e speeds of vehicles on a highway with speed limit 100 km/h are normally distributed with mean 115 km/h and standard deviation 9 km/h. (round your answers to two decimal places.)(a)what is the probability that a randomly chosen vehicle is traveling at a legal speed?3.01 %(b)if police are instructed to ticket motorists driving 120 km/h or more, what percentage of motorist are targeted?

There are 13,992 integers between 1 and 1,000,000 with a sum of digits equal to 15.

To find the number of integers between 1 and 1,000,000 with a sum of digits equal to 15, we can use a combinatorial approach.

We need to distribute the sum of 15 among the digits of the number. We can think of this as placing 15 indistinguishable balls into 6 distinct boxes (corresponding to the digits).

Using the stars and bars method, the number of ways to distribute the sum of 15 among 6 boxes is given by the combination formula:

C(n + r - 1, r - 1)

where n is the sum (15) and r is the number of boxes (6).

Plugging in the values, we have:

C(15 + 6 - 1, 6 - 1) = C(20, 5)

Calculating this combination, we find:

C(20, 5) = 13,992

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Answer:

-18w^2 + 6w - 4

Explanation:

Given the expression (6w — 11w^2)-(4+7w^2)

Open the bracket

6w — 11w^2 - 4 - 7w^2

= -11w^2-7w^2 + 6w -4

= -18w^2 + 6w - 4

Hence the required expansion is -18w^2 + 6w - 4

Answer:

a=10.35

Step-by-step explanation:

Hey There!

All you have to do is plug in the L and W value

a= 4.5(2.3)

4.5x2.3=10.35

so a=10.35

The 98% confidence interval estimate of the population mean is

15.823 < μ < 22.177

In the given situation the wind on a random day in Bryan  is normally distributed with the following values;

Standard Deviation = ( δ ) = 5.1 mph

A random day of 16 is taken into account for the consideration of Bryan's average value of 19mph.

n = 16

By taking the confidence level of T - Factor, we get the;

At a 98% confidence level, the t is,

tα /2,df = t₀.₀₄,₂₄ = 2.492                ( df = hours in a day)

Margin of error = E = tα/2,df * (δ /√n)

                              = 2.492 * (5.1 / √16)

                              = 3.177

The 98% confidence interval estimate of the population mean is,

x - E < μ < x + E

19 - 3.177 < μ < 19 + 3.177

15.823 < μ < 22.177

The 98% confidence interval estimate of the population mean is

15.823 < μ < 22.177

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Answer:

It is already simplified

Step-by-step explanation:

0.09375 in decimals

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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The researcher should consider the following steps when creating the two groups: Random assignment, Pairing students with similar abilities, Controlling for potential confounding variables,

Collecting data and analyzing results.
Random assignment:

To minimize any potential bias, the researcher should randomly assign one student from each pair to receive extra homework problems while the other does not.
Pairing students with similar abilities:

In order to make a valid comparison, the researcher should pair students with similar algebra skills or previous performance in the subject.

This way, any observed differences in the test results are more likely to be due to the extra homework rather than differences in ability.
Controlling for potential confounding variables:

The researcher should control for any other factors that could influence students' algebra test results, such as attendance, study habits, and teacher quality.

After the two-week period, the researcher should collect the test scores of both groups and compare their performance.

This can be done using statistical methods, such as a paired t-test, to determine if there is a significant difference between the groups.

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In the formulas for constructing interval estimates based on sample proportions, the expression Pu (l - Pu) has a maximum value of 1/4.Let's discuss interval estimates based on sample proportions first. A proportion is the number of items in one category divided by the total number of items in all categories.

A sample is a smaller version of a population that we use to gather data and infer characteristics about the population. A confidence interval is a range of values that contains the true population parameter with a certain level of confidence. When we want to estimate the proportion of a population that has a certain characteristic, we use a sample proportion to estimate it.

A formula is used to construct a confidence interval around the sample proportion. The formula for constructing interval estimates based on sample proportions is given by: Lower Bound: P - zα/2 * sqrt(PQ/n)Upper Bound: P + zα/2 * sqrt(PQ/n)Where P is the sample proportion, Q is (1 - P), n is the sample size, and zα/2 is the z-score corresponding to the desired level of confidence. The expression Pu (l - Pu) has a maximum value of 1/4.

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Answer:

amount = £1415.57  

Step-by-step explanation:

given data

computer buy = £1600

depreciates rate = 4% per year

time = 3 year

solution  

we get here amount that is express here as

amount = P × \((1-r)^{t}\)    ...................................1                                    

here r is rate and t is time put here value

amount will  be              

amount = 1600 × \((1-0.04)^{3}\)  

solve it we get

amount = £1415.57  

Answer:  The level of the dose be after 3 hours=  0.03125 mg.

Step-by-step explanation:

General exponential decay equation : \(y=A(1-r)^x\) , where A = initial value , r= rate of decay , x =Time period.

Here, drug’s effectiveness  is decreasing exponentially.

AS per given , we have

A= 250 mg

x=3

r= 95% = 0.95

Then, \(y=250(1-0.95)^3 = 250(0.05)^3=250*0.000125=0.03125\)

Hence, the level of the dose be after 3 hours = 0.03125 mg.

Answer:

214.34 about (213.75 on calculator)

Step-by-step explanation:

95% of 250=237.5

95% of 237=225.15

95% of 225=213.75

Answer: D) 32

the second answer is C) 2

Step-by-step explanation: 4+2.4 = 6.4 * 12= 76.8/2.4=32

6-4= 2 * 3= 6/3=2

Answer:

Step-by-step explanation:

To answer these question we have to substitute the values we are given into the question!

1) \(\frac{12(x+y)}{y}\)

We are told that x is 4 and y is 2.4, this makes our question\(\frac{12(4+2.4)}{2.4}\)

Now we can solve it!

The answer is 32!

2) \(\frac{3(a-4)}{b}\)

We are told that a is 6 and b is 3, this make our question \(\frac{3(6-4)}{3}\)

Now can solve it!

Hope this helps, have a lovely day! :)

Answer:

69 plus 45 mius 450 equals 98

a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.

b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.

a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.

X^2 + 3x + 2.25 = (x + 1.5)^2

The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.

b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:

X^2 + 0.6x + 0.09 = (x + 0.3)^2

The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.

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The algebraic expression for the word phrase is 12 + z/4

The word phrase is given as:

twelve more than the quotient of a number z and 4

The quotient of a number z and 4 is represented as:

z/4

So, we have:

twelve more than z/4

twelve more means 12 +

So, we have:

12 + z/4

Hence, the algebraic expression for the word phrase is 12 + z/4

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Answer:

see explanation

Step-by-step explanation:

Given f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Given g(x) = \(7^{x}\) + 5

Then this is the graph of f(x) shifted vertically up by 5 units

Mr. Brust needs 427 cans to cover the wall of dimensions 20 feet long and 9 feet tall.

Area of rectangle is the product of its sides

i.e., Area of rectangle = length  x breadth

The area of a circle is pi times the radius squared (A = π r²).

The circumference of a circle is defined as the linear distance around it.

( C= 2πr)

The can of red bull is in shape of cylinder.

If we open the cylinder it will have two circular surfaces( at bottom and top) and one rectangular sheet.

Like the given figure given.

It shows that the two circle will have the diameter 2.5 inches.

d= 2.5 inch

 = 0.208 ft

radius, r= \(\frac{d}{2}\)

r= \(\frac{0.208}{2}\)

r= 0.104 ft

Circumference of the circle be,

= 2πr

= 2 x 3.14 x 0.104

= 0.653 ft

The rectangular sheet will have,

length=  0.653 ft, breadth= 6.5 inches = 0.541 ft

      = length x breadth

      = 0.653 x 0.541

      =\(0.3532 ft^{2}\)

       = 2 x π\(r^{2}\)

       = 2 x 3.14 x 0.104 x 0.104

       = 6.28 x 0.010816

       = 0.0679 \(ft^{2}\)

        = Area of rectangular sheet + Area of 2 circle( top and bottom of can)

        = 0.3532 + 0.0679

        = 0.4211 \(ft^{2}\)

Now, we have the wall of dimensions

length= 9 ft, breadth= 20 ft

= length x breadth

=9 x 20

= 180 \(ft^{2}\)

         =\(\frac{area \;of\; wall}{area \;of\; can}\)

         =\(\frac{180}{0.4211}\)

         = 427.45 cans

         ≈ 428 cans

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we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

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Answer:

\( \sf \: 375g \: is \: 2.5\% \: of \: 15kg\)

Step-by-step explanation:

Conversion of 15 kg into grams,

→ 1 kg = 1000 g

→ 15 kg = 15000 g

Let's find the percentage,

→ (375g ÷ 15kg) × 100

→ (375/15000) × 100

→ 0.025 × 100

→ 2.5%

Hence, the answer is 2.5%.

Answer(s):

1. $5000

2. 100x

3a. at least

3b. 9 meals

My shown work:

1. $100 per meal. Monthly expenses are $3100.

50 meal [$100 x 50 = x]

x = $5000

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

2. x = number of meals sold

Inequality (y=mx+b)

Giving me: 900 = 100x

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

100 x 9 = 900

Jonah's mom's would have to spend $45.878 to fill up her tank after the 40% increase in gas prices if her car takes 14 1/2 gallons of gas to fill up.

To find the cost that Jonah's mom would have to spend after the 40% increase in gas prices to fill up her 14 1/2 gallon tank, we need to follow these steps:

1. Find the increased price per gallon by multiplying last summer's price ($2.26) by 1.40 (since there's a 40% increase): $2.26 x 1.40 = $3.164 per gallon.
2. Convert 14 1/2 gallons to a decimal: 14.5 gallons.
3. Multiply the increased price per gallon ($3.164) by the number of gallons needed to fill up the tank (14.5 gallons): $3.164 x 14.5 = $45.878.

So, after the 40% increase in gas prices, Jonah's mom would have to spend $45.878 to fill up her 14 1/2 gallon tank.

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-2x-33=x
simplify by adding 2x on both sides

-33=3x

divide by 3 on both sides

x=-11

The probability of exactly three successes in eight trials is 0.2568

From the question, we have the following parameters that can be used in our computation:

n = 8

x = 3

p = 45%

The probability is then calculated as

P(x = x) = C(n, r) * pˣ * (1 - p)ⁿ⁻ˣ

Substitute the known values in the above equation, so, we have the following representation

P(x = 3) = 8C3 * (45%)³ * (1 - 45%⁵

Evaluate

P(x = 3) = 0.2568

Hence, the probability is 0.2568

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Answer:

B

Step-by-step explanation:

So we have the equation:

\(\frac{3x+9}{2}=\frac{x-4}{3}\)

First, let's get rid of the fractions. We can multiply by the LCM of 2 and 3 which is 6. So, multiply both sides by 6:

\(6(\frac{3x+9}{2})=6(\frac{x-4}{3})\)

On the left, the 6 and 2 cancel, leaving a 3.

On the right, the 6 and 3 cancel, leaving a 2.

So:

\(3(3x+9)=2(x-4)\)

Distribute:

\(9x+27=2x-8\)

Subtract 2x from both sides:

\(7x+27=-8\)

Subtract 27 from both sides:

\(7x=-35\)

Divide both sides by 7:

\(x=-5\)

And we're done!

The value of x is -5.

Our answer is B.

\(\large{\bf Step-by-step~explanation:}\)

Since we are solving for x, our goal is to isolate the variable.

\(\bf Step~1:\)

To solve, we have to cross multiply these fractions. We do this by multiplying 2 by (x - 4), and 3 by (3x + 9).

\(\bf 2*x-4=2x-8\\3*3x+9= 9x+27\)

\(\bf Step~2:\)

After that, we replace the fractions with the expressions.

\(\bf 2x-8=9x+27\)

\(\bf Step~3:\)

Since our goal is to isolate the variable x, we cannot have two variables, one on each side. To end up with only one, we either subtract 9x from both sides or 2x from both sides, to cancel one of the values out. I am going to choose 2x because when you subtract 2x from 9x, you will not end up with a negative number.

\(\bf 2x(-2x)-8=9x(-2x)+27\\-8=7x+27\)

\(\bf Step~4:\)

Now, we have to subtract 27 from both sides to get the term with the variable by itself.

\(\bf-8(-27)=7x+27(-27)\\-35=7x\)

*on these demonstrations, the numbers in parenthesis means to add/subtract, not multiply.

\(\bf Step~5 ~(Final~step!):\)

Finally, we divide both sides by 7 to get x's value.

\(\bf \frac{-35}{7} =\frac{7x}{7}\)

\(\bf -5=x\)

\(\large\boxed{\bf Our~final~answer:~x=-5; ~B}\)

Answer:

cubic polynomial, monomial

Step-by-step explanation:

Answer:

so the plants will grow more

Answer:

Multiply the different species in large number. Protect the plant species which are endangered. Improve the characteristics and quality of the plants. Produce quality and healthy plants on commercial base.

hope helpful <3

Answer:

Hi!!

Step-by-step explanation:

7 = chewing gum

6 = mints

2 = chocolate

Answer:

number of packs of chewing gum is 7

number of mints  is 6

number of chocolate bars is 2

Step-by-step explanation:

number of packs of chewing gum → x,  cost 6¢

number of mints → y = x-1 =3z,  cost  3¢

number of chocolate bars → z = y/3 = (x-1)/3, cost 10¢

put in equation 6x + 3y +10z = 80 plug in term of x

6x +3(x-1) +10((x-1)/3) =80 multiply each side by 3

18x +9(x-1) +10(x-1) =240 distribute

18x+9x-9+10x-10 =240 combine like terms

37x-19 = 240 add 19 in each side

37x =259

x = 7

plug into y = x-1 = 7-1 = 6 so y=6

and  z = y/3 =6/3 =2 so z = 2

The likelihood of finding that the sample mean is between 59,050 and 60,950 miles can be determined by calculating the probability using the normal distribution with a sample size of 90, a population mean of 60,000 miles, and a population standard deviation of 4,000 miles.

To find out the probability of getting a sample mean between 59,050 and 60,950, a simulator is used to determine the tread life of tires mounted on light-duty trucks that follows a normal probability distribution.

Here, the population mean is 60,000 miles and the standard deviation is 4,000 miles. The given sample size is 90.

We can use the formula for standardizing the score. The standardized score for the lower limit of 59,050 is -2.78, and that of the upper limit of 60,950 is 2.78. Now, we need to find the probability of getting the mean value between -2.78 and 2.78.

We can use the standard normal distribution table to find the value, which is 0.9950 for z = 2.78 and 0.0050 for z = -2.78. Hence, the required probability is 0.9900.

Therefore, the likelihood of finding that the sample mean is between 59,050 and 60,950, for a sample size of 90 tires, is 0.9900.

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Answer:

both a and b

Step-by-step explanation:

It is because in the elimination method it does not matter whether you eliminate x or y so if you use option a which multiplies -2 by 1st equation so it will become:

-4x+6y=40

4x+6y=8

so the -4x and 4x cancels and a is a valid option.

If you use the b which multiplies the second with 3 it becomes:

2x-3y=-10

4x+3y=24

so -3y and 3y cancel which also makes this a valid option.

Answer: both a and b

Sanyo  option (b) would be chosen using the elimination-by-aspects decision rule.

In the elimination-by-aspects decision rule, you compare the options based on specific aspects and eliminate those that do not meet a certain cutoff point for each aspect.

Here's how the comparison unfolds based on the given information:

1. Performance: The cutoff point is ranked 1. Sanyo and Sony meet the cutoff, but Pioneer does not.

  Eliminated: Pioneer

2. Price: The cutoff point is ranked 4. Sanyo and Pioneer meet the cutoff, but Sony does not.

  Eliminated: Sony

3. Quality: The cutoff point is ranked 4. All three options (Sanyo, Sony, Pioneer) meet the cutoff.

4. Style: The cutoff point is ranked 3. Sanyo meets the cutoff, but Sony and Pioneer do not.

  Eliminated: Sony and Pioneer

Based on the elimination process, the remaining option is Sanyo. Therefore, (b) Sanyo would be chosen using the elimination-by-aspects decision rule.

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