how many numbers bewteen 50 and 150 have at least one digit that is 2

1 1/2 can be split apart into 1 as the whole part and 3/2 as the fractional part.

To split apart the mixed number 1 1/2 into its whole part and fractional part, we need to understand the components of a mixed number.

A mixed number consists of a whole number part and a fractional part. In this case, 1 1/2 is a mixed number where 1 is the whole number part and 1/2 is the fractional part.

To separate the whole part and fractional part, we can rewrite the mixed number as an improper fraction.

The whole number part, 1, can be written as a fraction with a denominator of 1:

1 = 1/1

Now, let's convert the fractional part, 1/2, into an improper fraction. To do this, we multiply the whole number part, 1, by the denominator of the fraction and add the numerator:

1 x 2 + 1 = 2 + 1 = 3

The improper fraction is 3/2.

So, we have the whole part as 1 and the fractional part as 3/2.

It's worth noting that the whole part represents the whole number portion of the mixed number, while the fractional part represents the remaining portion of the number that is less than a whole unit.

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One pipe takes 6 hours working alone.

The other pipe takes 12 hours working alone.

This is a rate of work problem. The formula utilized is

\(w=r\times t\)

where

We are looking for how long it will take each pipe to completely fill the pool

For pipe 1 working alone to fill 1 pool, the work done is 1;

\(w=r\times t\\\\1 = r_1 \times t_1\\\\t_1=\frac{1}{r_1}\)

For pipe 2 working alone to fill 1 pool, the work done is 1;

\(w=r\times t\\\\1 = r_2 \times t_2\\\\t_2=\frac{1}{r_2}\)

From the question, it would take 9 hours if each pipe took turns to fill half the pool. That is;

\(\frac{t_1}{2}+\frac{t_2}{2}=9\\\\t_1+t_2=18\)

However, if both pipes worked together, it would take 4 hours for each pipe. That is;

\(w_1+w_2=w\\\\r_1t_1+r_2t_2=w\\\\4r_1+4r_2=1\\\\r_1+r_2=\frac{1}{4}\)

Remember that \(r_1=\frac{1}{t_1}\) and \(r_2=\frac{1}{t_2}\). So,

\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{4}\\\\\frac{t_1+t_2}{t_1t_2}=\frac{1}{4}\)

Also recall that \(t_1+t_2=18\). So,

\(\frac{18}{t_1t_2}=\frac{1}{4}\\\\t_1t_2=72\)

The only factors of 72 that satisfy the conditions

\(t_1+t_2=18\\\\t_1t_2=72\)

are 6 and 12.

Therefore, pipe 1 will take 6 hours, and pipe 2 will take 12 hours to fill the pool if working alone.

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The formula to calculate the geometric mean of two numbers is the square root of their product.

So in this case, the geometric mean can be calculated as follows:

Geometric Mean = √(8 * 12) = √96 = 10

The growth factors for the population of Chattanooga in the past two years have a geometric mean of 10.

The geometric mean is a measure of central tendency that is used to describe the average growth rate of a set of numbers. It is especially useful when working with data that represents exponential growth or decay, such as population growth or the rate of return on an investment. Unlike the arithmetic mean, the geometric mean takes into account both the size and the direction of growth. This makes it a better measure of central tendency for data that is not symmetrically distributed.

In the case of population growth, the geometric mean can be used to determine the average annual growth rate over a given period of time. For example, if the population of a city grows by 8% in one year and then by 12% the following year, the average annual growth rate over the two years can be estimated using the geometric mean.

It is important to note that the geometric mean is always smaller than the arithmetic mean for the same set of numbers, and it can be a better representation of the underlying growth trend in some cases.

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The distance traveled by Jasmine and Chelsea is given by the equations of speed and J = 20.4 km and C = 39 km , where T is the time taken and T = 0.6 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of Jasmine be represented as S₁ = 34 km/h

Let the speed of Chelsea be represented as S₂ = 65 km/h

Now , the distance traveled by Jasmine = J

And , the distance traveled by Chelsea = C

The measure of J = measure of C

So , the distances are the same

Let the time taken by both Jasmine and Chelsea be T

Now , Speed = Distance / Time

Substituting the values in the equation , we get

Distance D = 34T

And , distance D = 65T

Now , the total distance D = 59.4 km

So , 34T + 65T = 59.4

On simplifying the equation , we get

99T = 59.4

T = 0.6 hours

Hence ,

The distance traveled by Jasmine and Chelsea are 20.4 km and 39 km respectively

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The probability of landing heads up on the next flip is also 1/2.

Suppose we flip a fair coin five times and each time it lands heads up.

The probability of landing heads up on the next flip is 1/2.

In order to solve this problem, we need to determine the probability of landing heads up on the next flip.

Since a fair coin is being flipped, the probability of getting heads on any given flip is 1/2.

Since the coin has already landed heads up five times in a row, this does not affect the probability of getting heads on the next flip.

Therefore, the probability of landing heads up on the next flip is also 1/2.

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Answer:

No

For it to be the same, it should be:

x=5-b equal to x=-(b-5)

OR

x=5-b equal to -x=b-5

The cost of an adult ticket is £15.25.

We can start by creating a system of two equations to represent the situation. Let's say "c" is the cost of a child ticket, and "a" is the cost of an adult ticket.

From the information given, we know that the cost of an adult ticket is £9 more than the cost of a child ticket. So we can compose the first equation as:

a = c + 9

Next, we know that the total cost of the six tickets is £55.50. There are two adult tickets and four child tickets, so the second equation can be written as:

2a + 4c = 55.50

Now that we have two equations, we can substitute the first equation into the second equation to get:

2(c + 9) + 4c = 55.50

Expanding the first equation and simplifying it, we get:

6c + 18 = 55.50

Subtracting 18 from both sides of the equation, we get:

6c = 37.50

Divide both sides of the equation by 6, and we get:

c = 6.25

So the cost of a child ticket is £6.25.

Finally, we can use the first equation to find the cost of an adult ticket:

a = c + 9

a = 6.25 + 9

a = £15.25

Therefore, the cost of an adult ticket is £15.25.

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--The given question is incomplete; the complete question is

"Mr and Mrs Smith buy tickets for themselves and their four children.

The cost of an adult ticket is £9 more than the cost of a child ticket. The total cost of the SIX tickets is £55.50

Work out the cost of an adult ticket. In your work, let c be the cost of a child ticket and a be the cost of an adult ticket."--

A) Yes, the graph represents a proportional relationship because the rate at which the plane's altitude increases is directly proportional to the amount of time that has elapsed since takeoff.

B) The unit rate of change is the number of feet per minute that increases over time, which can be calculated by finding the slope of the line. To do this, we choose two arbitrary points on the line and calculate the change in altitude divided by the change in time for each point. Therefore, if we choose the points (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 12000), then the unit rate of change is (12000 - 0) / (2 - 0).

The unit rate of change is 6000 feet per minute, calculated by (12000 - 0) / (2 - 0).

If you have any additional questions or need further assistance, please let me know.

Answer:

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

Proportional relationship is:

At x = 0, the function gets the value of zero regardless the value of k. Hence the line passes through the origin.

A) The given graph passes through the origin and therefore it is a proportional relationship.

B) The value of y = k when x = 1 is the rate of change.

As per graph it is:

Answer:

\(2.5 \times 10^{-5}\)

Answer:

True

Step-by-step explanation:

If ∠XZY and ∠PZQ are vertical angles,

then ∠XZY≅∠PZQ

(vertical angles are congruent)

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = G(3, - 2) and (x₂, y₂ ) = H(7, - 2)

m  \(\frac{-2+2}{7-3}\) = \(\frac{0}{4}\) = 0

The slope of the line that contains the points G(3, -2) and H(7, -2) named is zero.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The given two points of line are G(3, -2) and H(7, -2)

slope of the line is the ratio of the rise to the run, or rise divided by the run

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=-2-(-2)/7-3

m=0/4

=0

Hence the slope of the line that contains the points named is zero.

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A. The formula for the moose population P(t) is given by: P(t) = -53.33t + 3000.

B. The model predicts the moose population to be approximately 2200 in 2005.

1a. To find a formula of the form P(t) = m * t + b for the moose population P in terms of t, the years since 1990, we need to determine the values of m and b using the given data points.

Let's assign t = 0 to the year 1990 and t = 9 to the year 1999, as there are 9 years between 1990 and 1999.

We have the following data points:

(0, 3000) and (9, 2520).

To find the equation of the line, we can use the formula:

m = (y₂ - y₁) / (x₂ - x₁),

where (x₁, y₁) = (0, 3000) and (x₂, y₂) = (9, 2520).

Plugging in the values:

m = (2520 - 3000) / (9 - 0) = -480 / 9 = -53.33 (approximately).

Now, we need to find the value of b, which is the y-intercept. We can use the point (0, 3000) to find b:

3000 = -53.33 * 0 + b

3000 = b

Therefore, b = 3000.

The formula for the moose population P(t) is given by:

P(t) = -53.33t + 3000.

B. To predict the moose population in 2005 (t = 15), we can substitute t = 15 into the equation:

P(15) = -53.33 * 15 + 3000

P(15) = -799.95 + 3000

P(15) = 2200.05 (approximately)

The model predicts the moose population to be approximately 2200 in 2005.

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Complete question is below

in 1993, the moose population in a park was measured to be 3000. by 1999, the population was measured again to be 2520. if the population continues to change linearly:

A. Find a formula of the form P(t) = m + b for the moose population, P, in terms of t, the years since 1990. P(t) =

B. What does the model from part A. predict the moose population to be in 2005?

The measurement for side DH which is perpendicular to BC is 6 + √(3) cm.

To find the measurement of DH, use the given information and apply some geometry concepts.

First, use the fact that FC is parallel to AB and AD is parallel to BC to conclude that triangle ABD is similar to triangle FCB (by the AA similarity criterion).

Next, use the fact that A line F is parallel to BE and triangle A line F and B is similar to triangle EFB to conclude that A  F/EB = AB/BE (by the similarity ratio of corresponding sides).

Using these two similarities, set up a proportion:

AB/BD = FC/CB

Substituting the given values:

AB/BD = 12/BD = 6/BC = 6/6 = 1

Therefore,  AB = BD.

Now, using the fact that EG is perpendicular A line F to conclude that triangle AEG is a right triangle.

Using the Pythagorean theorem, find the length of AG:

AG² = AE² + EG² = (A line F - FE)² + EG² = (12 - BD)² + 5²

But we know that AB = BD, so substitute AB for BD:

AG² = (12 - AB)² + 5²

Next, use the fact that DH is perpendicular to BC to conclude that triangle BHD is a right triangle.

Using the Pythagorean theorem, find the length of BD:

BD² = BH² + DH²

But AB = BD, so substitute AB for BD:

AB² = BH² + DH²

Now set up a system of equations:

AG² = (12 - AB)² + 5²

AB² = BH² + DH²

Substituting AB² for BH² + DH² in the first equation:

AG² = (12 - AB)² + 5² = (12 - AB)² + AB²

Expanding and simplifying:

AB² - 24AB + 119 = 0

Solving for AB using the quadratic formula:

AB = (24 ± √(24² - 41119))/2 = 12 ± 5√(3)

Since AB = BD:

BD = AB = 12 ± 5√(3)

We can discard the negative solution because BD must be positive.

Now we can use the Pythagorean theorem to solve for DH:

DH² = AB² - BH² = AB² - (BC - DH)² = (12 ± 5√(3))² - (6 - DH)²

Expanding and simplifying:

DH² = 33 ± 60√(3) - (36 - 12DH + DH²)

Simplifying further:

DH² - 12DH - 3 ± 60√(3) = 0

Solving for DH using the quadratic formula:

DH = 6 ± √(3)

Discard the negative solution because DH must be positive. Therefore, the measurement of DH is DH = 6 + √(3) cm.

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Image transcribed:

In the given figure,

FC//AB, AD// BC, A line F// BE,

EG I A line F and DH L.B.C. IF G

EG = 5cm, A line F =12cm and

BC = 6cm, find the measurement

of DH.

Answer:

m∠1 = m∠3 = 75°

m∠2 = m∠4 = 105°

Step-by-step explanation:

From the figure attached,

m∠1 + m∠2 = 180° [Supplementary angles]------(1)

Since, m∠2 - m∠1 = 30°

m∠2 = 30° + m∠1 -----(2)

By substituting the value of ∠2 from equation (2) to equation (1),

m∠1 + (m∠1 + 30°) = 180°

2(m∠1) + 30° = 180°

2(m∠1) = 150°

m∠1 = 75°

Therefore, m∠2 = 180°- m∠1 = 180° - 75°

                  m∠2 = 105°

Since, ∠ 2 ≅ ∠4 [Vertical angles]

m∠2 = m∠4 = 105°

Similarly, ∠1 ≅ ∠3 [Vertical angles]

m∠1 = m∠3 = 75°

Therefore , the required function for this given problem is F(t) = 25 - 14t.

A function is a relationship between a set of allowable inputs and outputs, where each input is associated to exactly one output. Let A and B represent any two non-empty sets; only when every element in A has one end and only one image in B will the mapping from A to B be a function.

Here,

Given:

armando can scan about 14 items per minute

armando has 25 items in his cart

No of items scan in t minutes =14t

So

A)F(t) = 25 - 14t

Domain:[0,2]

Range:[0,25]

Therefore , the required function for this given problem is F(t) = 25 - 14t.

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A-The first line has a direction vector of ⟨-2, 1, 3⟩, b-the second line has parametric equations x(t) = -4 - 2t, y(t) = 2 + t, z(t) = 17 + 5t, c-the two lines intersect at the point (1, 3, 10), d-the angle formed is 15.2 degrees, and e- the equation containing both lines is -2x + 7y - 5z = -59.

What is direction vector ?

A direction vector, also known as a directional vector or simply a direction, represents the direction of a line, vector, or a linear path in three-dimensional space. It is a vector that points in the same direction as the line or path it represents.

a) The direction vector for the first line is given by ⟨-2, 1, 3⟩.

b) The parametric equations for the second line, written in terms of the parameter t, are x(t) = -4 - 2t, y(t) = 2 + t, z(t) = 17 + 5t.

c) To find the intersection point, we set the x, y, and z coordinates of both lines equal to each other and solve for s and t:

4 - 2s = -4 - 2t

-2 + s = 2 + t

1 + 3s = 17 + 5t

Solving this system of equations yields s = 3 and t = 1. Therefore, the two lines intersect at the point (1, 3, 10).

d) The angle formed at the intersection point is given by the angle between their respective direction vectors. Using the dot product, the angle θ can be found as cos(θ) = (⟨-2, 1, 3⟩ · ⟨-2, 1, 5⟩) / (|⟨-2, 1, 3⟩| |⟨-2, 1, 5⟩|), which simplifies to cos(θ) = 0.96. Taking the inverse cosine, we find θ ≈ 15.2 degrees.

e) To find the equation of the plane containing both lines, we can use the point-normal form of a plane equation. We choose one of the intersection points (1, 3, 10) and use the cross product of the direction vectors of the two lines as the normal vector. The equation of the plane is given by -2x + 7y - 5z = -59.

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All of the factors listed in options a, b, c, and d are important in determining whether an individual is required to file an income tax return, except for option e, which states that none of the choices are correct.

When determining whether an individual is required to file an income tax return, several factors come into play. The first factor, option a, is the taxpayer's gross income. The Internal Revenue Service (IRS) sets specific income thresholds, and if an individual's gross income exceeds those thresholds, they are generally required to file a tax return.

The second factor, option b, is the taxpayer's filing status. Different filing statuses, such as single, married filing jointly, or head of household, have different income thresholds for filing requirements. Therefore, a taxpayer's filing status is an important consideration in determining whether they need to file a tax return.

The third factor, option c, is the taxpayer's total itemized deductions. Itemized deductions can reduce a taxpayer's taxable income, and if these deductions are substantial, it may affect the requirement to file a tax return.

The fourth factor, option d, is the availability of the additional standard deduction for taxpayers

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Using a system of equations, it is found that Carol is 10 years old.

The complete problem is:

"Gerrys age is 5 more than three times Carols age. If the sum of their age is 45, how old is carol?"

The variables are:

Gerry is 5 more than three times Carol's age, hence:

\(x = 5 + 3y\)

The sum of their ages is 45, hence:

\(x + y = 45 \rightarrow x = 45 - y\)

We then use the first equation to find Carol's age:

\(45 - y = 5 + 3y\)

\(4y = 40\)

\(y = \frac{40}{4}\)

\(y = 10\)

Carol is 10 years old.

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Answer:

\(\sqrt49\)

Step-by-step explanation:

Knowing that: A rational number is a number that is in the form of p/q, which  p and q are integers, and q whom is not equal to 0. Any number that can be written as a ratio (or fraction) of two integers is a rational number.49 is a rational number because it can be expressed as the quotient of two integers: 49 ÷ 1.

Hence, the answer is \(\sqrt 49\)

`Lenvy~

Answer:

1,000 km

Step-by-step explanation:

Assume that when two train pass each other, Lian has traveled x (km)

=> The time Lian has traveled when two trains pass each other is:

Time = Distance/ Rate = x/ 250 (hour)

As Lian and Yuto travelled from the two opposite train stations and the train stations are 1,880 km apart

=> When two train pass each other, Yuto has traveled 1,880 - x (km)

=> The time Yuto has traveled when two trains pass each other is:

Time = Distance/ Rate = (1,880 - x)/220 (hour)

As Lian and Yuto board at the same time, so that when two trains pass each other, the time both of them have traveled is equal

=> x/ 250 = (1,880 - x)/220

=> 220x = 250 x (1,880 -x)

=> 220x = 470,000 - 250x

=> 470x = 470,000

=> x = 1,000

So that, when two train pass each other, Lian has traveled x = 1,000 km

Answer:

1,000 kilometers

Step-by-step explanation:

Answer:

√113

10.6301458127

10.63 (2 d.p)

Step-by-step explanation:

The distance formula is:

√[(x₂ - x₁)² + (y₂ - y₁)²]

x₂ = (-1)

x₁ = 6

y₂ = 8

y₁ = 16

Substitute those values into the equation:

√[(-1 - 6)² + (8 - 16)²]

Perform the arithmetic (the subtractions inside the brackets:

√[(-7)² + (-8)²]

Square the values:

√[49 + 64]

Add them

√[113]

Calculate the square root of the value:

√[113] = 10.6301458127

Whether you want the answer in one of these forms, it's up to you/your teacher:

√113

10.6301458127

10.63 (2 d.p)

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation: The speed of reaction to differences between forecasts and actual results. is the answer i think

a) The Probability of getting a sum of 6 is 5/36.

b) The Probability of getting a sum of 10 is 1/12.

c) The Probability of getting a sum of 6 or 10 is 2/9.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty [Note 1][1][2]. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

Probability = (number of desired outcomes / number of all possible outcomes)

Roll of Dice: Green and Red.

(a) The  probability of totaling 6:

Number of outcomes needed = 5

Therefore,

P(sum of 6) = 5/36

b) The probability that the total is 10

Number of outcomes required = 3

Therefore,

P(sum of 10) = 3 / 36 = 1/12

c) The probability that the sum is 6 or 10:

P(sum is 6) + P(sum is 10)

(5/36) + (1/12) = (5 + 3) / 36

= 8/36 = 2/9

The events are mutually exclusive because they do not all occur at the same time.

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sqrt((x2-x1)^2+(y2-y1)^2)

Answer:

a)sol...A/Q

x+130=180(Sum of angles on a straight line is 180 degree)

=>x=180-130

=>x=50

Hrnce,the value of x is 50 degree.

b)sol...A/Q

\(circumference\ of\ circle=2\pi y\\

2\pi r=2\pi y\\

r= \frac{2\pi y }{2\pi} \\

Hence,r=radius=y\)

Therefore, the weight of the blood is approximately 53.96 N. False.

The volume of blood that circulates within a person varies according to their size and weight, but an adult human has around 5 liters of blood in circulation on average. A newborn weighing around 8 pounds will have roughly 270 mL, or 0.07 gallons, of blood in their body.

Children: An 80-pound youngster on average will have 0.7 gallons, or 2,650 mL, of blood in their body. Adults: The amount of blood in the body of a typical adult weighing 150 to 180 pounds should be between 1.2 and 1.5 gallons.

The weight of the blood can be calculated using the formula W = m*g, where m is the mass of the blood and g is the acceleration due to gravity.

In this case, the mass of the blood is 5.5 kg (not liters, as mass is measured in kg), so we can calculate the weight as:

W = 5.5 kg * 9.81 m/s = 53.9555 N

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Correct Question:

State true or false: Considering that an adult woman weighing 70 kg has 5.5 liters of blood, approximately Mind determines the weight of the blood. W=57. 13 N​

Answer: I think it's D.

Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.