How many 3 digit numbers have the following property: Non-negative difference of any two neighboring digits is more than 8?
Answers can be 8, 6, 7, 9, 10

Answer:

In slope intercept form, the equation would be y = x - 1.

Step-by-step explanation:

Answer:

\(y=x-1\)

Skills needed: Point-slope Form

Step-by-step explanation:

1) First, let's try to make sense out of the problem. We are given two coordinate points and have to create a line out of it.

---> The most efficient way to solve this is with point-slope form.

The point slope form, given One coordinate point and Slope is:

Given coordinate pair  \((x_1, y_1)\) and Slope \(m\)

---> \(y-y_1=m(x-x_1)\)

2) Now, we have one coordinate pair/point, but we need slope.

---> The slope is the rate of change, and can be found with a formula:

Given two coordinate points \((x_1,y_1)\) and \((x_2, y_2)\), the slope is:

---> \(\frac{y_2-y_1}{x_2-x_1}\)

Let's use this formula for the points above:

\(4=x_1, 6=x_2, 3=y_1, 5=y_2\)

\(\frac{5-3}{6-4} = \frac{2}{2} = 1\)

Based on the above: Slope = 1 (or \(m=1\))

3) Next, we use point slope form. Let's use coordinate pair (4, 3) -- It does not matter which one:

\(y-3=1(x-4)\)

The 1 does not mean anything (since anything multiplied by 1 is itself, so it can be taken out:

\(y-3=x-4\)

Now to get it to slope-intercept form (\(y=mx+b\)) ---> We add 3 to both sides

---> \(y-3+3=x-4+3 \\ y=x-1\)

y=x-1 is the final equation.

Answer:

Pearl pale hand

Step-by-step explanation:

If the average GPA of juniors, seniors, and graduate students in your class differ, you should use a one-way ANOVA test. This is the proper statistical test used to compare the average GPAs of different groups.

ANOVA is used to test whether there are any significant differences between the means of three or more independent groups. In this case, we have three independent groups (juniors, seniors, and graduate students) and we want to determine whether their average GPAs differ significantly by  proper statistical test.

If the ANOVA test indicates that there are significant differences between the means, we can use post-hoc tests (such as Tukey's test or Bonferroni's test) to determine which specific group means differ significantly.

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Step-by-step explanation:

find distance of AC first

ac= √(y2-y1)²+(x2-x1)²

since there is no y we will consider it zero

so Ac= √(16-(-8))²

ac=24

ab is 1/3 of ac so it means

24*1/3=8

so ab is 8 units

The location of point B on the number line is 0.

Given that,
on the number line, point b is between points a and c. the distance between points a and b is 1/3 of ac.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
AB = 1/3 AC
AB = 1/3 (16 - (-8))
AB = 1/3 (16 + 8)
AB = 1/3 * 24
AB = 24 / 3
AB = 8
B - A = 8
B - (-8) = 8
B + 8 = 8
B = 8 - 8
B = 0

Thus, location of the point B on the number line is at 0.

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Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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Answer: \(\boxed{\frac{1}{100}\ or\ 0.01}\)

Step-by-step explanation:

Determine the value of \(y^{12} \ when\ y=10^{-\frac{1}{6}\)

\(=(10^{-\frac{1}{6} })^{12}\)

\(=\frac{1}{100}\ or\ 0.01\)

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ y^{12}\hspace{5em}y=10^{-\frac{1}{6}}\qquad \implies \qquad \left( 10^{-\frac{1}{6}}\right)^{12}\implies 10^{-\frac{1}{6}\cdot 12} \\\\\\ 10^{-2}\implies \cfrac{1}{10^2}\implies \cfrac{1}{100}\)

y=ax^4 + bx^3 + cx^2 + dx + e

Since a< 0 we know that it has to go to - infinity for x going to - infinity and x going to + infinity. That rules out choices B and C.

The maximum number of turning points a polynomial can have is n-1 where n is the degree of the polynomial

(turning points is change of direction)

The graph D has 5 turning points and the degree of the polynomial is 4 so it is not possible

A is your solution.

Answer:

the answer is C. -2.35 and 0.85

Step-by-step explanation:

1. \(2x^{2}\)+3x-4.=0

2. x=\(\frac{-3+\sqrt{9+8x4.} }{4}\), \(\frac{-3-\sqrt{9+8x4.} }{4}\)

3. 0.850781, -2.350781

Answer:

49a²b² - 9c²

Step-by-step explanation:

(7ab+3c)(7ab-3c)

= 49a²b² - 21abc + 21abc - 9c²

= 49a²b² - 9c²

So, the answer is 49a²b² - 9c²

Answer: 49a²b² - 9c²

Step-by-step explanation:

     We will apply the difference of two squares formula:

(7ab+3c)(7ab-3c)

(7ab)² - (3c)²

49a²b² - 9c²

Answer:

= 8x^2 + 12xy − 56y^2

Step by step:

(2x+7y)(4x−8y)

=(2x+7y)(4x+−8y)

=(2x)(4x)+(2x)(−8y)+(7y)(4x)+(7y)(−8y)

=8x^2−16xy+28xy−56y^2

=8x^2+12xy−56y^2

Answer:

Area of the trapezium = 30 \(cm^{2}\)

Step-by-step explanation:

a = 14

b = 4

h= 5

Area of trapezium =  \(\frac{1}{2} }\)  ( a + b) h = \(\frac{1}{2}\) (14+4) 5

= \(\frac{1}{2}\) x 18 x 5 = 6 x 5 [I solved  \(\frac{1}{2}\) and 18]

= 30!

Answer:

Step-by-step explanation:

100/120 = 15

15/100, which means that 18/120 as a percentage is 15%.

hope this helps :)

Answer:

D. (4, -7)

Step-by-step explanation:

To see if a point lands on the graph of a line, substitute the coordinates (x, y) to the x and y in the equation to see if the result is true:

Option A: (2, 7)
Substitute the values in:

\(y=-2x+1\\7=-2(2)+1\\7=-4+1\\7=-3\)
Not true.
So option A is out.

Option B: (3, -8)

Substitute the values in:

\(y = -2x + 1\\-8=-2(3)+1\\-8=-6+1\\-8=-5\)

Not true.
So option B is out.

Option C: (6, 8)

Substitute the values in:

\(y = -2x + 1\\8=-2(6)+1\\8=-12+1\\8=-11\)

Not true.
So option C is out.

Option D: (4, -7)

Substitute the values in:

\(y = -2x + 1\\-7=-2(4)+1\\-7=-8+1\\-7=-7\)
True.
So point (4, -7) lands on the graph of the line. You can also see this visually in a graphing calculator:
(See picture)

We must represent the number 4.082, the options you are giving us are from an apparent decomposition of the previous number

The correct option is B: Four and eighty-two thousandths, It is indeed 4 whole units and 82 thousandths. The other options are not correct

Answer:

-3<x<5

Step-by-step explanation:

Given the inequality 2x-3<7 and 5-x<8

Solve 2x-3<7

Add 3 to both sides

2x-3+3 < 7+3

2x < 10

2x/2 < 10/2

x < 5

Solve 5-x<8

subtract 5 from both sides:

5-x-5<8-5

-x < 3

multiply both sides  by -1

-(-x) > -3

x > -3

-3<x

Combine both solutions x < 5 and -3<x

-3<x<5

The solution to the compound inequality is -3<x<5

Answer:

K=40

Step-by-step explanation:

240/6=40 grams and egg

check 6x40=240

Answer:  K= 40

Step-by-step explanation: divide 240 by 6 :)

240/6=40

A reliable test is one that can measure what it is supposed to measure consistently, yield the same results when given a second time, and provide an unbiased score, ensuring that the results obtained are valid and reliable. Answer is D.

The reliability of a test refers to its consistency and stability over time and under different conditions. It is the extent to which a test is able to yield the same results repeatedly. A reliable test should be able to measure what it is supposed to measure consistently, without any errors or fluctuations. Additionally, it should provide an unbiased score, which means that it should not be influenced by any external factors such as personal biases or environmental factors. Therefore, the answer to the question is D, all of the above.

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Answer:

A diameter is a chord.

Step-by-step explanation:

A diameter is a chord.It is the longest chord.

264 is  the four-firm concentration ratio of this market.

What is ratio simple math?

The top four firms in the industry have 10% , 8% ,8%, 6% of the market.

the four-firm concentration ratio of this market is

                  =   (10² + 8² +8² + 6²

                   = 264

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a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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The point of intersection between the functions y = f(t) and y = 200 represents the number of years since 1950 when the population growth in the U.S. reached 200 million.

The function f(t) represents the population growth in the U.S. between 1950 and 2000 in millions. The function is defined as f(t) = 150e^(0.013t), where t is the number of years since 1950.

To find the point of intersection between y = f(t) and y = 200, we set the two equations equal to each other:

f(t) = 200.

Substituting the expression for f(t) from the given function, we have:

150e^(0.013t) = 200.

By solving this equation for t, we can determine the number of years since 1950 when the population growth in the U.S. reached 200 million.

The exact value of t can be found by applying logarithms, but since the focus is on describing the meaning of the point of intersection, we can state that the point of intersection represents the specific time in years since 1950 when the U.S. population growth reached 200 million.

Therefore, finding the point of intersection helps us identify the year when the U.S. population, according to the given exponential growth model, reached the specified value of 200 million.

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The expression is given as,

The given expression is simplified as follows:

Thus the result of the given expression is,

Therefore, the function y as a function of x is: y(x) = c1 e^(-x) - (1/2) e^x - (7/2) e^(3x) where c1 is a constant determined by the initial conditions.

We are given the differential equation:

y′′′ − 3y′′ − y′ + 3y = 0

To solve this equation, we can first find the characteristic equation by assuming that y = e^(rt), where r is a constant:

r^3 e^(rt) - 3r^2 e^(rt) - r e^(rt) + 3e^(rt) = 0

Simplifying and factoring out e^(rt), we get:

e^(rt) (r^3 - 3r^2 - r + 3) = 0

This equation has three roots, which we can find using numerical methods or by making educated guesses. We find that the roots are r = -1, r = 1, and r = 3.

Therefore, the general solution to the differential equation is:

y(t) = c1 e^(-t) + c2 e^t + c3 e^(3t)

where c1, c2, and c3 are constants that we need to determine.

Using the initial conditions, we can find these constants:

y(0) = c1 + c2 + c3 = -4

y′(0) = -c1 + c2 + 3c3 = -6

y′′(0) = c1 + c2 + 9c3 = -20

We can solve these equations simultaneously to find c1, c2, and c3. One way to do this is to subtract the first equation from the second and third equations, respectively:

c2 + 4c3 = -2

c2 + 8c3 = -16

Subtracting these two equations, we get:

4c3 = -14

Solving for c3, we get:

c3 = -14/4 = -7/2

Substituting this value of c3 into one of the earlier equations, we can solve for c2:

c2 + 8(-7/2) = -16

c2 = -1/2

Finally, we can use these values of c1, c2, and c3 to write the solution to the differential equation as:

y(t) = c1 e^(-t) - (1/2) e^t - (7/2) e^(3t)

Substituting x for t, we get:

y(x) = c1 e^(-x) - (1/2) e^x - (7/2) e^(3x)

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The pool will have approximately 12,555 gallons of water left in it after 12 days.

To find out how many gallons of water will be left in the pool after 12 days, given that it evaporates at a rate of 2% per day and has 16,000 gallons today, follow these steps:

1. Determine the rate of water remaining in the pool each day:

Since the pool loses 2% of water daily, the remaining percentage is 100% - 2% = 98%.

In decimal form, this is 0.98.

2. Calculate the amount of water after 12 days:

To do this, raise the daily remaining water rate (0.98) to the power of the number of days (12):

0.98¹² ≈ 0.7847.

This represents the percentage of water remaining in the pool after 12 days.

3. Multiply the initial water amount (16,000 gallons) by the percentage of water remaining after 12 days (0.7847):

16,000 * 0.7847 ≈ 12,555 gallons.

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Answer:

90

Step-by-step explanation:

Add up all the numbers in the data set and divide that number by the amount of numbers in the data set

85 + 97 + 84 + 88 + 95 + 100 + 81 = 630

630/7 = 90

The value of a for which the equation has an infinite number of solutions is 5.

The solution to the equation: The result is a distribution of weights to the variables involved, establishing a balance in the calculation.

The equation given is written below:

Both sides of the equation must have the same value for an infinite number of solutions.

12x + 30 = 6(2x + a)

Simplifying the equation:

12x + 30 = 12x + 6a

Canceling 12x both sides. We get,

the value of a = 5

The value of a for which the equation has an infinite number of solutions is 5.

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The probability of all four students needing another math class is 0.4096.

To find the probability that all four students need to take another math class, we need to use the concept of independent events. The probability of the first student needing another math class is 0.78, and the probability of the second student needing another math class is also 0.78.

Similarly, the probability of the third and fourth students needing another math class is also 0.78. Since these events are independent, we can multiply the probabilities together to get the probability of all four students needing another math class.

Therefore, the probability of all four students needing another math class is:

P = 0.78 x 0.78 x 0.78 x 0.78 = 0.4096

This means that there is a 40.96% chance that all four students randomly selected will need another math class.

It's important to note that this probability assumes that each student's math needs are independent of each other, and that the sample of four students is representative of the larger population of students at the college. If there are any dependencies or biases in the selection process or the population, the probability may be different.

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Complete Question:

78% of all students at a college still need to take another math class. If 4 students are randomly selected, find the probability that a. Exactly 2 of them need to take another math class. b. At most 2 of them need to take another math class. c. At least 2 of them need to take another math class. d. Between 2 and 3 (including 2 and 3) of them need to take another math class. Round all answers to 4 decimal places.

Let's call the length of the rectangle "L" and the width "W". We know that the width is 10 cm shorter than the length, so we can write.

W = L - 10
We also know that the area of the rectangle is 200 cm 2, so we can write:
A = L x W
Substituting W = L - 10, we get:
A = L x (L - 10)
Expanding the brackets, we get:
A = L^2 - 10L
Now we can substitute in A = 200 and solve for L:
200 = L^2 - 10L
0 = L^2 - 10L - 200
We can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -10, and c = -200. Plugging in these values, we get:
L = (10 ± sqrt(10^2 - 4(1)(-200))) / 2(1)
L = (10 ± sqrt(1100)) / 2
L = (10 ± 10sqrt(11)) / 2
L ≈ 19.9 or L ≈ -9.9
We can disregard the negative solution since we're dealing with lengths, so the length of the rectangle is approximately 19.9 cm.
Now we can use W = L - 10 to find the width:
W = 19.9 - 10
W ≈ 9.9 cm
Therefore, the length of the rectangle is approximately 19.9 cm and the width is approximately 9.9 cm.

To find the length and width of a rectangle whose width is 10 cm shorter than its length and whose area is 200 cm², follow these steps:
1. Define the variables: Let the length of the rectangle be L cm, and the width be W cm.
2. Use the given information: Since the width is 10 cm shorter than the length, we can write the equation W = L - 10.
3. Use the formula for the area of a rectangle: The area of a rectangle is given by the formula A = L × W.
4. Substitute the given area and the equation from step 2: In this problem, the area is 200 cm², so we have 200 = L × (L - 10).
5. Solve the equation for L: Expand the equation to get 200 = L² - 10L. Rearrange the equation to L² - 10L - 200 = 0.
6. Factor the quadratic equation or use the quadratic formula: (L - 20)(L + 10) = 0. This gives two possible values for L: L = 20 cm or L = -10 cm.
7. Discard the negative value: Since the length of a rectangle cannot be negative, we discard the value L = -10 cm. So, the length L is 20 cm.
8. Find the width using the equation from step 2: W = L - 10 = 20 - 10 = 10 cm.
Thus, the length and width of the rectangle are 20 cm and 10 cm, respectively.

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The number of solutions of the polynomial equation, 4x^(5)-8x^(4) +6x^(3)=0 is 5 and the solutions are x=0, x=3/2, and x=1.

The polynomial equation at hand is of degree 5, which means that the highest power of the variable present in any term is 5.

Therefore, we can infer that the equation can be written in the form of ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable. To solve this equation, we can try factoring it:

4x^(5)-8x^(4) +6x^(3)=0

2x^(3)(2x^(2)-4x+3)=0

2x^(3)(2x-3)(x-1)=0

The solutions are x=0, x=3/2, and x=1.

Therefore, the number of solutions of the polynomial equation is 5 and the solutions are x=0, x=3/2, and x=1.

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Answer:

Step-by-step explanation:

-19 5/6 > -20 1/6

|-19 5/6| < |-20 1/6|