Find 3 consecutive odd integers such that 10 times the first is 59 more than the third?

The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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Answer:

The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.

In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:

C = pi x d = 3.14 x 60 = 188.4 centimeters

When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:

distance = 35 x circumference = 35 x 188.4 = 6584 centimeters

We can convert centimeters to meters by dividing the distance by 100:

distance = 6584 ÷ 100 = 65.84 meters

Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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The statement that is true about the points shown below is: "The distance between them is zero because they have the same y-coordinate."

The distance between two points is typically calculated using the distance formula, which involves the difference between their x-coordinates and y-coordinates. However, in this case, the statement specifies that the points have the same y-coordinate.

The y-coordinate represents the vertical position on a graph, while the x-coordinate represents the horizontal position. When two points have the same y-coordinate, it means they lie on the same horizontal line.

Since distance is measured in a straight line, and these points are already on the same horizontal line, their distance from each other is zero. This is because they are effectively occupying the same position along the horizontal axis.

In summary, when two points have the same y-coordinate, their distance from each other is zero. This is because they lie on the same horizontal line and are already as close to each other as possible in the horizontal direction.

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Answer:

First # is 6, second # is 12.

Step-by-step explanation:

This is because if we make the demoniators the same, the first equation will be 2/8 + x/8 =1 and 2/8+6/8=1. The second one if we make both of the denomiators 12, 4/12+8/12=1

From the given information

x represents the rental cost

y represents the utility cost

Cost of rent is $700

Cost of Utility is $125

Given :

The total bill is $825. Utilities cost $575 less than rent.

We need to find the cost of months rent and utilities cost

So lets assume variables for each

Let x represents the cost of rent

and y represents the utilities cost

Total bill is 825

\(x+y=825\)

Utilities cost $575 less than rent.

Utility cost \(y=x-575\)

Replace the second equation in first equation

\(x+y=825\\x+x-575=825\\2x-575=825\\2x=825+575\\2x=1400\\x=700\)

The cost of rent is $700

\(y=x-575\\y=700-575\\y=125\)

Utility cost is $125

The cost of rent is $700

Utility cost is $125

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Using the property of \(Y_n\) being a bounded, continuous function of Xn and the fact that Xn converges in distribution to X, it can be shown that P(|Yn| > c) → 0 as n → ∞ for any finite number c.

To prove that for any finite number c,

P(|Yn| > c) → 0

as n → ∞, we can use the fact that Xn converges in distribution to X and the property of Yn mentioned in the problem statement.

Since Xn converges in distribution to X, we know that for any bounded, continuous function g(x),

E[g(Xn)] → E[g(X)] as n → ∞

By the property of Yn, we know that there exists a bounded, continuous function g(x) such that Yn = g(Xn) for all n. Therefore, we can rewrite the expression as:

P(|Yn| > c) = P(|g(Xn)| > c)

By the boundedness of g(x), we know that there exists a constant M such that |g(x)| ≤ M for all x. Therefore,

P(|Yn| > c) = P(|g(Xn)| > c) ≤ P(|Xn| > c/M)

Since Xn converges in distribution to X, we know that

P(|Xn| > c/M) → 0 as n → ∞

Therefore,

P(|Yn| > c) = P(|g(Xn)| > c) ≤ P(|Xn| > c/M) → 0 as n → ∞

This shows that for any finite number c,

P(|Yn| > c) → 0 as n → ∞, as desired.

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Answer:

1. The function that gives the lion population size P(t), t years from today is:

P(t) = 325(0.95)^t

2. To find the population in 4 years, we can substitute t=4 in the function:

P(4) = 325(0.95)^4

P(4) = 279.14

So the population will be approximately 279 lions in 4 years.

3. The exponential function for all three years is the same as in part 1:

P(t) = 325(0.95)^t

Answer:

(0, -6) , (6, 0)

Step-by-step explanation:

it could be (0, -6) or (6,0)

Answer:

Step-by-step explanation:

In a regular pentagon, all the angles and sides are equal. So, to find an angle, divide 540 by 5.

Sum of all angles of regular pentagon = 540

measurement of one angle = 540 ÷ 5

                                             = 108°

∠N = 108°

Answer:

B

Step-by-step explanation:

a) Examining the data, the outlier in the data are

b) The measure I would use to describe the central tendency of the data is median

Outlier as used in data  analysis refers to a data that is abnormally away from other data. Outliers show high variability

In the given problem, $80 000 is the data that is farther away than any other data and hence the only outlier

The mean is usually a better measure of central tendency how ever the presence of outliers affects the result projected by mean.

The better choice to use here is the median

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Answer:

a

  \(P(E \ n\  Z) =  0.0196\)

b

\(P(E \ n\  Z \ n \ Y) =  0.0027\)

Step-by-step explanation:

From the question we are told that

The probability of that a person is being called for jury duty in any given year is \(P(J) = 0.14\)

Let P(E) be the probability a person being selected in the first year, Let P(Z) be the probability a person being selected in the second year

and Let P(Y) be the probability a person being selected in the third year

Generally the probability that a particular eligible person in this city is selected in both of the next 2 years is mathematically represented as

\(P(E \ n\ Z) = P(E) * P(Z) = P(J)^2\)

=>      \(P(E \ n\  Z) =  0.14^2\)

=>      \(P(E \ n\  Z) =  0.0196\)

Generally the  probability that a particular eligible person in this city is selected in both of the next 3 years is mathematically represented as

     \(P(E \ n\  Z \ n \ Y) =  P(E) * P(Z)  * P(Y) =  P(J)^3\)

=> \(P(E \ n\  Z \ n \ Y) =  0.14^3\)

=>  \(P(E \ n\  Z \ n \ Y) =  0.0027\)

This multiplication of each probabilities is valid because each probability is independent of one another

We have the following:

1.

2.

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

Step-by-step explanation:

The probability that the forester does not get the seedlings is 1/2 if the mean density of seedlings is 5 per square metre.

Density means the area within which a substance is collected or taken.

We have been given the mean density =5 square metre.

And we  have to calculate the probability that the forester will not get any seedlings.

So the probability that he will get the seedlings will be=5/10

which is 1/2

So the probability that he will not get the seedlings will be 1-1/2

that is 1/2.

Hence the probability that he will not get seedlings will be 1/2.

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Basis step: Let \(n=2\). Then

\(2! = 2\cdot1 = 2\)

and

\(2^2 = 4\)

so \(2! < 2^2\).

Inductive step: Assume \(k! < k^k\). We want to show that \((k+1)! < (k+1)^{k+1}\).

Now

\((k+1)! = (k+1) \cdot k! \\\\ ~~~~~~~~~~~ < (k+1) \cdot k^k \\\\ ~~~~~~~~~~~ < (k+1) \cdot k^{k+1} \\\\ ~~~~~~~~~~~ < (k+1) \cdot (k+1)^{k+1}\)

where the first inequality follows from the induction hypothesis; the second follows from multiplying the right side by some \(k>2\); and the third from adding the remaining terms to complete the binomial expansion \((k+1)^{k+1}\), all of which are positive since they are some power of \(k>2\).

QED

The calculated measure of the angle D is (c) 32 degrees

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

The triangles ABC and DEF

The triangles are similar triangles

This means that the corresponding angles are equal

Given that

A = 32 degrees

And the corresponding angle is D

We have

D = 32 degrees

Hence, the measure of the angle is (c) 32 degrees

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Answer:

Step-by-step explanation:

An easy way is to substitute values into both equations and compare:

A. x = 0.8

B. x = 0.9

C. x = 1.9

D. x = 1.1

As we see the most accurate one is A

Let's graph both function(Attached)

Let's round 0.775

\(\\ \sf\longmapsto 0.775\)

\(\\ \sf\longmapsto 0.77\)

\(\\ \sf\longmapsto 0.8\)

Option A is correct

The measure of angle ∠PQR is 42 degrees

The attached image represents the missing information in the question

From the attached image, we have:

LQP = PQR + RQL

Substitute known values

77 = PQR + 35

Evaluate the like terms

PQR= 42

Hence, the measure of angle ∠PQR is 42 degrees

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Answer:

1.25

Step-by-step explanation:

1.5 divided by 1.2 is 1.25

Hope this helps☺️

Answer:

1.25

Step-by-step explanation:

1.5 / 1.2 = 15/12 = 5/4 = 1 1/4 = 1.25

The domain of the graph of the exponential function is (d) all real numbers

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

The graph of the exponential function

The rule of an exponential function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is always greater than the constant term

From the graph, the constant term is 0

So, the range is y > 0

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Answer:

the ratio would be 9:4 because you just add

Step-by-step explanation:

just add the rstio

The distance between points P and Q is √73

First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:

distance = √( (a - c)² + (b - d)²)

Here we can see that the coordinates of the two shown points are:

P = (-3, 2)

Q = (5, -1)

Replacing that in the distance formula we will get:

distance = √( (-3 - 5)² + (2 + 1)²)

distance = √( (-8)² + (3)²)

distance = √73

So the correct option is the third one.

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Answer:A!

Step-by-step explanation: 100/20 =5

A boy is on a sled moving down a hill at 20 m/s, the momentum of the child is mathematically given as 5 kg.m/s, Option A.

Question Parameter(s):

A boy is on a sled moving down a hill at 20 m/s.

The combined mass of the sled and child is 100 kg

Generally, the equation for the momentum    is mathematically given as

F=ma

Therefore

x=100/20

x=5 kg.m/s

In conclusion, the momentum

x=5 kg.m/s

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Answer:

Volume = 7.912

Step-by-step explanation:

V = πr²h

V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )

V = 3.14 × 9/16 ×18/4

V = 3.14 × 0.56 × 4.5

V = 7.912

Answer:

total cost = sell price + (sell price * 0.07)