this visual representation shows the sets of real numbers. classify the number −25. select all terms that are correct. natural whole integer rational irrational −25 natural – negative 25 whole – negative 25 integer – negative 25 rational – negative 25 irrational – negative 25

ANSWER

x+y)^2=x^2+y^2+2xy -eq1

because

first we will take the LHS of eq1, i.e,

(x+y)^2

(x+y)(x+y)

x(x+y)+y(x+y)

x^2+xy+xy+y^2

x^2+2xy+y^2

Or

x^2+2xy+y^2

Hence, LHS=RHS

The required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

Here,

Gien expression,
= x³ - 6x² - x + 30
= (x - 5)(x + 2)(x -3)

Thus, the required factors of the given expression x³ - 6x² - x + 30 is (x - 5)(x + 2)(x -3).

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the measure of ∠B = 85°

Explanation:

m∠A = (x-23)°

m∠B = (2x+29)°

Complementary angles are angles that have their sum equal to 90°:

m∠A + m∠B =90°

(x-23)°+ (2x+29)° = 90°

x + 2x -23 + 29 = 90°

3x + 6 = 90

collect like terms:

3x = 90-6

3x = 84

x = 84/3

x = 28°

m∠B = (2x+29)° = 2(28) + 29

m∠B = 85°

Therefore, the measure of ∠B = 85°

Answer:

approx. 68%

Step-by-step explanation:

this is a normal distribution.

in a normal distribution, approximately 68% of the data is within one standard deviation of the mean (we also have 95% of data is within two standard deviations of the mean, and 99.7% of data is within three standard deviations of the mean).

one standard deviation in our question is 113.

315 is one standard deviation below the mean because 428 - 113 = 315.

541 is one standard deviation above the mean because 428 + 113 = 541.

so we expect approx. 68% of the data to be between 315 and 541.

Answer:

54 hope it helped you out

The function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1 because the limit of h(t) as t approaches 1 is equal to h(1).

First, we need to show that the limit of h(t) as t approaches 1 is equal to h(1).

Since h(t) = (2t-3t^2)/(1+t^3), we can rewrite the limit of h(t) as t approaches 1 as:

lim t->1 (2t-3t^2)/(1+t^3) = lim t->1 (2-3t)/(1+t^3)

We can now use the properties of limits to evaluate the limit.

Substituting t=1 into the expression for the limit, we have:

lim t->1 (2-3t)/(1+t^3) = (2-3(1))/(1+(1)^3) = -1/(2)

Now, we can use the definition of continuity to show that h(t) is continuous at a=1.

Since the limit of h(t) as t approaches 1 is equal to h(1), then h(t) is continuous at a=1.

Thus, we have successfully shown that the function h(t) = (2t-3t^2)/(1+t^3) is continuous at a=1.

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Answer:

7.625597485 DFNFNFJFKJFKF

Adam Vinatieri made 14 field goals and 7 extra points.

Given that,

a field goal is 3 points and the field goal after a touchdown is only 1 point.

Adam Vinatieri made 21 field goals and extra point kicks for 49 points.

Let x be the number of field goals and y be the extra point kicks.

So we get,

x + y = 21 -------------(1)

3x + y = 49 -----------(2)

Subtracting equation (1) from equation (2),

2x = 28

 x = 14

putting the value of x in equation (1),

14 + y = 21

       y = 7

Therefore Adam Vinatieri made 14 field goals and 7 extra points.

Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.

Adam Vinatieri is an American former football placekicker who played in the National Football League.

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The probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321. The expected amount of time until the first bulb goes out is 10 minutes. The probability density function (pdf) of the random variable T, representing the time when you leave the room after the last light bulb goes out, is given by \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\).

To find the probability that a single bulb will burn out within the next 10 minutes, we can use the exponential distribution. The exponential distribution with a mean of 10 minutes has a rate parameter λ = 1/10.

The probability density function (pdf) for an exponential distribution is given by \(f(x) = λ * e^{(-λx)}\)

In this case, we want to find the probability that a bulb burns out within the next 10 minutes, which corresponds to the cumulative distribution function (CDF) at x = 10. The CDF is given by \(F(x) = 1 - e^{(-λx)\)

So, substituting the values, we have:

\(F(10) = 1 - e^{(-(1/10)*10)\)

\(= 1 - e^{(-1)\)

= 1 - 0.3678794412

≈ 0.6321

Therefore, the probability that a single bulb will burn out within the next 10 minutes is approximately 0.6321.

The amount of time until the first bulb goes out follows an exponential distribution with a rate parameter of λ = 1/10 (since it has a mean of 10 minutes).

The probability density function (pdf) for the time until the first bulb goes out is given by\(f(t) = λ * e^{(-λt).\)

To find the expected amount of time until the first bulb goes out, we need to calculate the mean (or expected value) of this distribution.

The expected value of an exponential distribution with rate parameter λ is equal to 1/λ. In this case, the expected value is 1/(1/10) = 10 minutes.

Therefore, the expected amount of time until the first bulb goes out is 10 minutes.

To find the probability density function (pdf) of the random variable T, which represents the time when you leave the room (after the last light bulb goes out), we need to consider the distribution of the maximum of the exponential random variables.

Since there are 20 light bulbs in the room, and each follows an exponential distribution with a rate parameter λ = 1/10, the time until the last bulb goes out can be modeled as the maximum of 20 exponential random variables.

The pdf of the maximum of independent exponential random variables with the same rate parameter λ is given by \(g(t) = n * λ * e^{(-λt)} * (1 - e^{(-λt))^(n-1)}\), where n is the number of random variables.

In this case, n = 20, and λ = 1/10. Thus, the pdf of T is \(g(t) = 20 * (1/10) * e^{(-(1/10)t)} * (1 - e^{(-(1/10)t))^(19)}\)

This expression represents the pdf of the random variable T, which denotes the time when you leave the room after the last light bulb goes out.

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The measure of angle DAB in the circle shown with the given arc length is: 2.23 radians.

Arc length = θ × r, where r is the radius of the circle, and θ is the central angle in radians.

Given the following:

Length of arc = 6.47 cm

Radius (r) = 2.9 cm

θ = m∠DAB

Plug in the values into the arc length formula:

6.47 = θ × 2.9

6.47/2.9 = θ

θ = 2.23 radians

m∠DAB = 2.23 radians

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Answer:

DAB = 2.23 radians

Hope this helps!

Step-by-step explanation:

Answer:

We want to write and solve an inequality to determine the number of people who can go to the amusement park.

The solution is p ≤ 11

The friends have a maximum of $225 to spend.

The parking is independent of p, the number of friends, and it costs $5, discounting that we get: $225 - $5 = $220

Each ticket costs $20, so the cost for p people is:

p*$20

And this must be equal to or smaller than $220, then we get the inequality:

p*$20 ≤ $220

To solve it for p, we need to divide both sides by $20, we will get:

p*$20/$20 ≤ $220/$20

p ≤ 11

This inequality gives the number of people that can go to the amusement park.

Step-by-step explanation:

Hope this helps you!!!!!!!!!!! :D

The conditions for conducting one-sample t-procedures are as follows:

1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.

2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.

3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.

4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.

5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.

It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.

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INSTANCE.

In my opinion a red mustang is an instance of the car class.

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The ratio of successful shots to total shots for Hugo is 6:10, and for Victor it is 10:15.

In basketball, the shooting ratio represents the number of successful shots made compared to the total number of shots attempted. For Hugo, out of his 10 shots, he made 6 successful shots. Therefore, his shooting ratio is 6:10. Similarly, for Victor, he made 10 successful shots out of 15 attempts, resulting in a shooting ratio of 10:15.

By expressing the ratios in this way, we can easily compare the shooting performances of Hugo and Victor. Hugo made 60% of his shots (6 out of 10), while Victor made 66.7% of his shots (10 out of 15). This ratio provides a measure of their shooting accuracy and can be used to evaluate their performance on the basketball court.

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Answer:

1.)y² – 11y + 24

2.)17/15 or 1 ²/15

3.) 1 5/24

Step-by-step explanation:

1.)simplify (y – 8)(y–3)

soln

(y – 8)(y–3)

by using any bracket to expand the other

y(y–3) – 8(y–3)

= y² –3y –8y + 24

= y² – 11y + 24

2.)a = ⅔ and b = ¹/5

find 2a–b

soln

= 2(⅔) – ¹/5

= ⁴/3 – ¹/5

Look for the L.C.M which is 15

= 20 – 3/15

= 17/15 or 1 ²/15

3.)3⅔ – 1⅞

convert them to improper fractions

= 11/3 – 15/8

look for the L.C.M which is 24

= 88–45/24

= 43/24

= 1 5/24

Thanks for choosing brianly.

I hope I helped

The angle of impact is 30°

In a bloodstain, the angle of impact can be used to determine the appearance of the resulting bloodstain if the bloodstain has a tail or pattern.

Mathematically;

\(\mathbf{Angle \ of \ impact = sin^{-1} (\dfrac{width \ stain}{length \ stain} )}\)

\(\mathbf{Angle \ of \ impact = sin^{-1} (\dfrac{1.5}{3.0} )}\)

\(\mathbf{Angle \ of \ impact = 30 ^0}\)

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Answer:

13.994 grams

Step-by-step explanation:

Using the given balanced equation: 2Na + 2H2O → 2NaOH + H2

Calculate the molar mass of NaOH:

Na: atomic mass = 22.99 g/mol

O: atomic mass = 16.00 g/mol

H: atomic mass = 1.01 g/mol

Molar mass of NaOH = (1 * Na) + (1 * O) + (1 * H) = 22.99 + 16.00 + 1.01 = 40.00 g/mol

Determine the number of moles of Na:

Given mass of Na = 8.0465 g

Number of moles of Na = mass / molar mass = 8.0465 g / 22.99 g/mol = 0.35015 mol

Use stoichiometry to convert moles of Na to moles of NaOH:

According to the balanced equation, 2 moles of Na produce 2 moles of NaOH.

Number of moles of NaOH = 0.35015 mol * (2 mol NaOH / 2 mol Na) = 0.35015 mol

Convert moles of NaOH to grams:

Mass of NaOH = number of moles of NaOH * molar mass of NaOH = 0.35015 mol * 40.00 g/mol = 13.994 g

Using 5 significant figures, the mass of NaOH that can be produced from 8.0465 g of Na is approximately 13.994 g.

Let's denote this probability as p, where p represents the probability of a single calculator failing. Therefore, the probability of both calculators failing is given by \(p^2\).

If the failure rate of the second calculator is the same and independent of the first, we can assume that the probability of failure for each calculator remains constant. To determine the probability of both calculators failing, we need to multiply the probabilities of each calculator failing independently. Since the events are independent, we can multiply the individual probabilities together.

Probability of both calculators failing = Probability of first calculator failing * Probability of second calculator failing

= p * p

= \(p^2\)

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Answer:

30

Step-by-step explanation

After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times

1. To calculate the number of members after one year, multiply the initial number of members (101010) by the factor of 1.21.21:

101010 x 1.21.21 = 12312

2. To calculate the number of members after two years, multiply the initial number of members (101010) by the factor of 1.21.21 twice:

101010 x 1.21.21 x 1.21.21 = 149149

3. To calculate the number of members after three years, multiply the initial number of members (101010) by the factor of 1.21.21 three times:

101010 x 1.21.21 x 1.21.21 x 1.21.21 = 180180

After one year, the club had approximately 123123 members. After two years, the club had approximately 149149 members. After three years, the club had approximately 180180 members.

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(a) For the null hypothesis, we would use the claim that the average weight of a healthy 3-month-old colt is equal to 60 kg, that is,

H0 : μ = 60 kg.

(b) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is less than 60 kg, that is,

H1: μ < 60 kg.

(c) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is greater than 60 kg, that is, H1: μ > 60 kg.

(d) For the alternate hypothesis, we would use the claim that the average weight of a wild Nevada colt (3 months old) is different from 60 kg, that is, H1: μ ≠ 60 kg.

(e) For the test in part (b), the area corresponding to the p-value would be on the left of the mean because the alternate hypothesis is one-tailed and represents a left-tailed test.

For the test in part (c), the area corresponding to the p-value would be on the right of the mean because the alternate hypothesis is one-tailed and represents a right-tailed test.

For the test in part (d), the area corresponding to the p-value would be on both sides of the mean because the alternate hypothesis is two-tailed and represents a two-tailed test.

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Answer:

(-3,2)

Step-by-step explanation:

To solve this system, you first have to find what either x or y is.

In the top equation, x is by itself, so it is the easiest route to find.

x+3y=3

Subtract the 3y to get x by itself

x=3-3y

Now that we know that x=3-3-3y, plug it into the other equation for x.

3y-2(3-3y)=12

3y-6+6y=12

Solve to get y by itself

9y=18   Divide by 9

y=2

Finally, now that you have y, you can plug 2 back into x=3-3y for y.

x=3-3(2)

x=3-6

x=-3

Therefore, (-3,2)

If you want to double-check, just plug both x and y back into one of the equations

x+3y=3

-3+3(2)=3

-3+6+3

3=3

Answer:

y = -x - 6

Step-by-step explanation:

We can use the slope intercept form expression [ y = mx + b ], the slope, and the point to find the y-intercept.

-7 = 1(-1) + b

-7 = -1 + b

-6 = b

Input the data we know back into the expression.

y = -x - 6

Best of Luck!

Answer:

B, x = 2

Step-by-step explanation:

I'll explain in a seconda

Answer:

If you want to turn a percentage into a fraction divide by 100:

20%/100 = 0.2

0.2*16 = 3.2$

and if you want to turn a decimal into a fraction multiply by 100.

His discounted price will be 3.2$.

Have a nice day! :-)

and if you have questions please ask!

Percentage is the part of a whole given as a fraction of the hundred. The discounted price of the CD is $12.8.

Andrew has a coupon for 20 % off of the price of any CD.

The price of the CD purchased by the Andrew is $16.

Percentage is the part of a whole given as a fraction of the hundred.

As the Andrew has a coupon of 20 percent, the 20 percent will be off whatever he buys. Now the discount price for the $16 priced CD is equal to the 20 percent of the 16. Thus the discount is,

\(d=\dfrac{16\times20}{100} \\ \)

\(d=3.2\)

Thus the discount on the CD is 3.2.

Now the discounted price of the CD is equal to the difference of the price of the CD and the discount. Thus the discounted price of the CD is,

\(P=16-3.2\)

\(P=12.8\)

Thus the discounted price of the CD is $12.8.

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Answer:

sum of digit:2+1+4+4+6+7+6+5+4=39 . Which is not divisible by 9

Answer:

Step-by-step explanation:

it has 14 sides

360/14= 25.714

rounding to the nearest tenth we get:

25.7

The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:

\(81x^6 - (y + 1)^2\)

Replacing U and V:

\(81(3x^3)^2 - (V)^2\)

Simplifying:

\(81 \times 9x^6 - V^2\)

\(729x^6 - V^2\)

Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)

In this way, we can represent the original expression in a simplified form using the assigned values for U and V.

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Consider the expression: \(81x^6 - (y + 1)^2\)

If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?

In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.

The locations of the vertices of the dilated figures are (48,16), (32,40), and (8,24).

This problem can be solved by using the concept of scale factor. Scale factor is useful in finding proportional measurements.

Proportion implies having the same ratio.

Scale factor can be defined as the ratio of the measurement of the model to the measurement of the actual form in the simplest form. In other words, the ratio of any two corresponding lengths in two similar geometric figures is called a scale factor.

If the scale factor is more than 1, that is, scale factor > 1,

then it is an enlargement,

If the scale factor is less than 1, that is, scale factor < 1,

then it is a reduction.

We can obtain the answer by multiplying the given coordinates, first by a scale factor of 4 and then by a scale factor of 2/3.

(18,6) => (18x4, 6x4) => (72,24) => (72x2/3, 24x2/3) => (48,16)

(12,15) => (12x4, 15x4) => (48,60) => (48x2/3, 60x2/3) => (32,40)

(3,9) => (3x4, 9x4) => (12,36) => (12x2/3, 36x2/3) => (8,24)

Therefore, using the concept of scale factor, we get the locations of the vertices of the dilated figures as (48,16), (32,40), and (8,24).

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation: