Money Magic
Would you consider your budgeting strategy in this game a success? Why or why not?

The approximate value of K of the given quadratic equation is: 16.842

The general expression of a quadratic function is:

ax² + bx + c = 0

The quadratic formula to find the roots is expressed as:

x = [-b ± √(b² - 4ac)]/2a

The product of the 2 roots of the quadratic equation is equal to the constant term.

Let a and b be used to denote the roots of a given quadratic equation.

But according to given condition, one root is equal to the square of the other root. Thus: b = a²

Thus:

a + a² = k

a * a² = 48

a³ = 48

a = 2∛6

Thus:

2∛6 + (2∛6)² = k

k = 16.842

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Answer:

  428.75π ft³

Step-by-step explanation:

You want the exact volume of a cylinder 35 ft high with a radius of 3.5 ft.

The volume is given by the formula ...

  V = πr²h

  V = π(3.5 ft)²(35 ft) = 428.75π ft³ . . . . . use the given values

The exact volume of the cylinder is 428.75π ft³.

Answer:

(v+8) x (v+9)

We can multiply v into the other two terms in the second bracket, then we can do the same with 8.

(v*v + v*9) + (8*v + 8*9)

v² + 9v + 8v + 72

v² + 17v + 72.

The answers that describe the polygon ABCD if measure A is congruent to measure B, and measure C is congruent to measure D, and segment AB is parallel to segment CD are;

A. Parallelogram

B. Quadrilateral

C. Rectangle

D. Rhombus

E. Square

In Mathematics, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).

In conclusion, a square, parallelogram, rectangle, rhombus, and quadrilateral satisfies the given conditions.

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Answer:

Step-by-step explanation:

The local minimum value of a graph is the point where the graph changes from a decreasing function to an increasing function.

The final amount earned on the investment after 4 years is $900.40.

An investment of $800 is made at an annual interest rate of 3% compounded yearly for 4 years. To calculate the final amount earned on the investment after 4 years, we can use the formula for compound interest:

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

where:

A = the final amount

P = the principal investment, which is $800 in this case

r = the annual interest rate, which is 3% or 0.03 as a decimal

n = the number of times the interest is compounded per year, which is once per year in this case

t = the number of years, which is 4 in this case

Plugging in the values, we get:

A = 800(1 + 0.03/1)¹ˣ⁴

A = 800(1.03)⁴

A = 800(1.1255)

A = $900.40

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Answer:

Step-by-step explanation:

Any value of x may be substituted into this function. So the domain is:

          [tex]D=(-\infty , \infty)[/tex]   or   D=all real [tex]x[/tex]

I am not sure the format how you have been taught to write the answer.

The probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

To find the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday, we need to multiply the probabilities of these two events occurring.

The probability of selecting a gold short sleeve top on Monday is 2/6, or 1/3. There are 2 gold short sleeve tops out of a total of 6 uniforms.

After selecting a gold short sleeve top on Monday and not replacing it, there are 5 uniforms left, of which 2 are red short sleeve tanks. Therefore, the probability of selecting a red short sleeve tank on Tuesday is 2/5.

To find the probability of both events occurring, we multiply the probabilities together:

(1/3) * (2/5) = 2/15

Therefore, the probability of Carrie randomly selecting a gold short sleeve top on Monday and a red short sleeve tank on Tuesday is 2/15.

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The function g(x)=3^x change over the interval from x=8 to x=10 by a factor of 9

The function g(x)=3^x is an exponential function. As x increases, the value of g(x) increases at an increasing rate.

Therefore, over the interval from x=8 to x=10, g(x) will increase at an increasing rate.

To see this, we can calculate g(8) and g(10) and observe the difference between the two values.

g(8) = 3^8 = 6561

g(10) = 3^10 = 59049

So, the rate is

Rate = 59049/6561

Rate = 9

This means that the rate is by a factor of 9

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The value of x in the given similar triangles is 30.8.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.

Similar figures are described as items with the same shape but varying sizes, such as two or more figures. A hula hoop and the wheel of a bicycle are two examples of things whose forms are similar to one another.

Given that the triangles are similar, thus the ratio of their sides are equal.

Here, 28/10 = x / 11

Using cross multiplication we have:

x = 28 / 10 (11)

x = 30.8

Hence, the value of x in the given similar triangles is 30.8.

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I'm sorry, but I don't see a question or any context for your statement. Could you please provide more information or clarify your request?

To choose a simple random sample assign different numbers to the house and visit by choosing randomly.

To choose a simple random sample of the 3 homes to survey,

Jerome could assign each home a number from 1 to 10,

And then use a random number generator or a table of random numbers to select three numbers.

He would then visit the homes corresponding to those numbers for the survey.

For example,

if he assigned the following numbers to each home,

1, 2, 3, 4, 5, 6, 7, 8, 9 ,10

He could use a random number generator or table of random numbers to select three numbers, such as 2, 5, and 9.

He would then visit the homes at 2, 5, 9 for the survey.

If someone is not home when Jerome visits,

He should make a note of it and try to arrange a time to come back and conduct the survey.

If it is not possible to arrange another time,

He should make a note that the household was not surveyed and move on to the next household in the sample.

It is important to keep track of which households were surveyed and which were not.

And to try to minimize any biases that may arise from nonresponse.

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Answer:

C

Step-by-step explanation:

The exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

(a) Tο find the exact prοbability that there wοuld be exactly 70 accidents at the intersectiοn in οne year, we can use the Pοissοn distributiοn fοrmula:

P(X = k) =( [tex]e^{(-λ)[/tex] * [tex]λ^k[/tex]) / k!

where X is the number of accidents, λ is the average rate of accidents per week (1.4), and k is the number of accidents we're interested in (70).

To find the probability of 70 accidents in one year, we need to adjust the value of λ to reflect the rate over a full year instead of just one week. Since there are 52 weeks in a year, the rate of accidents over a year would be 52 * λ = 72.8.

So, we have:

P(X = 70) = ([tex]e^{(-72.8)[/tex]* [tex]72.8^(70)[/tex]) / 70!

Using a calculatοr οr sοftware, we can evaluate this expressiοn and find that:

P(X = 70) ≈ 0.00382

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

(b) Tο use the nοrmal distributiοn as an apprοximatiοn, we need tο assume that the Pοissοn distributiοn can be apprοximated by a nοrmal distributiοn with the same mean and variance. Fοr a Pοissοn distributiοn, the mean and variance are bοth equal tο λ, sο we have:

mean = λ = 1.4

variance = λ = 1.4

Tο use the nοrmal apprοximatiοn, we need tο standardize the Pοissοn randοm variable X by subtracting the mean and dividing by the square rοοt οf the variance:

[tex]Z = (X - mean) / \sqrt{(variance)[/tex]

Fοr X = 70, we have:

Z = (70 - 1.4) / [tex]\sqrt{(1.4)[/tex] ≈ 57.09

We can then use a standard nοrmal table οr calculatοr tο find the prοbability that a standard nοrmal randοm variable is greater than οr equal tο 57.09. This prοbability is extremely small and practically 0, indicating that the nοrmal apprοximatiοn is nοt very accurate fοr this particular case.

Therefοre, the exact prοbability οf there being exactly 70 accidents at the intersectiοn in οne year is apprοximately 0.00382.

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The approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

(a) Using the Poisson distribution, the probability of exactly 70 accidents at this intersection in one year (i.e., 52 weeks) is:

P(X = 70) = (e^(-λ) * λ^x) / x!

where λ = average rate of accidents per week = 1.4

and x = number of accidents in 52 weeks = 70

Therefore, P(X = 70) = (e^(-1.4) * 1.4^70) / 70! ≈ 3.33 x 10^-23

(b) We can use the normal approximation to the Poisson distribution to approximate the probability that there would be exactly 70 accidents at this intersection in one year. The mean of the Poisson distribution is λ = 1.4 accidents per week, and the variance is also λ, so the standard deviation is √λ.

To use the normal distribution approximation, we need to standardize the Poisson distribution by subtracting the mean and dividing by the standard deviation:

z = (x - μ) / σ

where x = 70, μ = 1.452 = 72.8, σ = √(1.452) ≈ 6.37

Now we can use the standard normal distribution table to find the probability that z is less than or equal to a certain value, which corresponds to the probability that there would be exactly 70 accidents at this intersection in one year:

P(X = 70) ≈ P((X-μ)/σ ≤ (70-72.8)/6.37)

≈ P(Z ≤ -0.44)

≈ 0.3300

Therefore, the approximation using the normal distribution gives a probability of approximately 0.3300 that there would be exactly 70 accidents at this intersection in one year.

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The value of M - N is [tex]8x^2[/tex] + 11x - 9 by subtracting the value of N from the value of M.

To find the value of M - N, we first need to subtract the second polynomial N from the first polynomial M.

M - N = ([tex]5x^2[/tex] + 7x - 4) - ([tex]-3x^2[/tex] - 4x + 5)

To subtract the polynomials, we need to add the opposite of the second polynomial (i.e., add the negative of N) to the first polynomial M:

M - N = [tex]5x^2[/tex] + 7x - 4 + [tex]3x^2[/tex] + 4x - 5

Now we can combine like terms:

M - N = ([tex]5x^2 + 3x^2[/tex]) + (7x + 4x) + (-4 - 5)

M - N = [tex]8x^2[/tex] + 11x - 9

Therefore, the value of M - N is [tex]8x^2[/tex] + 11x - 9.

In summary, we found the value of M - N by subtracting the polynomial N from the polynomial M and then combining like terms. The resulting polynomial is [tex]8x^2[/tex] + 11x - 9.

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When AB = AC and A is nonsingular, then the cancellation law holds; is, B = C. The statement is true.

In matrix algebra, the cancellation law is a crucial property to know. It states that if AB = AC, then B = C when A is a nonsingular matrix.

The given statement is true, which means that if AB = AC and A are nonsingular, then B = C. The cancellation law in matrix algebra is a property that helps in solving linear equations involving matrices. It states that if AB = AC and A is a nonsingular matrix, then B = C.

Therefore, we can say that if AB = AC and A is nonsingular, then B = C is true.

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Answer:

36

Step-by-step explanation:

Answer:

B) a 180° rotation about the origin

Step-by-step explanation:

Answer:simpler interest is 109.92.  Annual compounded interest is 111.98

Step-by-step explanation:

Answer: $209.2

Step-by-step explanation:
hey! i'm gonna try to make this as simple as possible;
with simple interest, the formula to this is I = PRT (Interest = Principle x Rate x Time).
we're going to take the $89 , 4.7% simple interest and the 5 years together into the same sentence like the formula.
89 (Principle, the money) x 4.7% (Interest rate)  x 5 (Time). we'll narrow down the decimal by moving the decimal forward once so we get a decimal of .47 / 0.47.
back to the equation, it is now 89 x .47 x 5. multiply all those and you'll get a sum of 209.15! by the end of the five years, patricia will have $209.15. to the nearest penny, she will have $209.2. (5 or more, it goes to the next number. 4 or less, it stays in the same place.)
hope this helped :)

The trip to the campsite took 2 hours for Sami.

The total time taken by Sami on his journey = 7 hours

Let the time taken by Sami while going from his house to the campsite be 'x' hours

And, the time taken by Sami while coming back from the campsite to his house be 'y' hours

Speed while going from house to campsite = 60 miles per hour

Speed while coming back from campsite to house = 40 miles per hour

Distance from house to campsite and back will be equal as Sami will take the same route.

Let the distance be 'd'.

So, according to the question,
Distance = Speed × Time

We know that,
Time taken while going from house to campsite + Time taken while coming back from campsite = 7 hours

x + y = 7 ...(1)

Distance while going from house to campsite = Distance while coming back from campsited  = 2d ...(2)

Distance = Speed × Timex = d/60 ...(3)

y = d/40 ...(4)

Substituting (2), (3) and (4) in (1), we get,

d/60 + d/40 = 7

Solving the equation, we get d = 120

Therefore, Time taken while going from house to campsite, x = d/60 = 2 hours

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The appropriate z-value to use in the situation given in the question is 1.28.

Given,Total number of adults in the sample = 2092

Number of adults using the internet = 1318

Number of internet users who expect businesses to have websites that give product information = 1041

Probability of internet users who expect businesses to have websites that give product information as per the teacher's statement = 80% = 0.8

To find the appropriate z-value to use in this situation, we need to calculate the standard error of proportion, which is given by:

SEp = √[p(1-p)/n]

where p is the proportion of internet users who expect businesses to have websites that give product information and n is the sample size.

Substituting the given values in the formula,

SEp = √[(1041/1318)(1-1041/1318)/1318]SEp = 0.019

z-value is given by:

z = (p - P)/SEp

where P is the proportion of internet users who expect businesses to have websites that give product information as per the teacher's statement.

Substituting the given values in the formula,

z = (0.8 - 1041/1318)/0.019

z = - 1.28

The appropriate z-value to use in this situation is -1.28.

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Statement to match the given number sentence is The absolute value of -5 is equal to the absolute value of 5.

It is the distance of a number from zero on a number line, and is always positive.

The absolute value of -5 is 5 because -5 is 5 units away from zero on the number line.

Similarly, the absolute value of 5 is 5 because 5 is also 5 units away from zero on the number line.

Therefore, the absolute value of -5 is equal to the absolute value of 5, and the statement for this number sentence is "The absolute value of -5 is equal to the absolute value of 5."

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Answer:

Step-by-step explanation:

The value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

Angles are measurements created by joining two lines, also known as the vertex. Geometric forms such as triangles but also rectangles contain internal angles produced by their sides.

Using the angle bisector theorem in the given triangles:

The ratios of the sides will be equal.

AB / BC = AD / DC

AB = 9 ; BC = 11.7 AD = 3.6

Put the values.

9/11.7 = 3.6 / AD

AD = 3.6*11.7 / 9

AD = 4.68

Thus, the value of length of side of triangle AD using the angle bisector theorem is obtained as: AD = 4.68.

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Answer: it slithers

Step-by-step explanation:

To further explain it They move by dragging their body throughout in the form of loops. Hence, snakes have a crawling or slithering type of movement

Answer:

Overlapping belly scales provide friction with the ground that gives snakes a preferred direction of motion, like the motion of wheels or ice skates.

Step-by-step explanation:

Hope this helps! =D

Mark me brinaliest!=D

The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below

To find the equation of the polynomial table using finite difference, we need to calculate the differences.

The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences

So, we have

x   1   2   3   4   5

y  -2  15  -4  49  282

1st 17 -19  53 233

2nd -36 72 180

3rd 108 108

Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.

We can use the formula for a cubic polynomial:

y = ax^3 + bx^2 + cx + d

Using the table of values, we have:

a + b + c + d = -2

8a + 4b + 2c + d = 15

27a + 9b + 3c + d = -4

64a + 16b + 4c + d = 49

Using a graphing calculator, we have

a = 18, b = -126, c = 269 and d = -163

So, we have

y = 18x^3 - 126x^2 + 269x - 163

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 3)(x + 1)(x - 2)

At (0, -12), we have

a(0 + 3)(0 + 1)(0 - 2) = -12

a = 2

So, we have

y = 2(x + 3)(x + 1)(x - 2)

Expand

y = 2x^3 + 4x^2 - 10x - 12

We can use the formula for a cubic polynomial:

y = a(x - x1)(x - x2)(x - x3)

Using the ordered pairs, we have:

y = a(x + 10)(x + 5)(x - 4)

At (-8, -2), we have

a(-8 + 10)(-8 + 5)(-8 - 4) = -2

a = -1/36

So, we have

y = -1/36(x + 10)(x + 5)(x - 4)

Expand

[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]

We have

g(x) = -9x^5 + 3x^4 + x^2 - 7

g(x) is a polynomial function of odd degree (5), so it will have at least one real root.

Also, the leading coefficient is negative;

So, g(x) has at least one root in the interval (-∞, ∞).

Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).

Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).

Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.

Therefore, g(x) has exactly one real root.

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Answer:

x = 8

Step-by-step explanation:

the angle between the tangent and the radius at the point of contact A is 90°

then Δ ABP is right at A

using Pythagoras' identity in the right triangle

BP² = AP² + AB² , that is

(x + 9)² = x² + 15² ← expand parenthesis on left side using FOIL

x² + 18x + 81 = x² + 225 ( subtract x² from both sides )

18x + 81 = 225 ( subtract 81 from both sides )

18x = 144 ( divide both sides by 18 )

x = 8

Answer:

X = 3,2

Step-by-step explanation:

1)Expand.

[tex]x^{2}[/tex] - 8X+3X - 24 = -30

2)Simplify [tex]x^{2}[/tex]-8X+3X-24 to [tex]x^{2}[/tex]-5X - 24.

[tex]x^{2}[/tex] – 5X – 24 = –30

3)Move all terms to one side.

[tex]x^{2}[/tex] - 5X - 24+ 30 = 0

4)Simplify [tex]x^{2}[/tex]–5X-24+30 to [tex]x^{2}[/tex] - 5X + 6.

[tex]x^{2}[/tex] - 5X + 6 = 0

5)Factor [tex]x^{2}[/tex]–5X+6.

(X-3)(X-2) = 0

6)Solve for X.

X = 3,2

(a) We can rewrite 32 as 2^5, so we have:

8^(2x) = (2^5)^(x+3)

Simplifying the right side, we get:

8^(2x) = 2^(5x+15)

(b) Now we can use the fact that 8 is 2^3, so we can rewrite the left side as (2^3)^(2x) = 2^(6x), giving us:

2^(6x) = 2^(5x+15)

Since the bases are equal, we can equate the exponents and solve for x:

6x = 5x + 15

x = 15

Therefore, the solution is x = 15.