 2y ≤ 12

x + 2y = 12

Step-by-step explanation:

The teachers can not give more than 12 hours of homework so this is the answer. those are the 2 equations you can use. It under 12 hours or equal to 12 hours.

Answer:

Part A: x + 2y ≤ 12.

Part B: y = -1/2x + 6.

Part C: (0, 0).

Step-by-step explanation:

Part A: The total hours of homework have to be 12 hours, and it has to be either 12 hours or less. So, we have ≤ 12.

They take 1 math course with x hours of homework, so in total, that is 1 * x = x hours of math homework.

They take 2 science courses with y hours of homework, so in total, that is 2 * y = 2y hours of science homework.

The inequality would then be x + 2y ≤ 12.

Part B: x + 2y = 12

2y = -x + 12

y = -1/2x + 6

You can  use the Math is Fun: Function Grapher and Calculator to find the graph of the line, shown below.

Part C: Since the inequality uses a ≤ symbol, we know that the shading will be underneath the line. An appropriate point below the line includes (0, 0). We will test out whether it works as a point included in the inequality.

x + 2y ≤ 12

0 + 2 * 0 ≤ 12

0 + 0 ≤ 12

0 ≤ 12

Since this is a true statement, (0, 0) holds true for the inequality.

Hope this helps!

Answer:

-58.41509433

Step-by-step explanation:

0.4+8(5-0.8*5/8)-5/(2.5)=34.4

[0.4+8(5-4/8)-(2)]=

[0.4+8(40-4)/8)-2=34.4 ( nominator)

15-(8.9-2.6/(2/3))*34*2/5 =-53

15-(8.9-3.9)*68/5

15-5*68/5=

15-68=-53 ( denominator)

(34.4/-53) *90

-58.41509433

Using the factor theorem, we have

[tex]7x^2+x-5=7(x-a)(x-b)[/tex]

and expanding gives us

[tex]7x^2+x-5=7(x^2-(a+b)x+ab)\implies\begin{cases}ab=-5\\a+b=-1\end{cases}[/tex]

So we have

[tex](a-4)(b-4)=ab-4(a+b)+16=-5-4(-1)+16=\boxed{15}[/tex]

Answer:

Volume of the sphere is 66.67r/h

Step-by-step explanation:

Hello,

Volume of a sphere = ⁴/₃πr³

Volume of a cylinder = πr²h

The volume of the cylinder = 50ft³

But the cylinder and sphere both have the same radius and height

Volume of a cylinder = πr²h

50 = πr²h

Make r² the subject of formula

r² = 50/πh

Volume of a sphere = ⁴/₃πr³

Put r² into the volume of a sphere

Volume of a sphere = ⁴/₃π(50/πh)r

Volume of a sphere = ⁴/₃ × 50r/h

Volume of a sphere = ²⁰⁰/₃ r/h

Volume of a sphere = 66.67r/h

The volume of the sphere is 66.67r/h

Answer:

Options B:  and C:

Step-by-step explanation:

Remember that 30% in fraction form is

The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:

And since it would add that to the current total we can right the current total as:

So our equation would be:

For option B:

We can factor out the H and you will be left with:

Combine or add the fractions inside the parenthesis and you will have:

For option C:

We can simplify the fractions which will result in:

Then factor out the H and you will have:

Options B:  and C:

Step-by-step explanation:

Remember that 30% in fraction form is

The amount of health points (H) restored would depend on the amount of the current H so it means it would add 30% of the current which we can write as:

And since it would add that to the current total we can right the current total as:

So our equation would be:

For option B:

We can factor out the H and you will be left with:

Combine or add the fractions inside the parenthesis and you will have:

For option C:

We can simplify the fractions which will result in:

Then factor out the H and you will have:

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

             ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                            PEACE!

Answer:

9000

Step-by-step explanation:

the inital ammout which is 9k is the size of the loan

-200 because he years 200 dollars per month

but the start up number is 9000 and he repays the load at 200 dollars a month

Answer:

The vertex of the graph moves to a point twice as far from the y-axis.

Step-by-step explanation:

How does the graph of y = a(x – h)2 + k change if the value of h is doubled?

The vertex of the graph moves to a point twice as far from the x-axis.

because the role of h is to indicate the distance of the vertex from the y-axis.

The vertex of the graph moves to a point half as far from the x-axis.

The vertex of the graph moves to a point half as far from the y-axis.

Transformation involves changing the position of a function.

When h is doubled in [tex]\mathbf{y = a(x - h)^2 + k}[/tex], the vertex of the graph moves to a point twice as far from the y-axis.

The function is given as:

[tex]\mathbf{y = a(x - h)^2 + k}[/tex]

When the value of h is doubled, the new function becomes:

[tex]\mathbf{y' = a(x - 2h)^2 + k}[/tex]

Rewrite as:

[tex]\mathbf{y' = a(x - h- h)^2 + k}[/tex]

The above equation means that:

Function y will be translated to the right by h units

Assume the vertex is:

[tex]\mathbf{Vertex = (2,5)}[/tex]

The new vertex will be:

[tex]\mathbf{Vertex = (4,5)}[/tex]

Comparing the vertices, it means that:

The new function will have its vertex twice as far from the y-axis

Hence, option (b) is correct.

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Answer:

8

Step-by-step explanation:

3x^2 - 4

Let x = 2

3 * 2^2 -4

Exponents first

3 *4 -4

Then multiply

12 -4

Now subtract

8

[tex]\text{Plug in and solve:}\\\\3(2)^2-4\\\\3(4)-4\\\\12-4\\\\8\\\\\boxed{\text{D). 8}}[/tex]

Answer:

c

Step-by-step explanation:

Answer:

x ≈ 5.7

Step-by-step explanation:

Using the Sine rule in Δ WXY

[tex]\frac{WY}{sinX}[/tex] = [tex]\frac{XY}{sinW}[/tex] , substitute values

[tex]\frac{x}{sin33}[/tex] = [tex]\frac{10}{sin107}[/tex] ( cross- multiply )

x sin107° = 10 sin33° ( divide both sides by sin107° )

x = [tex]\frac{10sin33}{sin107}[/tex] ≈ 5.7 ( to the nearest tenth )

Answer:

Step-by-step explanation:

Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.

If the weight of an alloy = x kgs

Then weight of copper = [tex]\frac{9}{7+9}\times (x)[/tex]

                                      = [tex]\frac{9}{16}\times (x)[/tex]

And the weight of zinc = [tex]\frac{7}{7+9}\times (x)[/tex]

                                      = [tex]\frac{7}{16}\times (x)[/tex]

If the weight of zinc = 31.5 kg

31.5 = [tex]\frac{7}{16}\times (x)[/tex]

x = [tex]\frac{16\times 31.5}{7}[/tex]

x = 72 kgs

Therefore, weight of copper = [tex]\frac{9}{16}\times (72)[/tex]

                                               = 40.5 kgs

2). i). 2 : 3 = [tex]\frac{2}{3}[/tex]

        4 : 5 = [tex]\frac{4}{5}[/tex]

Now we will equalize the denominators of each fraction to compare the ratios.

[tex]\frac{2}{3}\times \frac{5}{5}[/tex] = [tex]\frac{10}{15}[/tex]

[tex]\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}[/tex]

Since, [tex]\frac{12}{15}>\frac{10}{15}[/tex]

Therefore, 4 : 5 > 2 : 3

ii). 11 : 19 = [tex]\frac{11}{19}[/tex]

    19 : 21 = [tex]\frac{19}{21}[/tex]

By equalizing denominators of the given fractions,

[tex]\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}[/tex]

And [tex]\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}[/tex]

Since, [tex]\frac{361}{399}>\frac{231}{399}[/tex]

Therefore, 19 : 21 > 11 : 19

iii). [tex]\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}[/tex]

             [tex]=\frac{3}{2}[/tex]

     [tex]\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}[/tex]

              = [tex]\frac{4}{3}[/tex]

Now we equalize the denominators of the fractions,

[tex]\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}[/tex]

And [tex]\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}[/tex]

Since [tex]\frac{9}{6}>\frac{8}{6}[/tex]

Therefore, [tex]\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}[/tex] will be the answer.

IV). [tex]1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}[/tex]

                  [tex]=\frac{6}{5}\times \frac{3}{4}[/tex]

                  [tex]=\frac{18}{20}[/tex]

                  [tex]=\frac{9}{10}[/tex]

Similarly, [tex]\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}[/tex]

                       [tex]=\frac{4}{15}[/tex]                  

By equalizing the denominators,

[tex]\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}[/tex]

Similarly, [tex]\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}[/tex]

Since [tex]\frac{270}{300}>\frac{80}{300}[/tex]

Therefore, [tex]1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}[/tex]

V). If a : b = 6 : 5

     [tex]\frac{a}{b}=\frac{6}{5}[/tex]

        [tex]=\frac{6}{5}\times \frac{2}{2}[/tex]

        [tex]=\frac{12}{10}[/tex]

  And b : c = 10 : 9

  [tex]\frac{b}{c}=\frac{10}{9}[/tex]

 Since a : b = 12 : 10

 And b : c = 10 : 9

 Since b = 10 is common in both the ratios,

 Therefore, combined form of the ratios will be,

 a : b : c = 12 : 10 : 9

Answer:

₹711,674.04

Step-by-step explanation:

1.firstly we need to solve for the total area of Bella's back garden deck.

2. Then we need to estimate mate the total cost of the garden given that a square metre cost ₹5,391.47 to build.

Given

length of garden = 12 metres

width of garden = 11 metres

Hence the area of the garden is given as

[tex]Area= length* width[/tex]

[tex]Area = 12*11= 132m^2[/tex]

if a square metre cost ₹5,391.47 to build.

132 square metre will cost= ₹5,391.47*132= ₹711,674.04

Answer:

49

Step-by-step explanation:

[tex]3x^2+5x-2 = 0[/tex]

Apply discriminant formula : [tex]D = b^2- 4ac[/tex]

[tex]D=discriminant\\b=5\\a=3\\c=-2[/tex]

[tex]D = b^2- 4ac[/tex]

Plug in the values for a, b, and c.

[tex]D = 5^2- 4(3)(-2)[/tex]

Evaluate.

[tex]D = 25- 12(-2)[/tex]

[tex]D = 25- - 24[/tex]

[tex]D=25+24[/tex]

[tex]D=49[/tex]

Answer:

49

Step-by-step explanation:

3x²+5x-2 = 0

This is in the form

ax^2 + bx + c=0

a=3  b=5  c = -2

The discriminant is

b^2 -4ac

5^2 -4(3) (-2)

25 + 24

49

The discriminant is 49

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

y = 7/5x - 3

Comparing with the above formula

Hope this helps you

The value of the slope of the line is 7/5 and the y-intercept is -3

Given the line equation :

The general form of the equation is :

Comparing the equations :

Hence, the slope and y-intercept are 7/5 and -3

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Answer:

15

Step-by-step explanation:

Answer:

21.213

Step-by-step explanation:

Answer:

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Step-by-step explanation:

Step(i):-

Mean of the Population = 8.3 points

Standard deviation of the Population = 0.5 points

Let 'X' be the random variable in normal distribution

Let X = 6.8

[tex]Z = \frac{x-mean}{S.D} = \frac{6.8-8.3}{0.5} = -3[/tex]

Let X = 8.8

[tex]Z = \frac{x-mean}{S.D} = \frac{8.8-8.3}{0.5} = 1[/tex]

The probability that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8) = P(-3≤Z≤1)

                     = P(Z≤1)- P(Z≤-3)

                    =  0.5 + A(1) - ( 0.5 -A(-3))

                   = A(1) + A(3)       (∵A(-3)=A(3)

                  =  0.3413 +0.4986    (∵ From Normal table)

                 = 0.8399

Conclusion:-

The percentage that of people who gave the movie a rating between 6.8 and 8.8

P(6.8≤X≤8.8)  = 83.9≅ 84 percentage

Answer:

C

Step-by-step explanation:

0.1(x - 100)² + 250

0.1[(x - 100)(x - 100)] + 250

0.1(x² -200x + 10000) + 250

0.1x² - 20x + 1000 + 250

0.1x² - 20x + 1250

0.1x² - 25x + 5x + 1250

0.1x(x - 250) + 5(x + 250)

∴ (0.1x + 5)(x - 250) or (0.1x + 5)(x + 250)