the state transportation department is conducting a study on the length of green lights in a certain city. the green lights' lengths are normally distributed with a mean of 45 seconds and a standard deviation of 15 seconds. how many seconds separate the lowest 24% of the means from the highest 76% in a sampling distribution of 75 traffic lights? use the z-table below.

the particular solution to the differential equation. we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]

To find the particular solution to the differential equation {dy}/{dx} = (x+1) (y+1) with the initial condition y(4) = 3, we can use separation of variables and integration.

First, we can rewrite the equation as:

[tex]{1}/{(y+1)} dy = (x+1) dx[/tex]

Next, we can integrate both sides:

[tex]∫ {1}/{(y+1)} dy = ∫ (x+1) dx[/tex]

[tex]ln|y+1| = 1/2 x^2 + x + C[/tex]

where C is the constant of integration.

To determine the value of C, we can use the initial condition y(4) = 3:

[tex]ln|3+1| = 1/2 (4)^2 + 4 + C[/tex]

[tex]ln|4| = 10 + C[/tex]

[tex]C = ln|4| - 10 = -5.605[/tex]

Therefore, the particular solution to the differential equation with the initial condition y(4) = 3 is:

[tex]ln|y+1| = 1/2 x^2 + x - 5.605[/tex]

Solving for y:

[tex]|y+1| = e^(1/2 x^2 + x - 5.605)[/tex]

[tex]y+1 = \pm e^(1/2 x^2 + x - 5.605)[/tex]

[tex]y = -1 \pm e^(1/2 x^2 + x - 5.605)[/tex]

Since [tex]y(4) = 3[/tex], we can determine which sign to use:

[tex]3 = -1 + e^(1/2 (4)^2 + 4 - 5.605)[/tex]

[tex]3 = -1 + e^(7.395)[/tex]

[tex]4 = e^(7.395)[/tex]

Therefore, we use the positive sign: [tex]y = -1 + e^(1/2 x^2 + x - 5.605)[/tex]

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Answer:

Growth & 36.2%

Step-by-step explanation:

Exponential Growth Formula

A = A0 (1 + r)^t

A is the amount after certain number years

A0 is the initial amount

r is the rate

t is the number of years

Growth models are identified by the number between the parenthesis. If the number is greater than 1, then it represents a growth model. If the number is less than 1, then it represents a decay model.

To find the percentage by which it increases, you would simply convert the decimal. 1.362 becomes 36.2%. You move the decimal point two places to the right and add a percentage symbol next to it.

The mean number of adults who have hypertension in a sample of 25 adults is 8.75, assuming the national survey-reported percentage of adults with hypertension (35%) applies to the sample.

The mean number of adults who have hypertension in the sample of 25 can be calculated by multiplying the sample size (25) by the population proportion (0.35). Mathematically,

Mean = n * p = 25 * 0.35 = 8.75

Therefore, the mean number of adults who have hypertension in the sample is 8.75. Note that this is an expected value and there may be variability around this mean in different samples.

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In the last 10 softball games, the mode number of runs for Delisa is 3.

Mode is the value that appears most frequently in a given data set. It is one of the three measures of central tendency, along with mean and median.

To find the mode, we need to determine which number appears most frequently in the data set. In this case, the number of runs that Delisa scored in each game.

We have been given the data points,

2,1,3,3,1,3,2,4,3,5

The number 3 appears most frequently, occurring three times. Therefore, the mode number of runs for Delisa is 3.

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The distance between the points (15, -17) and (-20, -5) is 37.

The distance formula is a mathematical formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem and can be used to find the distance between any two points, whether they are on the same line or on different lines.

We can use the distance formula to find the distance between two points:

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

Let [tex]\rm (x_1,y_1)[/tex] = (15,-17) and [tex]\rm (x_2, y_2)[/tex] = (-20,-5)

Then, plugging into the formula, we get:

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

[tex]\rm = \sqrt{(-20-15)^2 + (-5-(-17))^2}[/tex]

[tex]= \sqrt{(-35)^2 + (12)^2}[/tex]

[tex]= \sqrt{1225+144}[/tex]

[tex]= \sqrt{1369}[/tex]

= 37

Therefore, the distance between the points (15, -17) and (-20, -5) is 37.

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Complete question:

Find the distance between point (15,-17) and (-20,-5).

Answer:

186 inches

Step-by-step explanation:

8×6=48

5.5×16=88

10×5=50

48+88+50=186

Brooklyn have to pay total for the 11 rides is $43 and for r rides she have to pay is $10+$3×r.

If Brooklyn goes on 11 rides, she will have to pay $10 for admission and $3 for each of the 11 rides she goes on. So her total cost would be:

$10 + (11 rides x $3/ride) = $10 + $33 = $43

If she goes on r rides, her total cost would be:

$10 + (r rides x $3/ride) = $10 + $3r

So, for example, if she goes on 15 rides, her total cost would be:

$10 + (15 rides x $3/ride) = $10 + $45 = $55

An arithmetic expression is a combination of numbers, operators (such as +, -, x, ÷), and parentheses that can be evaluated to produce a numerical result.

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Option D is the correct option i.e., 2.5 hours. Timing is everything when it comes to dining before a fight. Athletes must ingest enough calories to power their efforts without developing gastrointestinal pain or bloating while competing. Typically, a substantial dinner should be eaten two to three hours prior to the game. 

The body needs time to process and assimilate nutrients, which is the cause of this. A big dinner requires the body to divert a lot of blood flow to the digestive system, which can have an impact on an athlete's performance. Athletes' performance can be hampered by sluggishness, gastrointestinal pain, or even vomiting brought on by eating too close to a competition.

In general, it is recommended that athletes experiment with different meal timings and types of food during their training to determine what works best for their individual needs.

They should also consider the length of the event and the intensity of their activity to determine the amount and timing of their meals. A registered dietitian or sports nutritionist can help athletes create a personalized nutrition plan to optimize their performance.

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It is important to carefully read and understand the information given in the problem, as well as to apply the appropriate formulas and properties to find the solution

Sure, I'll be happy to help you with your question. In order to find the measure of the missing angle and arc, we first need to know what type of angle and arc we are dealing with. If it is a central angle and arc, then the measure of the angle is equal to the measure of the arc. However, if it is an inscribed angle and arc, then the measure of the angle is half the measure of the arc.

Once we have determined the type of angle and arc, we can use the given information to solve for the missing measure. For example, if we are given the measure of the angle and the measure of the arc, we can use the formula for the measure of a central angle or inscribed angle to solve for the missing measure.

Alternatively, we can also use the properties of circles, such as the fact that the sum of the angles in a triangle is 180 degrees and the fact that the angle at the center of a circle is twice the angle at the circumference, to solve for the missing measure.

In any case, . With enough practice and familiarity with these concepts, you can become proficient at solving problems involving missing angles and arcs.

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The value of x in the given right triangle can be found with help of trigonometric-ratios, given an angle 16° and hypotenuse 37 units is 35.566657. On rounding off to nearest tenths we get 35.6 units.

What are trigonometric-ratios?

In a given right triangle, the ratios of different sides are represented as six trigonometric ratios which are cosine,sine,cosecant,cot,secant and tan.

Sin of an angle=[tex]\frac{side opposite to the angle}{hypotenuse of triangle}[/tex]

Cosine of an angle=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

tan of an angle= [tex]\frac{side opposite to the angle}{side adjacent to the angle}[/tex]

And cosecant, secant and cot are the reciprocals of sine, cosine & tan respectively.

Here,on naming the given right triangle we can see that

∠A = 16° , AC=37 units and Side AB= x units

Applying cosine of angle  16°, we get

cos A=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

Cos 16°=[tex]\frac{side adjacent to the angle}{hypotenuse of the triangle}[/tex]

Cos  16°= [tex]\frac{AB}{AC}[/tex]

0.961261= [tex]\frac{AB}{AC}[/tex] {Cos  16°=0.961261}

0.961261=[tex]\frac{x}{37}[/tex]    {AB=x and AC=37}

           x = 0.961261 (37)

           x = 35.566657

On rounding off to nearest tenths x=35.6 units

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Refer to the attachment for complete question & naming of triangle.

The reflection that occurred is over the x-axis.

Based on the given coordinates, it can be observed that each point of the pre-image was reflected over the x-axis, resulting in a new image. Therefore, the type of reflection that occurred is a reflection over the x-axis.

To explain this with equations, we can use the transformation formula for a reflection over the x-axis:

(x, y) → (x, -y)

Using this formula, we can find the image coordinates of the pre-image points:

A' = (-1, -8)

B' = (5, 3)

C' = (-5, 1)

As we can see, the y-coordinates of each point have been negated, indicating a reflection over the x-axis. Therefore, the type of reflection that occurred is a reflection over the x-axis.

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Answer:

can u break that down

Step-by-step explanation:

Answer: 2^12

4^6

64^2

the cube root of 4,096

256 times 2

8^6

65,536/4

16 times 16 times 16

256 cubed root of 256

256/16^4

64 times 4 times 2

Step-by-step explanation: All of these expressions are equal to 16 cubed, which is 4,096.

Answer:

4096 have a nice day

Step-by-step explanation:

pl z mark me brianliest :)

The number completes the number sentence 3m= 5g.

The m refers the meatball which prices $2.50

so for 3m = 3*2.50

          3m = $7.5

g refers to grilled cheese which prices $1.50

so we have to find for how many grilled cheese which equals $7.5

On dividing we get, 7.5/1.50 = 5

Hence 3 meatballs equal 5 grilled cheese, 3m = 5g

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Solving the statement, we get the equation x=2.5-y

Exponents are a mathematical notation used to represent repeated multiplication of a number by itself. Exponents are written as a superscript to the right of the base number, which is the number being multiplied.

given equation:

3²ˣ × [tex]9^{y}[/tex] = 243

Simplifying the expression on the right-hand side, we get:

3²ˣ × [tex]9^{y}[/tex]  = 3⁵

Using the property of exponents that states that when multiplying powers with the same base, we can add their exponents, we get:

[tex]3^{2x+2y}[/tex] = 3⁵

For the equation to hold, the exponents on both sides must be equal. Therefore:

2x + 2y = 5

Dividing both sides by 2, we get:

x + y = 2.5

x=2.5-y

Hence, solving the statement, we get the equation x=2.5-y

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In the histogram , the number of students in Ms. Gioia's class took the science test is 27.

What is histogram?

A grouped frequency distribution with continuous classes is graphically represented by a histogram. It is an area diagram, and its size is proportional to the frequencies in the associated classes. Due to the base's coverage of the spaces between class boundaries, all of the rectangles in such representations are contiguous.

Here according to the histogram ,

The number of students score between 71-75 = 4

The number of students score between 76-80 = 6

The number of students score between 86-90 =8

The number of students score between 91-95 = 7

The number of student score between 96-100 = 2

Then number of students in Ms. Gioia's class took the science test is,

=> 4+6+8+7+2 = 27

Hence the number of students in Ms. Gioia's class took the science test is 27.

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Thus, it will take 4 days time for the Lester to spend on preparing the jar of 40 liters of jam.

If we were to assume that we had any two quantities (as well as 2 entities) and that we were tasked with figuring out their ratio, the ratio formula would be defined as a: where b = a/b

Given data:

Time to jam 30 liters ---> 3 days.

Time to jam 40 litres ---> x days (say)

Then, taking the proportion,

30 lit / 3 day = 40 lit / x days

x = 3*40 / 30 days

x = 4 days

Thus, it will take 4 days for the Lester to spend on preparing the jar of 40 liters of jam.

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a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). Inequalities can be used to describe a range of values that a variable can take, rather than just a single value.

a. Mason's error is that he flipped the inequality sign. The correct solution is x > 6.

b. To show the correct solution on the number line, we start by marking 6 on the number line with an open circle (since x is not equal to 6). Then, we shade the area to the right of 6, because x is greater than 6. The graph should look like this:

0 1 2 3 4 5 6o 7 8 9

--------

shaded

This indicates that any value of x greater than 6 (but not equal to 6) will satisfy the inequality x > 6.

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Based on the calculations using z-scores, we can conclude that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.

What is Coffee Haven?

"Coffee Haven" was used as an example name for one of the coffee shops in a previous question. It is not an actual coffee shop. The name was used to illustrate a point about comparing the sugar content of drinks between different coffee shops.

To compare the sugar content of the Grande Mocha Cappuccino between the two coffee shops, we can use z-scores to standardize the sugar content based on the mean and standard deviation of each shop's drinks.

For the first coffee shop, let's call it Coffee Haven, we know that the mean sugar content is 20g with a standard deviation of 8g. Therefore, the z-score for the Grande Mocha Cappuccino at Coffee Haven is:

z = (13 - 20) / 8 = -0.875

For the second coffee shop, Ruth's Roast's, we know that the mean sugar content is 16g with a standard deviation of 6g. Therefore, the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is:

z = (13 - 16) / 6 = -0.5

Comparing the two z-scores, we see that the z-score for the Grande Mocha Cappuccino at Ruth's Roast's is greater than the z-score for the Grande Mocha Cappuccino at Coffee Haven. This means that the Grande Mocha Cappuccino at Ruth's Roast's has less sugar relative to the other drinks at its respective store than the Grande Mocha Cappuccino at Coffee Haven.

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Answer: The answer is C, f(x) = 2x^2 + 3.

Step-by-step explanation: Check the graph below.

Answer:

a) 0.128 b) 0.51 c) 7.27

Step-by-step explanation:

a)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

= 0.1275….

b)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

0.1275… (4) = 0.51

c)

Lower Bound: 176

Upper Bound: 99999

μ: 143

σ: 29

0.1275… (57) = 7.27

72 books were divided up among 18 children means 18 kids and 72 books equal 4 books for each youngster.

An element of a whole is a portion. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a straightforward fraction. A fraction appears in the numerator or denominator of a complicated fraction. The numerator of a perfect fraction is less than the denominator.0

1) 8/3 split by 6/9: To begin, we divide both the numerator and denominator by 3 to reduce 6/9 to 2/3.

8/3 ÷ 2/3 = (8/3) x (3/2) = 4

The fraction we began with is not equivalent to this expression.

2) 8/3 times 2/3: By multiplying the numerators and denominators, we can reduce this expression:

(8/3) x (2/3) = 16/9

The fraction we began with is not equivalent to this expression.

3) 2/9 split by 8/9: We multiply the first fraction by the reciprocal of the second fraction to divide fractions:

(2/9) ÷ (8/9) = (2/9) x (9/8) = 1/4

The fraction we began with is not equivalent to this expression.

4) In order to simplify this equation, let's first reduce 8/2 to 4:

2 x 4 = 8

The fraction we began with is not equivalent to this expression.

The fraction that accurately describes the circumstance cannot be expressed using any of the given expressions.

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Answer:

2.5

Step-by-step explanation:

51x - 19.5 + 19.5 = 108 + 19.5

51x = 127.5

x = 127.5/51

= 2.5

Using functions,

a) 1. 48

2. 21

3. 75 - 4.5w

b) r = 75 - 4.5w

c) Graph is attached.

d) The restaurant has 30kgs of rice after 10 weeks.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here as per the question,

a)

1. 75 - (4.5 × 6)

= 75 - 27

= 48

2. 75 - (4.5 × 12)

= 75 - 54

= 21

3.  75 - (4.5 × w)

= 75 - 4.5w

b)

r = 75 - 4.5w

c) Image is attached for the graph.

d) 30 = 75 - 4.5w

Subtracting both sides by 30:

⇒ 0 = 75 - 4.5w - 30

Adding both sides by 4.5w:

⇒ 4.5w = 75 - 30

⇒ 4.5w = 45

Dividing both sides by 4.5:

⇒ w = 45/4.5

⇒ w = 10.

Therefore, the restaurant has 30kgs of rice after 10 weeks.

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The complete question is:

b. Use function notation to write a rule

that defines function r.

c. On the coordinate plane, sketch a

graph of function r.

d. Solve the equation r(u) = 30 and

explain what the solution means in

this situation.

According to given c represents the initial number οf birds οn the island

A pοlynοmial οf degree twο in οne οr mοre variables is referred tο as a quadratic pοlynοmial. The pοlynοmial functiοn that a quadratic pοlynοmial defines is knοwn as a quadratic functiοn.

functiοn represents a quadratic mοdel fοr the bird pοpulatiοn, we can write it in standard fοrm as:

f(t) = at² + bt + c

where a, b, and c are cοnstants.

Substituting t = 0 in the standard fοrm οf the quadratic functiοn, we get:

f(0) = a(0)² + b(0) + c

f(0) = c

Therefοre, the value οf c in the standard fοrm οf the quadratic functiοn represents the number οf birds present οn the island when cοunting first started.

Sο, the fοrm that reveals the number οf birds present οn the island when cοunting first started is the standard fοrm. f(t) = at²+ bt + c

where c represents the initial number οf birds οn the island.

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If ∠1 and ∠2 are vertical angles and m∠22 = 180°, then m∠1 = 90°

Vertical angles are pairs of angles that are opposite to each other when two lines intersect. Vertical angles are always equal in measure. Therefore, if ∠1 and ∠2 are vertical angles, then:

∠1 = ∠2

We are also given that m∠22 has a measure of 180°. Since ∠1 and ∠2 are vertical angles, they form a straight line, and their measures add up to 180°. Therefore:

∠1 + ∠2 = 180°

Since ∠1  = ∠2, we can substitute ∠1 for ∠2 in the above equation:

∠1 + ∠1 = 180°

Simplifying the equation, we get:

2∠1 = 180°

Dividing both sides by 2, we get:

∠1 = 90°

Therefore, ∠1 has a measure of 90°.

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The stratified random sampling is a method of various strata are selected from the sample. So, the right choice for answer is option(c).

The four probability sampling methods mainly applied in research methods include simple random sampling, cluster sampling, stratified sampling, and systematic sampling. In certain situations, we need to remove the sampling bias, and for that, we opt for stratified random sampling. Here we talking about stratified random sampling. A method of probability sampling (where all members of the population have an equal chance of being included) Population is divided into 'strata' (sub populations) and random samples are drawn from each. Therefore, the required choice is option (c), that is various strata are selected from the sample.

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The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.

The student question asks about the probability that the car manufacturer's claim of the hybrid car traveling at speeds more than 60 mpg is valid. The actual mpg is approximately normally distributed with a mean of 52 miles and a standard deviation of three miles.
To calculate the probability, we will use the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the Z-score
X is the value we want to find the probability for (in this case, 60 mpg)
μ is the mean (52 miles)
σ is the standard deviation (3 miles)
Plug in the values into the Z-score formula:
Z = (60 - 52) / 3
Calculate the Z-score:
Z = 8 / 3 ≈ 2.67
Now we have the Z-score of 2.67, which tells us how many standard deviations above the mean the value of 60 mpg is. The next step is to use a Z-table (also known as the standard normal table) to find the probability.
Look up the Z-score in the Z-table:
For a Z-score of 2.67, the corresponding probability in the Z-table is 0.9963.

This means that 99.63% of the data falls below 60 mpg.
Find the probability that the claim is valid:
Since we want to find the probability that the car travels at speeds more than 60 mpg, we need to find the area to the right of the Z-score in the normal distribution curve. To do this, we subtract the probability from 1
Probability = 1 - 0.9963 = 0.0037
The probability that the manufacturer's claim is valid is 0.0037, or 0.37%.

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