in older adults, a higher level of social support is related to question 20 options: lower levels of physical activity. a higher probability of being institutionalized. an early cognitive decline. a lower probability of depression.

The roots of the equation 5x⁴ - 12x³ - 11x² + 6x = 0 are -1, 0, 2/5, and 3. These roots correspond to the answer choice (G) -1, 0, 2/5, 3. To find the roots of the given equation, we need to factorize it and solve for x.

By factoring out an x from the equation, we have:

x(5x³ - 12x² - 11x + 6) = 0

Now we can set each factor equal to zero and solve for x. From the first factor, we find x = 0 as one of the roots.

To solve the second factor, we can use various methods such as synthetic division or factoring by grouping. By using synthetic division or factoring by grouping, we find that the remaining roots are x = -1, x = 2/5, and x = 3.

Therefore, the roots of the equation 5x⁴ - 12x³ - 11x² + 6x = 0 are -1, 0, 2/5, and 3, corresponding to answer choice (G).

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We can create 19 words using the letters U, S, and C where each letter is used at least once and the total length is 6, and at least as many Us as Ss and at least as many Ss as Cs

The given letters are U, S, and C. There are 4 different cases we can create words using the letters U, S, and C.

All letters are distinct: In this case, we have 3 letters to choose from for the first letter, 2 letters to choose from for the second letter, and only 1 letter to choose from for the last letter.

So the total number of ways to create words using the letters U, S, and C is 3 x 2 x 1 = 6.

Two letters are the same and one letter is different: In this case, there are 3 ways to choose the letter that is different from the other two letters.

There are 3C2 = 3 ways to choose the positions of the two identical letters. The total number of ways to create words using the letters U, S, and C is 3 x 3 = 9.

Two letters are the same and the third letter is also the same: In this case, there are only 3 ways to create the word USC, USU, and USS.

All three letters are the same: In this case, we can only create one word, USC.So, the total number of ways to create words using the letters U, S, and C is 6 + 9 + 3 + 1 = 19

Therefore, we can create 19 words using the letters U, S, and C where each letter is used at least once and the total length is 6, and at least as many Us as Ss and at least as many Ss as Cs, and the word is lexicographically first among all of its rearrangements.

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1.1 The relationship between sampling distribution and confidence interval is that the sampling distribution helps us understand the distribution of sample statistics (such as the sample mean or proportion) when repeatedly sampling from a population.

The confidence interval, on the other hand, provides a range of values within which we can be confident that the true population parameter lies based on the sample data.

In other words, the sampling distribution gives us information about the variability and distribution of sample statistics, while the confidence interval uses this information to estimate the range of likely values for the population parameter.

1.2 To calculate the probability that the sample mean is between 9.0 and 11.0, we need to standardize the values using the z-score formula and then look up the corresponding probabilities from the standard normal distribution.

First, calculate the z-scores:

z1 = (9.0 - 10) / (3 / √40) = -1.8257

z2 = (11.0 - 10) / (3 / √40) = 1.8257

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the sample mean is between 9.0 and 11.0 can be calculated as the difference between the two probabilities:

P(9.0 < x < 11.0) = P(z1 < Z < z2)

1.3 (a) To calculate the probability that the percentage of voters who support the candidate is between 40% and 45% in a sample of 200 voters, we can use the sampling distribution of sample proportions. Assuming the sample proportion follows a normal distribution, we can standardize the values using the z-score formula and then calculate the corresponding probabilities.

First, calculate the z-scores:

z1 = (0.40 - 0.40) / √[(0.40 * (1 - 0.40)) / 200] = 0

z2 = (0.45 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Next, look up the probabilities associated with these z-scores using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is between 40% and 45% can be calculated as the difference between the two probabilities:

P(40% < p < 45%) = P(z1 < Z < z2)

(b) To calculate the probability that the percentage of voters who support the candidate is more than 50%, we can again use the sampling distribution of sample proportions. We standardize the value using the z-score formula and calculate the corresponding probability.

Calculate the z-score:

z = (0.50 - 0.40) / √[(0.40 * (1 - 0.40)) / 200]

Look up the probability associated with this z-score using a standard normal distribution table or a calculator. The probability that the percentage of voters who support the candidate is more than 50% can be calculated as:

P(p > 50%) = P(Z > z)

1.4 To determine the 95% confidence interval for the true mean resistance, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

First, calculate the standard error:

Standard Error = population standard deviation / √(sample size)

              = 0.35 / √10

Next, find the critical value corresponding to a 95% confidence level from a t-distribution table with 9 degrees of freedom (n-1). The critical value for a 95% confidence level is approximately 2.

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The required difference of the polynomial functions is -9s^2 + 4s - 2

Given the following difference of polynomial expressed as:

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

We are to find the difference

(–6s2 + 12s – 8) – (3s2 + 8s – 6)

Expand

–6s^2 + 12s – 8 - 3s^2 - 8s + 6

Collect the like terms

–6s^2- 3s^2 + 12s - 8s - 8 + 6

-9s^2 + 4s - 2

Hence the required difference of the polynomial functions is -9s^2 + 4s - 2

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complete question

Find each difference.

(–6s2 + 12s – 8) – (3s2 + 8s – 6) =

–9s2 + 4s – 14

–9s2 + 4s – 2

–9s2 + 20s – 14

–9s2 + 20s – 2

The solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

To solve the given differential equation y''(t) = 1 - t^17 with the initial condition y(1) = 12, we can integrate the equation twice.

Integrating the equation once will give us y'(t):

y'(t) = ∫(1 - t^17) dt

y'(t) = t - (1/18)t^18 + C₁

Now, we need to apply the initial condition y(1) = 12 to determine the value of the constant C₁:

12 = 1 - (1/18) + C₁

C₁ = 12 + (1/18) - 1

C₁ = 217/18

Next, we integrate y'(t) to find y(t):

y(t) = ∫(t - (1/18)t^18 + 217/18) dt

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + C₂

Finally, we apply the initial condition y(1) = 12 to determine the value of the constant C₂:

12 = (1/2) - (1/342) + (217/18) + C₂

C₂ = 12 - (1/2) + (1/342) - (217/18)

C₂ = (20619 - 1 + 6 - 819)/(342)

C₂ = 19805/342

Therefore, the solution to the differential equation y''(t) = 1 - t^17 with initial condition y(1) = 12 is:

y(t) = (1/2)t^2 - (1/342)t^19 + (217/18)t + (19805/342)

None of the provided options (a, b, c, d) match the correct solution.

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Answer:

2 or 3

Step-by-step explanation:

solve, we say leading diagonal - lagging diagonal

leading diagonal =5andx 5×x=5X

lagging diagonal= 3 and 2 3×2= 6

then,

5x-6= x^2

X^2-5x+6=0

X^2-3x-2x+6=0

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

(x-2)(x-3)=0

x=2 or 3

Answer:

Speed = 0.895 feet per minute

Step-by-step explanation:

Distance covered by the sloth = 38 of a foot

                                                   = \(\frac{1}{38}\) foot

Time taken to move this distance = 34 of a minute

                                                        = \(\frac{1}{34}\) minute

Since, formula for the speed is,

Speed = \(\frac{\text{Distance covered}}{\text{Time taken}}\)

           = \(\frac{\frac{1}{38}}{\frac{1}{34}}\)

           = \(\frac{1}{38}\times \frac{34}{1}\)

           = \(\frac{17}{19}\)

           = 0.895 feet per minute

The total cost to fill Kenny's entire attic given the cost per cubic yards is $904.50; option A

\(V = 1/4h \sqrt{ { - a}^{4} + 2 {ab}^{2} } + 2 {ac}^{2} - {b}^{4} + 2 {bc}^{2} - {c}^{4} \)

= 1/4×9 √-4⁴ + 2(4×5)² + 2(4×3)² - 5⁴ + 2(5×3)² - 3⁴

= 9/4√256 + 2(20)² + 2(12)² - 3125 + 2(15)²- 81

= 9/4√256 + 2(400) + 3(144) - 3125 + 2(225) - 81

= 9/4√256 + 800 + 432 - 3125 + 450 - 81

= 9/4√-1268

= 54 cubic yard

Total cost to fill Kenny's entire attic = 54 × $16.75

= $904.50

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Answer:

x=8.499

y=0.167

Step-by-step explanation:

the equation says:x^2-9y^2=72....(1)

x+3y=9.......(2)

divide (2) from (1),it becomes:

x-3y=8

making x subject of formula,

x=8+3y....(3)

submitting (3) into (1),it becomes

(8+3y)^2-9y^2=72

64+48y=72

48y=72-64=8

y=8/48=0.167......(4)

submitting (4) into (2),it becomes

x+3(0.167)=9

x+0.501=9

x=9-0.501

x=8.499

Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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HIPAA (Health Insurance Portability and Accountability Act) regulations require that institutions establish strong internal controls to mitigate risks and protect data centers from data breaches. HIPAA provides a national framework for securing health data.

What is HIPAA?HIPAA is a United States federal law that was enacted in 1996. The act's primary purpose is to ensure that individuals can keep their health insurance when they switch jobs. HIPAA also aims to protect the confidentiality and privacy of medical records. HIPAA regulations establish a national standard for privacy and security of protected health information (PHI).

It also requires institutions to set up effective internal controls to prevent the unauthorized disclosure of PHI. HIPAA has become the national framework for securing health data. HIPAA regulations require that institutions establish strong internal controls to mitigate risks and protect data centers from data breaches. HIPAA provides a national framework for securing health data.

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The scale factor of the preimage to image is 3. Then the correct option is C.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The picture rectangle has points on coordinates (0, 0), (0, 8), (9, 8), and (9, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

The scale factor is given as,

SF = 9 / 3

SF = 3

The scale factor of the preimage to image is 3. Then the correct option is C.

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The complete question is given below.

What is the scale factor in the dilation?

On a coordinate plane, the image rectangle has points (0, 0), (0, 8), (9, 8), and (8, 0). The pre-image has points (0, 0), (0, 2.5), (3, 2.5), and (3, 0).

a) One-sixth

b) One-third

c) 3

d) 6

Answer:

Step-by-step explanation: C  !!!!!! / 3

Edge 2023

1/6

1/3

3   <--------------- correct

6

Answer:

A fruit bouquet artist charges $1.50 for each piece of fruit in a bouquet, x, plus an additional $17 for the basket and decorations. Customers receive free delivery when their order is over $40.

Step-by-step explanation:

$1.50 represents the cost of each piece of fruit, but we don't know how many fruits are included in the basket, so let x be the number of fruit. That total must be added to the cost of the basket.

If consumers receive free delivery for orders over $40, then 17+1.50x must be greater than $40.

(x+1) & (x-5) are the factors of given equation.

The given Equation is,

x3- \(3x^{3}\) - 9

Here, If we substitute x =5, in the given equation, then we find

     (5)3 - 3(5)3 - 9*5 -5 = 0

x-5 is factor of given equation to find another factor dividing given equation by x-5

    we will get =(x2+2x+1) after dividing the equation by x - 5

Hence x3- \(3x^{3}\) - 9 =(x2+2x+1) (x-5)

                            =(x+2)2 (x-5)

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The equation that represents the function shown on the graph is (d) y = 4x

The graph that completes the question is added as an attachment

On the graph, we have the following ordered pairs

Line starts at (0. 0) and through (2, 8), (4, 16), then end at (5, 20)

These ordered pairs are

(x, y) = (0. 0), (2, 8), (4, 16), (5, 20)

The ordered pair (0, 0) implies that the line passes through the origin

This means that the equation can be represented as

y = Y/X * x

Where

(X, Y) = any of (2, 8), (4, 16), (5, 20)

So, we have

y = 8/2 * x

Evaluate the quotient

y = 4 * x

This gives

y = 4x

Hence, the equation is (d) y = 4x

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Answer: d

Step-by-step explanation:

yw

Answer:

B im pretty sure

Answer:

3/2 or 1 1/2

Step-by-step explanation:

5÷3 1/3

5/1 ÷ 10/3 because you have to get it into an improper fraction form in order to divide

5/1 × 3/10 because you have to multiply the first number by the reciprocal

5  and 10 cancel out so you would have 2 at the bottom

3/2 or 1 1/2

Answer:

For 1st q its A

For 2nd q its B

For 3rd q its A

For 4th q its A

Step-by-step explanation:

Reflection dont change vertices orientation

1/2 is like dividing by 2 so half

(X,Y) reflection on x axis will make y negative

If u rotate 90° clock wise it will go to Q1

Now i can have my brainliestplease thanksss

The given statement is TRUE

If an angle is counterclockwise then the angle is said to be positive.

We can conclude and find the explanation such that,

If any angle is measured in the direction equivalent to counterclockwise from the starting point of the terminal side then that angle is termed a positive angle whereas if an angle is measured from the direction clockwise then the angle is termed as a negative angle.

Refer to the attached images to find the phenomenon of positive and negative angles.

For example: According to the first figure let us draw an angle of 90°

We will calculate this angle as = \(\frac{90}{360}\)

= 1/4

Thus, moving counterclockwise in the positive x-axis.

According to the second figure let us draw the angle of 360°

We will calculate this angle as = \(\frac{360}{360}\)

= 1

Thus, 1 complete rotation is done around the circle moving counterclockwise from the positive side of the x-axis.

Therefore,

The given statement is TRUE

If an angle is counterclockwise then the angle is said to be positive.

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Answer:

A.) 6

B.) 24

C.) $60

Step-by-step explanation:

Given that :

Cost of Mango = $2

Purchase of 6 mangoes earns 2 free mangoes

(a) Robin purchased $36.00 worth of mangoes.

How many free mangoes did Robin get?

$36 / price per Mango

$36 / $2 = 18 mangoes

18 / 6 = 3

Hence, free mangoes (3 * 2) = 6 free mangoes

(b) How many mangoes did he get all together?

18 mangoes + 6 mangoes = 24 mangoes

(c) Peter also bought mangoes. He received 40 mangoes. How much did Peter pay?

Set of mangoes purchased:

40/ (6 + 2) = 40/8 = 5 sets of mangoes

Hence, amount paid :

2 * 6 * 5 sets

$60

If A,B, and C are the letters selected and we use A twice, B twice, and C once. The number of ways different passwords exist in this scenario are 30.

A password, sometimes known as a passcode (in devices made by Apple, for instance), is a hidden piece of information that is typically a long string of characters and is used to verify a user's identity. Passwords were always thought to be memorized, but today's average person has access to a huge number of password-protected services, making it difficult to remember a different password for each one. The secret is kept by a party known as the claimant, and the person confirming the claimant's identity is known as the verifier, according to the nomenclature of the NIST Digital Identity Guidelines. The verifier can determine the identity of the claimant when the claimant successfully uses a recognized authentication technique to show the verifier that they know the password.

A, B and C are selected

A is used twice B is used twice and C is once

Total ways = 5!/2!.2! = 30

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Answer:

D

Step-by-step explanation:

When multiplying numbers with the same base but different exponents, add the exponents together.

In linear equation, 1/5 min far will he travel in 1 hour .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

6/8 = 3/4

1/5 min/hr *  1 hr = 1/5 min

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two angles that add up to 90 degrees are called complementary angles.

Answer:

6 < x

Step-by-step explanation:

4(3x + 2) <5(3x - 2)

Distribute

12x +8 < 15x -10

Subtract 12 x from each side

12x +8-12x < 15x-12x -10

8 < 3x - 10

Add 10 to each side

8+10 < 3x-10+10

18 < 3x

Divide by 3

18/3 < 3x/3

6 < x

Answer: y = \(\frac{1}{5}\)x + 8

Step-by-step explanation:

       This is asking us to remove the parameter. In other words, we want an equation with only the relation between x and y, so we need to remove the t. There are a few ways to do this, but I am going to set one equation equal to t and then plug it into the next one.

     Given:

x = 5t

    Divide both sides of the equation by 5:

t = \(\frac{1}{5}\)x

     -

    Given:

y = t + 8

    Plug in:

y = (\(\frac{1}{5}\)x) + 8

    Answer:

y = \(\frac{1}{5}\)x + 8

The congruence 12x ≡ c (mod 30) has solutions if and only if c is even, and in this case there are 15 incongruent solutions for x modulo 30.

To solve this congruence, we can first simplify it by dividing both sides by the greatest common divisor of 12 and 30, which is 6. This gives us the equivalent congruence:

2x ≡ c/6 (mod 5)

Now we can use modular arithmetic to find the solutions. Since 2 and 5 are relatively prime, we know that 2 has a modular inverse modulo 5, which is 3, since 2*3 ≡ 1 (mod 5). Multiplying both sides of the congruence by 3, we get:

6x ≡ 3c/6 ≡ c/2 (mod 5)

Since 6 is congruent to 1 modulo 5, we can simplify this to:

x ≡ 3c/2 (mod 5)

Now we need to find the values of c such that there are solutions to this congruence. Since we are looking for solutions modulo 30, we only need to consider the values of c modulo 30.

If c is even, then c/2 is an integer and we can find a solution for x modulo 5. Specifically, there is exactly one solution for x modulo 5 for each value of c/2 modulo 5, since 3 is a primitive root modulo 5. Therefore, there are 15 incongruent solutions for x modulo 30 in this case.

If c is odd, then c/2 is not an integer and there are no solutions for x modulo 5. Therefore, there are no solutions for x modulo 30 in this case.

In summary, the congruence 12x ≡ c (mod 30) has solutions if and only if c is even, and in this case there are 15 incongruent solutions for x modulo 30.

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Answer:

Anne = 9, Mark = 12, Sue = 15

Step-by-step explanation:

Total number of chocolates = 36

Sum of the ratio =  3 + 4 + 5 = 12

Number of chocolates Anne got :

                                     \(= \frac{3}{12} \times 36 = 9\)

Number of chocolates Mark got :

                                   \(= \frac{4}{12} \times 36 = 12\)

Number of chocolates Sue got :

                                       \(= \frac{5}{12} \times 36 = 15\)

Answer:

a = - 4

c = 7/2

x = 1, -1/2

Step-by-step explanation:

1) 6(3a+4) = 12a

3a +4 = 2a

a = -4

2) 4c -9 = 5

4c = 14

c = 7/2

3) 2x² - x -1=0

2x² -2x +x -1 =0

2x(x -1)+1(x-1)=0

X = 1 or -1/2