Using the digits 1 to 9 at most one time each, fill in the boxes to complete the statement below
See attached pic!​

The scores are measurements of a discrete variable is 10 and the median is 5.  The scores are measurements of a continuous variable is 10 and the median by locating the precise midpoint of the distribution is 5.

To find the median of a set of data, we first need to put the data in order.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

The median is the middle value when the data is in order. Since there are 10 scores, the middle two scores are the 5th and 6th scores, which are both 5. Therefore, the median is 5.

To find the median of a continuous variable, we also need to put the data in order, but this time we treat the scores as if they are measurements on a continuous scale.

2, 3, 4, 4, 5, 5, 5, 6, 6, 7

Next, we locate the precise midpoint of the distribution. Since there are 10 scores, the midpoint falls between the 5th and 6th scores. The 5th score is 5 and the 6th score is also 5. Therefore, the midpoint is (5+5)/2 = 5.

So, the median is 5 when we treat the scores as measurements on a continuous scale.

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Answer:

(x-6)(x-1)

Step-by-step explanation:

I am sure about this. You can use to solve it too.

Answer:

(x-6)(x-1)

Step-by-step explanation:

x to the power of 2 -7x + 6

x to the power of 2 -x-6x +6

x(x-1)-6(x-1)

(x-6) (x-1)

The probability that more than 2 students will attend is 0.9179.

Part (a) List the values that X may take on.

X may take on the values 0, 1, 2, 3, ..., 13.

Part (b) Give the distribution of X.

The distribution of X can be represented as follows: X-0:0, 1:0.23, 2:0.23, 3:0.23, 4:0.23, 5:0.23, 6:0.23, 7:0.23, 8:0.23, 9:0.23, 10:0.23, 11:0.23, 12:0.23, 13:0.23

Part (c) How many of the 13 students do we expect to attend the festivities? (Round your answer to the nearest whole number.)

We can expect 3 students to attend the festivities.

Part (d) Find the probability that at most 3 students will attend. (Round your answer to four decimal places.)

The probability that at most 3 students will attend is 0.6923.

Part (e) Find the probability that more than 2 students will attend. (Round your answer to four decimal places.)

The probability that more than 2 students will attend is 0.9179.

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let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

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

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

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

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Answer:

\(C = 25.1 \text{ cm}\)

Step-by-step explanation:

We can find the circumference of the circle by plugging the given radius value 8 cm into the formula:

\(C = \pi d\)

Note: This formula can also be written as \(C = 2\pi r\) because \(2r = d\).

↓ plugging in the given radius

\(C = 8\pi \text{ cm}\)

↓ rounding to the nearest tenth

\(\boxed{C = 25.1 \text{ cm}}\)

Answer:

256. fffddddddssddddd

The rocket's maximum height is 800 feet. It reached its maximum height at 5 seconds after launch.

To solve this problem, we need to find the vertex of the parabola represented by the equation Y= -16t^2+160t. The vertex of a parabola is the point where the parabola changes direction, from increasing to decreasing or vice versa.

The vertex of the parabola is given by the following formula:

(-b/2a, c - b^2/4a)

In this case, the value of b is 160 and the value of a is -16. Plugging these values into the formula, we get the following:

(-160/2(-16), 800 - 160^2/4(-16))

(5, 800)

Therefore, the rocket reached its maximum height at 5 seconds after launch. The maximum height is 800 feet.

In this problem the expression that represente the paint in terms of time is:

and the area is represent as:

Part A: So to have the area in terms of p we can replace the first equation in the secon one so wi will get:

Part B: now we can replace the 8 minutes in the equation so we get:

The midpoint of a line segment divides the line into equal parts.

The value of x is: 10

From the question, we understand that Q is the midpoint of PR.

This means that:

PQ = QR

So, we have:

\(2x + 5 = 20\)

Collect like terms

\(2x = 25 - 5\)

Subtract 5 from 25

\(2x = 20\)

Divide by 2

\(x = 10\)

Hence, the value of x is 10

See attachment for the illustration of midpoint

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For each of the given statements the truth value are as follow:

a. ∀n ∃m (n²< m) is False.

b. ∃n ∀m (n < m²) is true.

As given in the question,

Domain of all the presents variables consists of integers.

Truth value for the given statements are as follow:

a.  ∀n ∃m (n²< m)

For integers -2

(-2)² = 4

There is no such integer present whose square is less than the integer.

Truth value of above statement is false.

b.  ∃n ∀m (n < m²)

For integers -3

(-3)² = 9

-3 < 9 is the true for all positive and negative integers.

Therefore, the truth value of the given statements are as follow:

a. ∀n ∃m (n²< m) is False.

b. ∃n ∀m (n < m²) is true.

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Answer:

Step-by-step explanation:

We can use the identity for the cosine of the difference of two angles, which states that:

cos(a - B) = cos(a)cos(B) + sin(a)sin(B)

If we rearrange this identity and subtract cos(B)cos(a) from both sides, we get:

cos(a - B) - cos(B)cos(a) = sin(a)sin(B)

Now, let's consider the expression cos(B) - cos(a). We can write this as:

cos(B) - cos(a) = - (cos(a) - cos(B))

Using the identity for the cosine of the sum of two angles, which states that:

cos(a + B) = cos(a)cos(B) - sin(a)sin(B)

We can rewrite the expression above as:

cos(B) - cos(a) = -2sin((a+B)/2)sin((a-B)/2)

Now, if we substitute (a - B) for a in the identity for the cosine of the difference of two angles that we derived earlier, we get:

cos(a - B) - cos(B)cos(a) = sin(a)sin(B)

And if we substitute (B - a) for B in the expression we derived for cos(B) - cos(a), we get:

cos(B) - cos(a) = -2sin((B+a)/2)sin((B-a)/2)

If we compare these two expressions, we see that they have the same sine term on the right-hand side. Therefore, we can conclude that:

cos(a - B) - cos(B)cos(a) = cos(B) - cos(a)

Or equivalently:

cos(a - B) = cos(B) - cos(a) + cos(B)cos(a)

This result shows that the values of cos(a - B) and cos(B) - cos(a) are related through the product of their cosine terms and a constant offset.

The differential equation

\(ay'' + by' + c = 0\)

has characteristic equation

\(ar^2 + br + c = 0\)

with roots \(r = \frac{-b\pm\sqrt{b^2-4ac}}{2a} = \frac{-b\pm\sqrt{D}}{2a}\).

• If \(D>0\), the roots are real and distinct, and the general solution is

\(y = C_1 e^{r_1x} + C_2 e^{r_2x}\)

• If \(D=0\), there is a repeated root and the general solution is

\(y = C_1 e^{rx} + C_2 x e^{rx}\)

• If \(D<0\), the roots are a complex conjugate pair \(r=\alpha\pm\beta i\), and the general solution is

\(y = C_1 e^{(\alpha+\beta i)x} + C_2 e^{(\alpha-\beta i)x}\)

which, by Euler's identity, can be expressed as

\(y = C_1 e^{\alpha x} \cos(\beta x) + C_2 e^{\alpha x} \sin(\beta x)\)

The solution curve in plot (A) has a somewhat periodic nature to it, so \(\boxed{D < 0}\). The plot suggests that \(y\) will oscillate between -∞ and ∞ as \(x\to\infty\), which tells us \(\alpha>0\) (otherwise, if \(\alpha=0\) the curve would be a simple bounded sine wave, or if \(\alpha<0\) the curve would still oscillate but converge to 0). Since \(\alpha\) is the real part of the characteristic root, and we assume \(a>0\), we have

\(\alpha = -\dfrac b{2a} > 0 \implies -b > 0 \implies \boxed{b < 0}\)

Since \(D=b^2-4ac<0\), we have

\(b^2 < 4ac \implies c > \dfrac{b^2}{4a} \implies \boxed{c>0}\)

The solution curve in plot (B) is not periodic, so \(D\ge0\). For \(x\) near 0, the exponential terms behave like constants (i.e. \(e^{rx}\to1\)). This means that

• if \(D>0\), for some small neighborhood around \(x=0\), the curve is approximately constant,

\(y = C_1 e^{r_1x} + C_2 e^{r_2x} \approx C_1 + C_2\)

• if \(\boxed{D=0}\), for some small neighborhood around \(x=0\), the curve is approximately linear,

\(y = C_1 e^{rx} + C_2 x e^{rx} \approx C_1 + C_2 x\)

Since \(D=b^2-4ac=0\), it follows that

\(b^2=4ac \implies c = \dfrac{b^2}{4a} \implies \boxed{c>0}\)

As \(x\to\infty\), we see \(y\to-\infty\) which means the characteristic root is positive (otherwise we would have \(y\to0\)), and in turn

\(r = -\dfrac b{2a} > 0 \implies -b > 0 \implies \boxed{b < 0}\)

Answer:

The relative change from Ohio to Indiana is 49.04

Step-by-step explanation:

The determinant of the given 10 x 10 matrix is 1024.

A matrix is described as  a rectangular array or table with rows and columns and numbers, symbols, or expressions that is used to represent a mathematical object or a property of such an object.

We apply the knowledge that the determinant of a diagonal matrix is the product of its diagonal entries in order to find the determinant of a 10 x 10 matrix with 2s on the main diagonal and zeros elsewhere,

Determinant = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

We then calculate for the product and have:

Determinant = \(2 ^ 1^0\) = 1024

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\(f(x) +g(x) = 3x^2 +x -9\)

Given:

\(f(x) = x -9\)

\(g(x) = 3x^2\)

Writing \(f(x) +g(x)\):

\(f(x) +g(x) \\ (x -9) +(3x^2) \\ x -9 +3x^2 \\ 3x^2 +x -9\)

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

The probability that the hacker guesses the password on their first try is extremely low.

What is the probability that the hacker guesses the password on his first try?

There are 26 lowercase letters, 26 uppercase letters, and 10 numerical digits, for a total of 62 possible characters for each position in the password. Since the password is 9 characters long, there are \(62^{9}\) possible passwords.

The probability that the hacker guesses the password on their first try is 1 out of the total number of possible passwords:

Probability = 1 / (\(62^{9}\))

Using a calculator, this can be simplified to approximately 1.2 x \(10^{-16}\)

Therefore, the probability that the hacker guesses the password on their first try is extremely low.

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Answer:

Solution

Domain= -3,3,1,2

Range = 2,2,0,4

Domain is Front of comma and Range us after comma

Step-by-step explanation:

Domain = {-3,3,1,2}

Range= {2,2,0,4}

Answer:

1/15 teaspoons

Step-by-step explanation:

30 lb/8 lb = 0.25/x (cross multiply)

(8 * 1/4) / 30 =

8/4 / 30 = 1/15 teaspoons

Answer:

A=√26

-

2

Step-by-step explanation:

thank me later bye

The measure of the third side of the triangle is 5.9cm

Let the sides of the triangles be a, b and c. The perimeter of the triangle will be expressed as:

Given the following parameters:

a = 6.3cm

b = 8.4cm

P = 20.6cm

c = t

Substitute the values into the formula:

20.6 = 6.3 + 8.4 + t

20.6 = 14.7 + t

t = 20.6 - 14.7

t = 5.9cm

Hence the measure of the third side of the triangle is 5.9cm

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Answer:-75 1/4 or in decimal -75.25

Step-by-step explanation: i took the test

Answer:

-75 1/4

Step-by-step explanation:

took the test in k12 :)

Solution

- Now that we have the expression for the limit, let us find the slope at x = 3

- The slope is given by

Final Answer

The slope at x = 3, is 69

Answer:

2. $2.4

3. $3.6

4. $4.8

5. $6

There are 45 monkeys in the zoo.

A percentage is a way of expressing a fraction or a portion of a whole as a number out of 100. The word "percent" means "per hundred."

Let's suppose x is the total number of monkeys in the zoo.

We know that 25 ≤ x ≤ 49, and that 20% of the monkeys are Langur monkeys and 1/4 of them are Colobus monkeys. This means that the number of Langur monkeys is 0.2x and the number of Colobus monkeys is (1/4)x

The total number of monkeys can be expressed as;

x = 0.2x + (1/4)x + other monkeys

Simplifying this, (11/20)x = other monkeys

Since we know that the number of monkeys is between 25 and 49, we can substitute these values into the equation and solve for "x":

25 ≤ (11/20)x ≤ 49

45.4 ≤ x ≤ 89.1

Since x must be an integer, the only solution in this range So, x = 45

Therefore, there are 45 monkeys in the zoo.

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\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation