a triangle has integer side lengths of 3,6, and x. for how many values of x will the triangle be acute?

For the largest prime with 2010 digits, the smallest positive integer k such that p²-k is divisible by 12 is mod 24.

First, we need to find the largest prime number with 2010 digits. We know that a prime number greater than 5 must end in either 1, 3, 7, or 9. Therefore, we can start with the number 9 followed by 2009 nines, which gives us a 2010-digit number. We then check whether this number is prime or not using a primality test.

Next, we need to find the smallest positive integer k such that p^2 - k is divisible by 12. We can rewrite this as k ≡ p² (mod 12).

Since p is odd, we know that p² ≡ 1 (mod 8), and since 12 = 3 × 4, we can use the Chinese Remainder Theorem to solve the congruence system k ≡ 1 (mod 8) and k ≡ 1 (mod 3).

Using the fact that 8 and 3 are coprime, we can solve for k using the formula k ≡ a_1N_1y_1 + a_2N_2y_2, where N_1 = 3, N_2 = 8, a_1 = 1, a_2 = 1, y_1 = [tex]3^{(-1)}[/tex] (mod 8) = 3, and y_2 = [tex]2^{(-1)}[/tex] (mod 3) = 2.

Plugging in the values, we get k ≡ 25 (mod 24).

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Answer:

P + A = 70

2P = A + 2

1) P + A = 70

2P = A + 2

2) Solve the system of equations:

Subtract P from both sides of the first equation:

A = 70 - P

Substitute A for 70 - P in the second equation:

2P = (70 - P) + 2

Simplify:

2P = 72 - P

Add P to both sides of the equation:

3P = 72

Divide both sides of the equation by 3:

P = 24

Substitute P for 24 in the first equation:

A = 70 - 24

A = 46

Penelope worked 24 hours and Artemis worked 46 hours.

Answer:

We can use the Law of Cosines to find the length of side AC:

cos(A) = (b² + c² - a²) / 2bc

cos(A) = (85² + 530² - 850²) / (2 × 85 × 530)

cos(A) = -0.3589 (using a calculator)

Since the cosine of an angle is negative in the second quadrant, we have:

A = 180° - cos⁻¹(-0.3589)

A = 114.49°

Now we can use the Law of Cosines again to find the length of AC:

a² = b² + c² - 2bc cos(A)

AC² = 85² + 530² - 2 × 85 × 530 cos(114.49°)

AC ≈ 99.6

Therefore, the length of AC is approximately 99.6. Answer: (B)

To use the discriminant to determine the number and type of solutions for a quadratic equation, we simply need to calculate b² - 4ac and examine the value.

The discriminant of a quadratic equation is a value that can be used to determine the nature and number of solutions for the equation. The discriminant is found by calculating b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

If the discriminant is positive, then the equation has two real solutions. If the discriminant is zero, then the equation has one real solution (a double root). If the discriminant is negative, then the equation has no real solutions but two complex solutions.

If it is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.

For example, consider the quadratic equation 2x² + 4x + 3 = 0. The coefficients are a = 2, b = 4, and c = 3. The discriminant is b² - 4ac = 4² - 4(2)(3) = 16 - 24 = -8. Since the discriminant is negative, the equation has no real solutions but two complex solutions.

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Answer:

61°

Step-by-step explanation:

∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.

Using a system of equations, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed to obtain the desired mixture.

Let x be the amount of the $3.40/lb chocolate needed, and y be the amount of the $9.00/lb chocolate needed to make 44.8 lbs of a $5.00/lb mixture.

We can set up the following system of equations:

x + y = 44.8 (total amount of mixture)

3.4x + 9y = 5(44.8) (total cost of mixture)

Solving this system of equations, we get:

x = 32 lbs of the $3.40/lb chocolate

y = 12.8 lbs of the $9.00/lb chocolate

Therefore, to obtain the desired mixture, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed.

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The area of a penny is .001m²

The quantity of space contained within a circle's perimeter is known as its area. The area that the circle occupies is that which lies inside its perimeter. It is also known as the total number of square units included within that circle. In square units, the area of a circle is equal to πr²or πd²/4 where (Pi) = 22/7 or 3.14.

r stands for circle radius.

circle's diameter is given as d.

Diameter of Penny is  0.750 inches

Converting inch into meter

1 inch=0.0254 meter

0.750 inch= 0.01905 meter

Area of a circle is =π×r²

=π×(0.01905)²

=.001139≈ .001m²

A penny's surface area is.001 m² to the nearest tenth.

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Answer:

1/12

Step-by-step explanation:

Assuming both the die and coin are fair, there is a 1/2 chance of flipping heads and a 1/6 chance of rolling a specific number on the die.

Multiplying, 1/2 * 1/6 is 1/12.

Hope this helps!

Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.

The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.

Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.

a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.

b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.

So in both cases null hypothesis cannot be rejected.

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The complete question is :

f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:

a. z = −0.94

b. z = 2.12

To show that the properties of a probability distribution for a discrete random variable are satisfied, we need to verify that the probability distribution function (PDF) satisfies, The PDF must be non-negative for all values of the random variable and The sum of the probabilities for all possible values of the random variable must be equal to 1.

Let X be a discrete random variable taking values x1, x2, ..., xn, and let P(X) be the probability distribution function for X, such that P(X = xi) = pi for all i.

The PDF must be non-negative for all values of the random variable. This means that for any value xi of the random variable, the probability pi must be greater than or equal to zero. That is,

pi ≥ 0 for all i.

This property ensures that probabilities are never negative, which is a necessary condition for a valid probability distribution.

The sum of the probabilities for all possible values of the random variable must be equal to 1. That is,

∑ pi = 1 for all i.

This property ensures that the total probability of all possible outcomes is equal to 1, which is a necessary condition for a valid probability distribution.

Therefore, if the PDF satisfies these two properties, we can conclude that it represents a valid probability distribution for the given discrete random variable.

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Answer:

hello!!!!

Payment per year

1,000×12months=12,000

total payment over the lifetime of the loan.

12,000×10years=120,000

Answer:

$120,000

Step-by-step explanation:

If you make monthly payments of $1,000 for 10 years, the total payment over the lifetime of the loan would be $1,000 x 12 months x 10 years = $120,000

The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.

To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula

CI = p ± z × sqrt((p × (1 - p)) / n)

where

p = proportion of the sample who answered "Yes"

z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)

n = sample size

Plugging in the values given in the question, we get

p = 0.54

z = 1.96

n = 1019

CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)

CI = 0.54 ± 0.030

CI = (0.51, 0.57)

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I have solved the question in general, as the given question is incomplete,

The complete question is:

Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?

the probability of the complement of (A ∪ B) is 0.3.

How to find and what is Morgan's law?

Since A and B are mutually exclusive, we have:

P(A ∩ B) = 0

The complement of (A ∪ B) is the set of outcomes that are not in A or B. So:

(A ∪ B)′ = A′ ∩ B′

Using De Morgan's law, we have:

A′ ∩ B′ = (A ∪ B)′

We can now use the formula for the probability of the complement:

P((A ∪ B)′) = 1 - P(A ∪ B)

Since A and B are mutually exclusive, we have:

P(A ∪ B) = P(A) + P(B)

So:

P((A ∪ B)′) = 1 - (P(A) + P(B))

Substituting the given probabilities, we get:

P((A ∪ B)′) = 1 - (0.2 + 0.5)

P((A ∪ B)′) = 1 - 0.7

P((A ∪ B)′) = 0.3

Therefore, the probability of the complement of (A ∪ B) is 0.3.

De Morgan's laws are a pair of fundamental laws in Boolean algebra and set theory that describe the relationship between the intersection and union of sets and their complements. The two laws are:

The complement of the union of two sets is equal to the intersection of their complements.

Symbolically: (A ∪ B)′ = A′ ∩ B′

The complement of the intersection of two sets is equal to the union of their complements.

Symbolically: (A ∩ B)′ = A′ ∪ B′

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The required value of the function  (f + g)(x) for given f(x) and g(x) as ( 3 / √x )  - ( 2 / x³ ) and √(5x - 7) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

Function f(x) is equals to,

( 3 / √x )  - ( 2 / x³ ) for all x > 0

Function g(x) is equals to,

g(x) = √(5x - 7)

To get the value of (f + g)(x),

Substitute the value of f(x) and g(x) and  add the functions f(x) and g(x) together,

Sum of f(x) and g(x) is equals to,

(f + g)(x)

= f(x) + g(x)

= ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7)

Therefore, value of the function (f + g)(x) is equals to ( 3 / √x )  - ( 2 / x³ )  + √(5x - 7).

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The above question is incomplete, the complete question is:

The function f is defined by f of x is equal to 3 divided by the square root of x minus 2 divided by x cubed for x > 0, g as a function of x is equal to the square root of quantity 5 x minus 7 Find (f + g)(x).

The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.

It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.

To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.

0-3 interval:

Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:

slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2

pauses [3, 5]:

Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:

slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5

[5–7] Interval:

Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:

slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1

Interval 7 and 9:

Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:

slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5

As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.

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$2010.458 is her new balance after she makes one new transaction for $51.

What does a credit balance mean?

The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.

                                   When you return something you purchased with your credit card, you can receive an additional credit.

Credit balance  = $1,603

   APR = 28.6%

        = 28.6%  * $1,603

         =   458.458

Credit balance  = $1,603 + 458.458

                        = $2061.458

  net balance =  $2061.458 - 51

                      = $2010.458

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Answer:

slope is 1 1/4

Step-by-step explanation:

5/4 = 1 1/4 simplified

The standard deviation that the student would have in order to be publicly recognized is given as 1.17

We would have to assume that the students score follows a normal distribution

This is given as

X ~ (μ, σ)

(μ, σ) are the mean and the standard deviation

1 - 12 percent =

0.88 = 88 percent

using the excel function given as NORMS.INV() we would find the standard deviations

=NORM.S.INV(0.88)

= 1.17498

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A student would have to score approximately 0.89 standard deviations above the mean to be in the top 12% and be publicly recognized.

we can use the empirical rule to estimate the number of standard deviations a student has to score above the mean to be in the top 12 percent, assuming it is a normal distribution

The empirical rule states that for a normal distribution:

we will use the complement rule since our aim is to find the number of standard deviations a student has to score above the mean to be in the top 12%.

The complement of being in the top 12% is being in the bottom 88%.

From the empirical rule, we have that 68% of the data falls within one standard deviation of the mean.

Therefore, the remaining 32% (100% - 68%) falls outside one standard deviation of the mean.

Since we want to find the number of standard deviations a student has to score above the mean to be in the bottom 88%, we can assume that the remaining 32% is split evenly between the two tails of the distribution.      

Applying the z-score formula:

z = (x - μ) / σ

The z-score for a cumulative area of 0.44 is approximately -0.89  found by looking up the z-score corresponding to the cumulative area of 0.44 (half of 0.88) in a standard normal distribution table.

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The pseudoinverse of the given matrix is:A+ = [tex][[-2.00, 0.50, 0.00, -1.00][/tex], [ [tex]0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00],  [ 0.50, -0.50, 0.00,[/tex][tex]0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50],  [ 0.00, 0.00, -1.50, 1.00]].[/tex]

The Moore-Penrose pseudoinverse is a tool used to solve a system of linear equations when the rank of the matrix is less than the number of columns. When a matrix has a rank that is less than the number of columns, it is said to be "singular", meaning that it has no unique solution. To solve this problem, the Moore-Penrose pseudoinverse uses a combination of inverse matrix and transpose matrix operations to calculate a solution that is as close as possible to the true solution. The pseudoinverse is defined mathematically as[tex]A+ = (A*A)^-1A*,[/tex] where A is the original matrix and A* is its transpose. The pseudoinverse of the given matrix is:A+ = [[-2.00, 0.50, 0.00, -1.00], [ 0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00],  [ 0.50, -0.50, 0.00, 0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50],  [ 0.00, 0.00, -1.50, 1.00]].It is calculated by taking the inverse of the matrix multiplication of the transpose of the matrix and the original matrix, and then multiplying that by the original matrix transpose. This process allows for the calculation of the closest solution possible to the original set of equations given by the matrix.

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The fractiοn οf students whο chοse card as their favοrite game type is: 1/6. Thus, option D is correct.

A circle is a clοsed twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a single fixed pοint called the center οf the circle. The distance frοm the center οf the circle tο any pοint οn the circle is called the radius οf the circle.

A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane such that its distance frοm a fixed pοint (the center) remains cοnstant.

A circle is a very impοrtant and cοmmοn geοmetric shape that has many practical applicatiοns in mathematics, physics, engineering, and οther fields.

Tο determine the fractiοn οf students whο chοse card as their favοrite game type, we need tο find the pοrtiοn οf the circle graph that represents the card categοry.

Frοm the graph, we can see that the card categοry cοvers 16.66% οf the entire circle graph.

i.e.

16.66/100 = 1/6

Therefore, the fraction of students who chose card as their favorite game type is:

1/6

So, the answer is option D: 1/6.

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Complete question:

The circle graph shows the favourite game type of students in Ms. Hunter's class.

What fraction of the students chose card?

a. 2/3

b. 5/9

c. 3/10

d. 1/6

Answer:

Step-by-step explanation:

Answer:

4 hours and 28 minutes

Answer:

225 degrees

Step-by-step explanation:

It is: 5/8 of 360 = 225 degrees.

5/8 of a circle is equivalent to 225 degrees.

Given,

5/8 of a circle.

Now,

A full circle represents 360 degrees .

So,

1 complete circle = 360 degrees

Let 5/8 of a circle represents x degrees,

1 complete circle = 360 degrees

5/8 of circle = x degrees

Cross multiply,

x = 5/8 * 360

x = 225 degrees.

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The red car is traveling at a pace of about speed of 56.67 feet per second along the road.

The mathematical relationship between speed, distance, and time will be explained here. A moving body's speed is the distance it covers in a given amount of time. The speed is calculated using the time in hours and the distance in kilometers per hour. If the distance is in m and the time is in seconds, the speed is m/sec.

Let x represent the distance the red automobile has traveled from where it started, and y represent the separation it has from the police car. We learn the following from the Pythagorean theorem:

[tex]x^2 + y^2 = d^2[/tex]

where d is the separation between the two vehicles.

When we divide the two sides by the passage of time, we obtain:

[tex]2x(dx/dt) + 2y(dy/dt) = 2d(dd/dt)[/tex]

Given that dy/dt = -85 ft/s, we need to get dx/dt.

The police car is also mentioned as being 50 feet off the side of the road. Hence, we can state that [tex]d = sqrt(x^2 + (y - 50)^2)[/tex].When we differentiate this phrase according to time, we get:

[tex]dd/dt = (1/2)*(x^2 + (y - 50)^2)^(-1/2)*(2x*dx/dt + 2(y - 50)*dy/dt)[/tex]

By changing the specified values, we obtain

[tex]-85 = (1/2)*sqrt(x^2 + (180 - 50)^2)^(-1/2)*(2x*dx/dt + 2(180 - 50)*(-85))[/tex]

If we condense this phrase, we get:

[tex]dx/dt = 170/3 ≈ 56.67 ft/s[/tex].

The red car is therefore traveling at a pace of about 56.67 feet per second along the road.

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Answer:

A) 15 idek

Step-by-step explanation:

The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.

This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.

Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.

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Complete question is:

Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)

50

An error

80

70

100

The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.

We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.

Answer:

Jika 16,5% dari suatu jumlah adalah 891, kita dapat menggunakan persamaan:

0,165x = 891

di mana x adalah jumlah aslinya. Kita ingin menyelesaikan persamaan ini untuk x.

Kita dapat memulai dengan membagi kedua sisi dengan 0,165:

x = 891 / 0,165

x = 5400

Jadi, jumlah aslinya adalah 5400.
Konsultasi Tugas Lainnya: WA 0813-7200-6413

Answer:

You need to know that the ratio of their sides are congruent

Answer: The top three finishers can be arranged in 15 x 14 x 13 ways, since there are 15 choices for the first place, 14 choices for the second place (since one person has already been selected for first place), and 13 choices for the third place (since two people have already been selected for first and second place).

So the answer is:

15 x 14 x 13 = 2730

Therefore, the top three finishers can be arranged in 2730 different ways. Answer: 2730.

Step-by-step explanation:

Answer:

[tex]2730[/tex]

Step-by-step explanation:

We can solve this problem without using any complex formulas, though there is a formula for solving such problems

Out of the 15 participants, only one participant can be in first place but this can be any one of the participants

So choice for first place = 15 participants

Once a participant has won in the first place, there are 14 remaining participants who can come second place

For third place there are only 13 participants who can make it

The total number of ways in which top three participants can be arranged is

15 x 14 x 13 = 2730 ways

The formula is

[tex]P(n, r ) = \dfrac{n!}{(n-r)!}[/tex]

where n is the population to be considered; here n = 15

r = number of items to be considered ; here r = 3

[tex]P(n, r)[/tex] sometimes written as [tex]_nP_r[/tex] represents the number of subsets  r that can be taken from a larger set  n when the order of the subset matters.

using the formula we get

[tex]P(n, r ) = \dfrac{15!}{(15-3)!} = \dfrac{15!}{12!} = 15 \times \ 14 \times 13 = 2730[/tex]