prove: if a is any integer and the polynomial f pxq " x2 ` ax ` 1 factors (poly mod 9q, then there are three distinct non-negative integers y less than 9 such that f pyq " 0 (poly mod 9q.

The median length of time required to review an application is 63.5 minutes.

To find the median, we need to arrange the times in order from smallest to largest:

50, 56, 71, 90

Since we have an even number of observations, we take the average of the middle two observations to find the median. In this case, the middle two observations are 56 and 71, so we add them together and divide by 2:

(56 + 71) / 2 = 127 / 2 = 63.5

Therefore, the median length of time required to review an application is 63.5 minutes.

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Answer:

Y=7-2x

x-2(7-2x)=6

x-14+4x=16

5x=20

x=4

y=7-2(4)

y=-1

Answer:

2, 3

Step-by-step explanation:

The focus is located approximately 0.69 ft from the vertex. Rounded to two decimal places, the answer is (a) 0.52 ft.

The general equation for a vertical parabola in standard form is given by:

y = (1/4p)x^2

where p is the distance from the vertex to the focus.

In this case, the vertex is located at (0, 0) and the opening is 6 ft wide, which means that the parabola opens downwards. Therefore, the equation of the parabola is:

y = -(25/9)x^2

Comparing this with the standard form of the equation, we get:

4p = -25/9

Solving for p, we get:

p = -25/36

Since the focus is located at a distance of p from the vertex along the axis of symmetry, the focus is located at:

f = |p| = 25/36 ≈ 0.69 ft

Therefore, the focus is located approximately 0.69 ft from the vertex. Rounded to two decimal places, the answer is (a) 0.52 ft.

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Answer:

a and c

Step-by-step explanation:

Answer:

A)12

Step-by-step explanation:

Answer:

1.00 significant figures

The required, 0.9967 rounded to 2 significant figures is approximately 1.0.

To round 0.9967 to 2 significant figures, we look at the first two non-zero digits: 0.9967

The first two non-zero digits are 99. Since there is no third significant digit, we round according to the following rules:

If the third digit is 5 or greater, round up the second digit.

If the third digit is less than 5, leave the second digit unchanged.

In this case, the third digit is 6, which is greater than 5. So, we round up the second digit:

Thus, 0.9967 rounded to 2 significant figures is approximately 1.0.

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Based on the above, the interval will their systolic pressure be lowest is 4pm to 5pm.

From the function given above, the lowest systolic pression can be seen from 5 and 8 hours after taken the medication.

Therefore, this will fall into or between the interval of  2pm to 5pm.

And as such,  looking at the question, the option that best fit into this time range is 4pm to 5pm.

Therefore,  Based on the above, the interval will their systolic pressure be lowest is 4pm to 5pm.

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Sam and Sandy ate 1/2 of a pizza with 12 pieces. They ate 6 pieces in total.

Start with the given information: Sam and Sandy ate 1/2 of a pizza, and the pizza has 12 same-size pieces.

To find out how many pieces they ate, we need to calculate 1/2 of the total number of pieces.

Multiply the total number of pieces by 1/2:

12 * 1/2 = 12/2 = 6

The result of the calculation is 6. Therefore, Sam and Sandy ate 6 pieces of the pizza.

So, step by step, we calculated that Sam and Sandy ate 6 pieces of the pizza.

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Sure, I can help you with that. To start with, let's rewrite the given equation x" – 12x + 3x³ = 0 as a system of first-order equations in x and y=x'. To do this, we can let y = x' and rewrite the equation as:

x' = y
y' = 12x - 3x³

This is a system of two first-order differential equations, where x and y are the variables. Now, to find the critical points of this system, we need to solve for x and y when y' = 0. Substituting y = x' in the second equation, we get:

12x - 3x³ = 0
=> 3x(4-x²) = 0

Therefore, the critical points are (0,0), (2,0), and (-2,0), in order of increasing x coordinate. We can write them as:

(x,y) = (0,0), (2,0), (-2,0)

These critical points represent the equilibrium solutions of the system, where the motion of the spring is stationary. In the next three problems, we may need to analyze the stability of these solutions and their behavior under small perturbations.

Now, we have a system of first-order equations:
x' = y
y' = 12x - 3x^3

To find the critical points, we need to solve for x and y when x' = 0 and y' = 0:

1. 0 = y
2. 0 = 12x - 3x^3

From the first equation, y = 0. To solve the second equation for x:

0 = 12x - 3x^3
0 = 3x(4 - x^2)

This gives us three possible x coordinates: x = 0, x = 2, and x = -2.

So, the critical points are:
(x, y) = (-2, 0), (0, 0), (2, 0)

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The value of the measure of the line segment CD is,

⇒ CD = 10

We have to given that;

In circle,

CD = 2 + x

BC = 8

AB = 12

Hence, We can formulate;

AB² = BD × CD

12² = (8 + 2 + x) × 8

144 = 8 (10 + x)

18 = 10 + x

x = 18 - 10

x = 8

Thus, The value of the measure of the line segment CD is,

⇒ CD = 2 + x = 2 + 8 = 10

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The measure of the other diagonal line is 6.8 inches

A kite is a quadrilateral with two distinguishable consecutive sides. The area of a kite can be calculated by the multiplication of the two diagonal lines divided by 2.

Mathematically, we have:

\(\mathbf{A = \dfrac{pq}{2}}\)

where:

∴

Using the formula for an area of a kite to determine the other diagonal length, we have:

\(\mathbf{51.68 \ inches^2 = \dfrac{15.2 \ inches \times q}{2}}\)

\(\mathbf{q = \dfrac{51.86 \ inches^2 \times 2}{15.2 inches} }\)

q = 6.8 inches

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Hey there!☺

\(Answer:\boxed{6p^2+4}\)

\(Explanation:\)

\(6p^2-6+10\)

Let's start by simplifying.

\(6p^2+-6+10\)

Now we will combine like terms.

\((6p^2)+(-6+10)\\6p^2+4\)

\(6p^2+4\) is your final answer.

Hope this helps!

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is the following equation -

x² - 3x = x² - 1

In order to solve it using intersect method, we will plot the graphs of both functions and find the point of intersection of graphs of both the equations.

Assume -

f(x) = x² - 3x

g(x) = x² - 1

Now, the point of intersection of both the graphs will be the solution to the equation given by -

f(x) = g(x)

It can be seen from the graph that, both the graphs intersect at the coordinate (0.333, -0.8889). This coordinate will be the solution set of the equation -

f(x) = g(x)

Therefore, the coordinate that represent the solution of the equation -

x² - 3x = x² - 1 is (0.333, -0.8889).

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Answer: 0.167

Step-by-step explanation:

Given: Total batteries = 10

Batteries that are still working = 6

Number of ways to pick 3 working batteries = \(^6C_3=\dfrac{6!}{3!3!}\)

\(=\dfrac{6\times5\times4\times3!}{6\times3!}\\\\=20\)

Number of ways of pick 3 batteries out of 10 =

\(^{10}C_3=\dfrac{10!}{3!7!}=\dfrac{10\times9\times8\times7!}{6\times7!}\\\\=120\)

Required probability = \(\dfrac{20}{120}=0.167\)

Hence, the probability that all of the first 3 she chooses will work = 0.167

Answer:

$444.25

Step-by-step explanation:

15 / 100 * 425 = 15 + 4.25 = $19.25

So $425 + $19.25 = $444.25

Answer:

$444.25

Step-by-step explanation:

If a random variable "z" follows a standard normal distribution and the probability of "z" being greater than "k" is 0.39, then the value of "k" such that satisfies the equation [p(z > k) = 0.39] will be 0.28

As per the question statement, a random variable "z" follows a standard normal distribution.

We are required to determine the value of "k" such that the equation   [p(z > k) = 0.39] is satisfied.

To solve this question, first we will have to calculate the probability of "z" being greater than "k" and then from the Z-table, we will determine the z-score corresponding the above calculated probability value. This z-score will be our desired answer, i.e.,

Given, P(Z > k)  = 0.39

Or, P(Z < k) = (1 - 0.39)

Or, P(Z < k) = 0.61

Now, from the Z table, we get the z-score corresponding to probability value of 0.61 is 0.28

Hence, (k = 0.28)

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Answer:

f(2) = 8

Step-by-step explanation:

f(x) = x^2 + 8x – 12

Let x = 2

f(2) = 2^2 + 8*2 – 12

     = 4 + 16 -12

        =20-12

        = 8

Answer:

\(f(x) = {x}^{2} + 8x - 12 \\ f(2) = (2)^{2} + 8(2) - 12 \\ = 4 + 16 - 12 \\ f(2) = 8\)

I hope I helped you^_^

Answer:

i can't see those word very Well am confuse

Step-by-step explanation:

please Mark Me as brainly.

Answer:

3.75 minutes

Step-by-step explanation:

Set up an equation where x is the number of minutes:

0.25x + 35 = 0.5x + 20

Solve for x:

0.25x + 35 = 0.5x + 20

35 = 0.25x + 20

15 = 0.25x

3.75 = x

So, both plans will cost the same with 3.75 minutes

Answer:

2

Step-by-step explanation:

The values rewritten into an equivalent form as fractions include the following:

In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

For instance, 5 by 8 should be read as "five eighths" and it simply means that five (5) parts out of eight (8) equal parts in which the whole part is divided.

Similarly, -3 by 2 should be read as "negative three halves" and it simply means that two (2) parts out of negative three (3) equal parts in which the whole part is divided. Additionally, the number 3 represents the numerator while the number 2 represents the denominator.

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Chris and Mary, who live 14 miles apart, will meet after apart, will meet after a certain number of hours. Chris walks at a rate of 3 mph, and Mary walks at a rate of 4 mph.

To determine the number of hours it takes for Chris and Mary to meet, we can use the concept of relative speed. The relative speed is the sum of their individual speeds, which is 3 mph + 4 mph = 7 mph.

Since they are walking towards each other, their combined speed of 7 mph represents the rate at which the distance between them is decreasing. The distance between them is initially 14 miles. We can use the formula: time = distance / speed to find the number of hours it takes for them to meet.

Applying the formula, time = 14 miles / 7 mph = 2 hours. Therefore, Chris and Mary will meet after 2 hours of walking.

The concept of relative speed helps us determine how the distance between two objects changes over time when they are moving towards each other.

By considering their individual speeds and using the formula for time, we can calculate the time it takes for Chris and Mary to meet. In this case, their combined speed of 7 mph allows them to cover the initial distance of 14 miles in 2 hours, resulting in their meeting point

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Answer:

We are not given the ratio of cordial to water used in the mixture, so we can assume that the entire bottle of cordial is mixed with water to make the drink.

Since the bottle of cordial holds 800 ml of cordial, the total volume of the mixture would be 800 ml + volume of water added. Let's call the volume of water added x.

Therefore, the total volume of the drink would be 800 ml + x.

We are asked to find the minimum capacity of the container in liters, so we need to convert the total volume of the drink from milliliters to liters:

800 ml + x = (800 + x)/1000 liters

Now we can set up an inequality to find the minimum value of x that would make the total volume of the drink at least 1 liter:

800 ml + x ≥ 1000 ml

Simplifying this inequality, we get:

x ≥ 200 ml

Therefore, the minimum volume of water that needs to be added to the cordial to make a drink with a total volume of at least 1 liter is 200 ml.

So the minimum capacity of the container would be:

800 ml + 200 ml = 1000 ml = 1 liter

Therefore, the minimum capacity of the container in liters would be 1 liter.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let your number be X. To increase X by 40% we can multiply it by 1.4, let's call this new number Y.

So Y = X * 1.4

Now to decrease Y by 40% we can multiply it by 1 - .4 = .6. Lets call this new number C.

So C = Y *.6 = (X * 1.4) * .6 = X * (1.4 * .6) = X * .84.

Therefore, C = .84 * X.

So we can see C is 84% of X, or 16% less than X.

Thus, if you increase a number by 40% then decrease it by 40%, the net percentage is -16% .

      Final result in terms of 'x' will be → 0.75x

Let the number = x

As per first statement → "A number 'x' is decreased by 40%"

Algebraic expression for the statement → (x - 40% of x)

                                                                  → (x - 0.4x)

                                                                  → 0.6x

Second statement → "Then increased by 25%"

Algebraic expression for the statement → (0.6x + 25% of 0.6x)

                                                                  → \((0.6x+\frac{25}{100}\times 0.6x)\)

                                                                  → \((0.6x+0.15x)\)

                                                                  → \(0.75x\)

           Therefore, final result in terms of x will be (0.75x).

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The space that does the base of the trash can occupy  is 379.94 cm².

Given: radius of  trash is 11 centimeters

           approximation of pi = 3.14

space that does the base of the trash can occupy when on the floor is given by the surface area that the trash will occupy in the surface .

Since , trash has a circular base

surface area that the trash will occupy in the surface = pi * (radius of trash)²

space that does the base of the trash can occupy  =  pi * (radius of trash)²

It has been given that , radius of  trash is 11 centimeter and approximation of pi = 3.14

space that does the base of the trash can occupy  =  3.14 * (11)²

space that does the base of the trash can occupy  =  3.14 * 121

space that does the base of the trash can occupy  =  379.94 cm²

Hence , the space that does the base of the trash can occupy  is 379.94 cm².

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John is likely to choose a root beer from the cooler 5/27 times, or 18.5% of the time.

p(root beer)=5/27=18.5%

John is likely to choose a root beer from the cooler 5/27 times, or 18.5% of the time. Divide the number of root beers in the cooler (five) by the total number of things in the cooler to arrive at this calculation (27). In this instance, the cooler is filled with 12 Coke cans, 10 water bottles, and 5 root beers. Hence, there are 27 things in the cooler, and the likelihood that John will choose a root beer is 5/27. By dividing the fraction by 100, this figure can be stated as a percentage, giving the answer of 18.5%.Hence, John has an 18.5% chance of grabbing a root beer from the cooler.

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Answer:

144 square foot

Step-by-step explanation:

Area of rectangle: Length × breadth

Area of rectangle = 16 × 9

                             = 144 square foot