The traffic light at the center of town is green for 45 seconds, then yellow for 5 seconds, then red for 40 seconds, at which point the cycle repeats. If a car approaches the traffic light at a random time, what is the probability that the traffic light will be green?
a. 1/9
b. 1/8
c. 1/2
d. 8/9

Check the picture below.

If these two shapes are combined then the new shape is generated. Then the new shape will be given below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A cube and a cylinder are given.

If these two shapes are combined then the new shape is generated. Then the new shape will be

The shape is given below.

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The answer will be D. 7/10 because you have 10 numbers and you want to have a number greater than 3 so it would be 10-3=7 and 7 would go over 10 because there are 7 numbers greater than 3 but less than 10.

The probability he chooses a number greater than 3 is 7/10, the correct option is D.

Probability is the likeliness of an event to happen.

Jalen randomly chooses a number 1-10

Probability = ( No. of favourable outcomes)/ Total Outcomes

The chances of getting the number more than 3 is 7

Total numbers are 10

The probability he chooses a number greater than 3 is 7/10.

Therefore, the correct option is D.

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Answer:

B. 330

Step-by-step explanation:

The question indicates the order doesn't matter, so it's a combination and not a permutation.

The combinations are calculated using this formula:

[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]

In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...

[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]

So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.

Answer:

The correct answer is option B.  330

Step-by-step explanation:

It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.

To find the possible ways

There are total 11 paintings.

We have to choose 4 of them

Possible number of ways = 11C₄

 = (11 * 10 * 9 )/(1 * 2* 3 * 4)

 = 330 ways

Therefore the  correct answer is option B.  330

H(t) = -16t² + vt + s

Where -16 is half of the gravitational constant of almost 32 ft/sec (downward, thus negative),

v is the initial velocity (90), and

s is the starting height (160)

so we have:

H(t) = -16t² + 90t + 160

How long before it hits the ground? Solve for h(t) = 0:

0 = -16t² + 90t + 160

Divide both sides by -2:

0 = 8t² - 45t - 80

Quadratic equation:

t = [ -b ± √(b² - 4ac)] / (2a)

t = [ -(-45) ± √((-45)² - 4(8)(-80))] / (2(8))

t = [ 45 ± √(2025 + 2560)] / 16

t = [ 45 ± √(4585)] / 16

throwing out the negative time:

t = (45 + √4585) / 16

t ≈ 7.04 seconds

-6b > 36

Answer: 55.4

Step-by-step explanation:

The right triangle shown here is a 30-60-90 triangle. This means that its angles measure 30, 60, and 90 degrees. (I got the 30 degrees by subtracting the other two angles from 180 degrees, as the sum of the angle measures in a triangle is 180 degrees.)

The sides in such a triangle have the ratio of x:x[tex]\sqrt{3}[/tex]:2x

The x is across from the 30 degree angle, the x[tex]\sqrt{3}[/tex] is across from the 60 degree angle, and the 2x is across from the 90 degree angle.

The x in this triangle equals to 8 as the eight is across from the 30 degree angle.

This means that the x[tex]\sqrt{3}[/tex] side will equal 8[tex]\sqrt{3}[/tex].

That side is also the height of the triangle. The area of the triangle is then 1/2(8)(8[tex]\sqrt{3}[/tex]), or about 55.4.

Answer:

Tan <A = 1/2

Step-by-step explanation:

SOH CAH TOA

TOA (opposite/adjacent)

So, the answer is 1/2

because the opposite of <A is 1 and the adjacent is 2.

For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:

[tex]tg (A) = \frac {1} {2}[/tex]

Answer:

[tex]tg (A) = \frac {1} {2}[/tex]

Answer:

The answer is the second choice.

Step-by-step explanation:

The value of the domain which is not part of the function is x = -2.

Given data:

The domain of a function is the set of values that are allowed to plug into the function which are the inputs.

The domain of the three line segments is represented as:

Domain of line 1 ranges from [ -5 , -2 ).

Domain of line 2 ranges from ( -2 , 2 ).

Domain of line 3 ranges from [ 2 , 5 ].

So, the value -2 is not included in the domain values of the function.

Hence, x = -2 is not in the domain of function.

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Answer:

Step-by-step explanation:

The sample is not biased.  The members were selected at random from the gym's female population.

The question is biased.  It described the weight lifting machines as "easy" and the free weights as "harder".

The second and third choices are correct.

[tex]

y-15=3x \\

-2x+5y=-3 \\ \\

-2x+y-15=0 /\cdot2 \\

-2x+5y-3=0 /\cdot(-2) \\ \\

-4x+2y-30=0 \\

4x-10y+6=0 \\ \\

-8y-24=0 \\

\boxed{y=-3} \\ \\

-3-15=3x \\

\boxed{x=-6}

[/tex]

The answer is C. (-6, -3)

Hope this helps.

r3t40

For this case we have the following system of equations:

[tex]y-15 = 3x\\-2x + 5y = -3[/tex]

We multiply the first equation by -5:

[tex]-5y + 75 = -15x[/tex]

Now we add the equations:

[tex]-2x-5y + 5y + 75 = -3-15x\\-2x + 75 = -3-15x\\-2x + 15x = -75-3\\13x = -78\\x = \frac {-78} {13}\\x = -6[/tex]

We find the value of the variable "y" according to the first equation:

[tex]y = 3x + 15\\y = 3 (-6) +15\\y = -18 + 15\\y = -3[/tex]

The solution of the system is: (-6, -3)

Answer:

(-6, -3)

Option C

Answer: First option.

Step-by-step explanation:

You can use the inverse tangent function to find the value of the angle T:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

You can identify in the figure that:

[tex]\alpha=T\\opposite=RG=8\\adjacent=TR=15[/tex]

Then, knowing these values, you can substitute them into  [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex].

Therefore, you get that the value of the angle T rounded to the nearest degree is:

[tex]T=arctan(\frac{8}{15})\\\\T=28\°[/tex]

This matches with the first option.

ANSWER

[tex] \lim_{x \to \: a}(x) = a[/tex]

[tex]\lim_{x \to \: a}(a) = a[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

EXPLANATION

For real number 'a',

[tex] \lim_{x \to \: a}(x) = a[/tex]

is true because we have to plug in 'a' for x.

[tex]\lim_{x \to \: a}(a) = a[/tex]

This is also true because limit of a constant is the constant.

[tex]\lim_{x \to \: 5}(4) = 5[/tex]

is false. The correct value is

[tex]\lim_{x \to \: 5}(4) =4[/tex]

[tex]\lim_{x \to \: 5}(x) = 5[/tex]

is also true because we have to substitute 5 for x.

[tex]\lim_{x \to \: a}(a) = x[/tex]

is also false

The limit should be

[tex]\lim_{x \to \: a}(a) = a[/tex]

Answer:

A, B, D

Step-by-step explanation:

Answers for the rest of the quick check

1. A,B,D

2. 16, D

3. 10a, B

4. 3, D

Good Luck :)

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{15}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{15-8}{9-5}\implies \cfrac{7}{4}[/tex]

The graph of inequality have many solution .

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

According to the question

The system of inequalities:

y ≥ 2x – 4

x + 2y ≤ 7

y ≥ -2

x ≤ 1  

values to the graph of inequalities we will have to make inequalities into equal sign

y ≥ 2x – 4

y = 2x – 4

x                    y

0                  -4

1                   -2

2                  0

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x + 2y ≤ 7

x + 2y = 7

x                    y

0                  3.5

1                   3

2                  2.5

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

y ≥ -2

y = -2

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≥ or > is used, shade above the line.

x ≤ 1

x = 1

Now,

As per graph of inequalities rules:

The solid line for ≤ and ≥.If the symbol ≤  or < is used, shade below the line.

Therefore, the darker part in graph  is  common part of all 4 inequalities with point (1,-2) and (1,3) .

Hence, The graph of inequality have many solution .

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Answer:

  C.

Step-by-step explanation:

The mapping for 90° counterclockwise rotation is ...

  (x, y) ⇒ (-y, x)

If we consider how this applies to points X and Y, which both have a y-coordinate of 0 and a negative x-coordinate, (-a, 0), for example, we see it maps to ...

  (-a, 0) ⇒ (0, -a)

That is, both points X' and Y' will be on the negative y-axis. The only figure showing this is figure C.

______

Comment on the other answer choices

Figures A and D show clockwise rotation. In Figures A and B, the rotation is not about the origin, but is about a different point. (In Figure B, the points easy to consider are the ones on the -x axis, points X and Z. They should appear on the -y axis after rotation, but do not.)

if you add 3 to it it would be 6

Final answer:

The minimum cost of production for the company is $260 for 70 dolls.

Explanation:

The minimum cost of production for the company can be determined by examining the options given. The correct statement is:
The minimum cost of production is $260 for 70 dolls.

In the given function, the cost of production is represented by the variable x. The equation cost = 50 + 10x describes the cost of producing x number of dolls. By substituting x with 70 in the equation, we can calculate the cost as follows:

Cost = 50 + 10 * 70 = 50 + 700 = $750

Therefore, the minimum cost of production for the company is $260 for 70 dolls.

Answer:

1/2x+y=-4

Step-by-step explanation:

Answer:

x + 3y = - 8

Step-by-step explanation:

Given

y = - [tex]\frac{1}{2}[/tex] x - 4

Multiply all terms by 2

2y = - x - 8 ( add y to both sides )

x + 2y = - 8 ← in standard form

The answer is:

The maximum height before landing will be 69.7804 feet.

Since there is no information about the angle of the launch, we can safely assume that it's launched vertically.

So, we can calculate the maximum height of the pumpkin using the following formulas:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]v=vo-gt[/tex]

Where,

y, is the final height

[tex]y_o[/tex], is the initial height

g, is the acceleration of gravity , and it's equal to:

[tex]g=32.2\frac{ft}{s^{2} }[/tex]

t, is the time.

Now, we are given the following information:

[tex]y_{o}=12ft\\\\v=61\frac{ft}{s}[/tex]

Then, to calculate the maximum height, we must remember that at the maximum height, the speed tends to 0, so, calculating we have:

Time calculation,

We need to use the following equation,

[tex]v=vo-gt[/tex]

So, substituting we have:

[tex]v=61\frac{ft}{s}-32.2\frac{ft}{s^{2}}*t\\\\-61\frac{ft}{s}=-32.2\frac{ft}{s^{2}}*t\\\\t=\frac{-61{ft}{s}}{-32.2\frac{ft}{s^{2}}}=1.8944s[/tex]

We know that it will take 1.8944 seconds to the pumpkin to reach its maximum height.

Maximum height calculation,

Now, calculating the maximum height, we need to use the following equation:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

Substituting and calculating, we have:

[tex]y=y_o+v_{o}*t-\frac{1}{2}gt^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}[/tex]

[tex]y=12ft+61\frac{ft}{s}*1.8944s-\frac{1}{2}32.2\frac{ft}{s^{2}}*(1.8944s)^{2}\\\\y_{max}=12ft+115.5584ft-16.1\frac{ft}{s^{2}}*(3.5887s^{2})\\\\y_{max}=127.5584ft-57.7780ft=69.7804ft[/tex]

Hence, we have that the maximum height before the landing will be 69.7804 feet.

Have a nice day!

Answer:

x=4

Step-by-step explanation:

16-4=12

3x=12

3*4=12

Answer: [tex]x=4[/tex]

Step-by-step explanation:

You need to find the value of the variable "x".

To solve for "x", the first step is to apply the Subtraction property of equality, which states that:

[tex]If\ a=b\ then\ a-c=b-c[/tex]

Then, you need to subtract 4 from both sides of the equation:

[tex]3x + 4 = 16\\3x + 4-4 = 16-4\\3x=12[/tex]

And finally, you can apply the Division property of equality, which states that:

[tex]If\ a=b\ then\ \frac{a}{c}=\frac{b}{c}[/tex]

Then you can divide both sides of the equation by 3, getting:

[tex]\frac{3x}{3}=\frac{12}{3}\\\\x=4[/tex]

The given function y=0.8^x is an exponential decay function. It's end behavior is defined such that as x grows significantly large, y approaches 0, and as x becomes significantly negative, y approaches infinity.

The function

represents exponential decay because the base (0.8) is between 0 and 1. When the base of the power function is in this range, it results in a decreasing or 'decay' function. This contrasts with an exponential growth function, where the base would be greater than 1.

Regarding the end behavior of this function, we can analyze it using the concept of limits. As x approaches positive infinity (x -> +∞), y will approach zero (y -> 0) because a fraction (0.8 in this case) to a large power tends to zero. This illustrates the decay aspect of the function. Conversely, as x approaches negative infinity (x -> -∞), y will approach positive infinity (y -> +∞).

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The function y = 0.8^x is an exponential decay function. As x increases, y decreases exponentially. The end behavior of the function is that it approaches 0 as x approaches positive and negative infinity.

The function y = 0.8^x is an exponential decay function. In an exponential decay function, the base is between 0 and 1, and as x increases, y decreases exponentially. This function represents the decay of a quantity over time, where the quantity is decreasing by 20% for each unit increase in x.

Regarding the end behavior and limits, as x approaches positive and negative infinity, the function approaches 0. This means that the y-values get closer and closer to 0 as x becomes larger and smaller. In other words, the function approaches the x-axis but never reaches it.

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Answer:

Use the hyper link

Step-by-step explanation:

I took a picture on the unit.

Answer:

A.The longer leg is √3 times as long as the shorter

B. The hypotenuse is twice as long as the shorter leg

Step-by-step explanation:

The 30-60-90 is a special triangle with two acute angles 30° and 60°

The side across from the 30°= shorter leg

The side across from 60°=longer leg

The side across from 90°=hypotenuse

If we take the shorter side to be x and hypotenuse to be 2x then the  longer leg will be;

Apply Pythagorean relationship

a² + b² =c²

c²-a²=b² where-----------c=2x and a=x

(2x)² - x² = b²

4x² - x² =b²

3x² = b²

√3x²=b

x√3 =b

Hence longer leg is √3 times longer than the shorter leg which is x and the hypothenuse 2x is twice the shorter leg which is x

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

* lets revise the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the y-axis is

  (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are ( h ± a , k )  

- The coordinates of the co-vertices are ( h , k ± b )

- The coordinates of the foci are (h , k ± c), where c² = a² + b²

* Now lets solve the problem

∵ The equation of the hyperbola of vertex (h , k) is

    (y - k)²/a² - (x - h)²/b² = 1

∵ The equation is (y - 2)²/3² - (x - 2)²/4² = 1

∴ k = 2 , h = 2 , a = 3 , b = 4

∵ The foci of it are (h , k + c) and (h , k - c)

- Lets find c from the equation c² = a² + b²

∵ a = 3

∴ a² = 3² = 9

∵ b = 4

∴ b² = 4² = 16

∴ c² = 9 + 16 = 25

∴ c = √25 =  5

- Lets find the foci

∵ The foci are (h , k + c) and (h , k - c)

∵ h = 2 , k = 2 , c = 5

∴ The foci are (2 , 2 + 5) and (2 , 2 - 5)

∴ The foci are (2 , 7) and (2 , -3)

Answer:

The foci are (2 , 7) and (2 , -3)

Step-by-step explanation:

Zoe will need 84 pieces if they are 6” by 6”

For this case we have that by definition, 1 foot equals 12 inches.

So:

[tex]3 \ ft = 36 \ in\\7 \ ft = 84 \ in[/tex]

So, the area of the Zoes carpet is:

[tex]A = 36 * 84 = 3024 \ in ^ 2[/tex]

If the cardboard pieces are[tex]6 \ in\ by\ 6 \ in[/tex], then the area is:

[tex]36 \ in ^ 2[/tex]

To indicate the number of necessary pieces we divide:

[tex]\frac {3024} {36} = 84[/tex]

Thus, 84 pieces of cardboard are needed

Answer:

84

Answer:

  g(10) is undefined

Step-by-step explanation:

A vertical asymptote is a place where a function is literally undefined. That is commonly because the function is a rational function with a denominator of zero at that point (division by zero is undefined), but it can also be for any of a variety of other reasons.

Answer:

4 and -4

Step-by-step explanation:

> means greater than

x² > 10

4² > 10 → True, 16 is greater than 10

-4² > 10 → True, 16 is greater than 10

Answer:

Step-by-step explanation:

Use the distance formula for coordinate geoemetry and the fact that x1 = 3, y1 = 5, x2 = 6 and y2 = 8 to fill in the formula:

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }[/tex]

fills in accordingly:

[tex]d=\sqrt{(6-3)^2+(8-5)^2}[/tex]

which simplifies a bit to

[tex]d=\sqrt{(3)^2+(3)^2}[/tex]

which is

[tex]d=\sqrt{18}[/tex]

The square root of 18 simplifies down to [tex]3\sqrt{2}[/tex], which is 4.2426 in decimal form

Answer:

4.24 units

Step-by-step explanation:

We can use the distance formula to solve this.

Distance formula: d = √((x₁ - x₂)² + (y₁ - y₂)²), where (x₁, y₁) and (x₂, y₂) are the two coordinates.

Plug in: d = √((3 - 6)² + (5 - 8)²)

Subtract: d = √((-3)² + (-3)²))

Square: d = √(9 + 9)

Add: d = √18

Square root: d = 4.24264... ≈ 4.24 units

Simplify brackets

7 + 1

Simplify

8

Answer: C. 8

Answer:

minus and minus is plus

7+ 1 is 8 :)

Answer:

6 × 8

Step-by-step explanation:

Since the dilation factor is 4, and the image was ENLARGED, that means the original photo was smaller.  Smaller by a factor of 4.

So, we take the new dimensions (24x32) and we divide each side by the dilation factor of 4:

(24/4) x (32/4) = 6 x 8

It couldn't be the first answer choice (3x8) because  that doesn't maintain the ratio of the enlarge picture.  The other possible answers do match the right ratio... but only 6x8 is scaled by a factor of 4.

Answer:

6 x 8

Step-by-step explanation:

When you look at DQ,4 and you break it apart a little bit, you will realize that the dilation is 4 and in this case it will increase by 4.

(Don't mind the Q it is just there to tell you where the center point is)

So if you look at the options:

3 x 8  ---- that will not work because 3x4= 12 which is not 32 and not 24 so we should kick that one out.

6 x 8  ---- This is good because 6x4=24 and 8x4=32!

We don't have to go any further (you can if you want though)!

Again, 6 x 8 is your answer.

Answer:

[tex]AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm[/tex]

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

[tex]AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm[/tex]

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

[tex]\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD[/tex]

Consider right triangle CAH.By the Pythagorean theorem,

[tex]CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8[/tex]

The length cannot be negative, so CD=8 cm and

[tex]CA=\sqrt{3}CD=8\sqrt{3}\ cm[/tex]

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

[tex]AB=2CA=16\sqrt{3}\ cm[/tex]

By the Pythagorean theorem,

[tex]BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm[/tex]