Suppose that 2 were subtracted from each of the values in a data set that
originally had a standard deviation of 7.5. What would be the standard
deviation of the resulting data?
A. 2
B. 7.5
C. 9.5
O D. 5.5

Answer:

The choice four ;

\(x = \frac{z - y}{3} \)

Step-by-step explanation:

\(3x + y = z \\ 3x = z - y \\ x = \frac{z - y}{3} \)

Seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

The expression says  seven less than the product of thirteen times a number, and two squared.

Let

the number  = x

Hence, the product of thirteen times a number, and two squared is as follows:

13(x)(2²)

Therefore,  seven less than the product of thirteen times a number, and two squared is as follows;

(13x × 2²) - 7

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We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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The all the factors of x³ + 5x² + 2x – 8 are (x+4)(x-1) and (x+2) , the correct options are (c) , (d) and (f) .

In the question ,

it is given that the equation is f(x) = x³ + 5x² + 2x – 8 ,

we have to find the factors of f(x) = x³ + 5x² + 2x – 8 .

We know that ,The Factor Theorem states if (x-t) is a factor of f(x) if and only if f(t)=0 .

So , Option(a)  Let g(x) = x + 5 be a factor

that means for  x = -5 , f(-5) = (-5)³ + 5(-5)² + 2(-5) – 8 = 2 ≠ 0 ,

hence it is not a factor .

In option (b) Let g(x) = x - 5 be a factor

that means For  x = 3 , f(3) = (3)³ + 5(3)² + 2(3) – 8 = 70 ≠ 0 ,

hence it is not a factor .

In option (c) Let g(x) = x + 4 be a factor

that means For  x = -4 , the equation is f(-4) = (-4)³ + 5(-4)² + 2(-4) – 8 = 0 ,

hence it is a factor .

In option (d) Let g(x) = x - 1 be a factor

that means For  x = 1 , f(1) = (1)³ + 5(1)² + 2(1) – 8 = 0 ,

hence it is a factor .

In option (e) Let g(x) = x + 3 be a factor

that means For  x = -3 , it becomes f(-3) = (-3)³ + 5(-3)² + 2(-3) - 8 = 4 ≠ 0 ,

hence it is not a factor .

In option (f) Let g(x) = x + 2 be a factor

that means For  x = -2 ,the equation f(-2) = (-2)³ + 5(-2)² + 2(-2) - 8 \(=\) 0 ,

hence it is a factor .

Therefore , the factors are (x+2) , (x - 1) and (x + 4) .

The given question is incomplete , the complete question is

Select all of the factors of x³ + 5x² + 2x – 8.

(a) x + 5

(b) x – 3

(c) x + 4

(d) x – 1

(e) x + 3

(f) x + 2

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Answer:

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\huge\textbf{Equation:}\)

\(\mathsf{n^2 = 5n - 4}\)

\(\huge\textbf{Convert:}\)

\(\mathsf{5n - 4 = n^2}\)

\(\huge\textbf{Subtract }\boxed{\bf n^2}\huge\textbf{ to both sides:}\)

\(\mathsf{5x - 4 - n^2 = n^2 - n^2}\)

\(\huge\textbf{Simplify it:}\)

\(\mathsf{-n^2 + 5x - 4 = 0}\)

\(\huge\textbf{Factor the LEFT side of the equation:}\)

\(\mathsf{(-n + 1)\times (n - 4) = 0}\)

\(\huge\textbf{Simplify that as well:}\)

\(\mathsf{-n + 1 = 0 \ or\ even\ \ n - 4 = 0}\)

\(\huge\textbf{Lastly, simplify that as well:}\)

\(\mathsf{n = 1\ or\ n = 4}\)

\(\huge\textbf{Therefore, your answer should be: }\)

\(\huge\boxed{\frak{n = 1\ or \ n = 4}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

D the amount of money he pays for each lunch

Step-by-step explanation:

In each lunch Devante has, he pays 2,50 $ according to:

Money in t = t₀     he has  35,50 $      paid 3 lunches and spent

35,50 - 28  =  7,5

Then the cost of each lunch is    7,5 / 3   =  2,5 $

After that

bought    5 lunches and spent   28  - 15,5  = 12,50

Again    12,5 / 5   =  2,5 $

Now the model for the situation is a straight line with a slope 2,5

In an  x , y cartesian system in which  y is money in the account  and x is the number of lunches, such a straight line will be

y  =  b  -  m*x      ( b the intercept on y  and  m the negative slope)

y  =  35,50 - 2,5*x

So  answering the question is lyrics  D  the amount of money he pays for each lunch

Answer:

which one substitution or elimination

Step-by-step explanation:

Substitution: (-1,-3 )

Elimination: (-1,-3)

i hope this helps you :)

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Answer:

Given - a = 4

b = 9

c = 1

To find - Value of equation

Solution -

3b ÷ c^1 - a

Putting the value of a,b and c in the equation

3(9) ÷ (1)^1 - 4

27 ÷ 1 - 4

27 ÷ (-3)

27 × (1 /(-3)

27/(-3)

(-9)

Answer:

-9

Step-by-step explanation:

Substitute the values into the expression.

= 3(9)÷(1)1-4

evaluate/simplify each part first.

= 27÷1-4

= 27÷(-3)

simplify (positive divided by a negative is a negative)

= -9

Answer:

the answer is 6

Step-by-step explanation:

the answer is 6

9514 1404 393

Answer:

  -4

Step-by-step explanation:

The point (x, y) = (0, 0) is on the line, so it represents a proportional relation. Any ratio of y to x will be the slope. The choice that makes this computation easiest is ...

  x = 1, y = -4

  y/x = -4/1 = -4

The slope of the line is -4.

Answer:

First one, second one, fourth one, and last one

Step-by-step explanation:

Answer:

The equation is

X²+2x-48 = 0

Shorter one is 6 inches

Other side= 8 inches

Step-by-step explanation:

The equation for a right angle triangle normally is

A² = B² + C²

Where A = hypotenuse

Then B and C are the order sides of the triangle.

This time

Hypotenuse= 10 inches

The shorter one is X

While the other one is X+2

The equation

10²= x² +(x+2)²

100= x² + x² + 4x +4

100 - 4 = 2x² +4x

96= 2x² +4x

48 = x² +2x

X²+2x-48 = 0

Solving for x

X² +8x-6x-48= 0

X(x+8)-6(x+8)=0

(X-6)(x+8)= 0

X= 6 or x= -8

Definitely x is posiy

So x= 6

Shorter one is 6 inches

Other side= 6+2= 8 inches

I'll use the method of transformations.

If \(f_X(x)\) denotes the PDF of \(X\), and \(y=g(x)=x^3 \iff x=g^{-1}(y) = y^{1/3}\), we have

\(f_Y(y) = f_X\left(g^{-1}(y)\right) \left|\dfrac{dg^{-1}}{dy}\right|\)

\(\dfrac{dg^{-1}}{dy} = \dfrac13 y^{-2/3}\)

\(\implies f_Y(y) = f_X\left(y^{1/3}\right) \left|\dfrac13 y^{-2/3}\right| = \boxed{\begin{cases} \dfrac53 y^{2/3} & \text{if } 0 \le y \le 1 \\ 0 & \text{otherwise} \end{cases}}\)

(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

0

Step-by-step explanation:

Assuming the six sided dice are numbered 1 through six

The max each could roll is 6

6+6 = 12

They cannot reach a sum of 13

Answer:

Step-by-step explanation:

saw it on chegg

.05x+.17y=.13

x+y=60

The two correct equations are "\(0.05 x+0.17 y=0.13\) and \(x+y=60\)". A further solution is provided below.

According to the question,

Let,

Given total acid solution,

= 60 mL

then,

→  \(x+y = 60\)...(equation 1)

We know that the concentration of mixture = 13%

hence,

→  \(5 \ percent \ of \ x + 17 \ percent \ of \ y =13 \ percent (x+y)\)

or,

→  \(0.05x+0.17y=0.13(60)\)

Thus the above answer is correct.

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Answer:

No

Step-by-step explanation:

Because .5 = 7.2

So 1 = 14.4

Answer:

Option:C 2/3

Equation= y=2/3x-5

Answer:

2/3

Step-by-step explanation:

to find slope m, use this method

m=(y2-y1)/(z2-x1)

therefore m=(1-(-7))/((9-(-3))

m=8/12.

m=2/3

Answer:

13

Step-by-step explanation:

By counting the amount of dots there is on the graph you would end up with 13 trees.

Answer:

Step-by-step explanation:

Since order does not matter \(_{12}C_3\\ \\ \frac{12!}{3!9!}\\ \\ 220\)

Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

Answer: 0.001

Step-by-step explanation:

For this problem, we are given the dimensions of a rectangular prism and are asked to determine its volume.

The volume of a rectangular prism is given by the product of the three dimensions, therefore we have:

The correct answer is 328.02 cubic centimeters.

The question is incomplete. Here is the complete question.

In a recent year, the socres for the reading portion of a test were normally distributed, with a mean of 23.3 and a standard deviation of 6.4. Complete parts (a) through (d) below.

(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 18. (Round to 4 decimal places as needed.)

(b) Find a probability that a random selected high school student who took the reading portion of the test has a score that is between 19.9 and 26.7.

(c) Find a probability that a random selected high school student who took the reading portion of the test ahs a score that is more than 36.4.

(d) Identify any unusual events. Explain your reasoning.

Answer: (a) P(X<18) = 0.2033

              (b) P(19.9<X<26.7) = 0.4505

              (c) P(X>36.4) = 0.0202

               (d) Unusual event: P(X>36.4)

Step-by-step explanation: First, determine the z-score by calculating:

\(z = \frac{x-\mu}{\sigma}\)

Then, use z-score table to determine the values.

(a) x = 18

\(z = \frac{18-23.3}{6.4}\)

z = -0.83

P(X<18) = P(z< -0.83)

P(X<18) = 0.2033

(b) x=19.9 and x=26.7

\(z = \frac{19.9-23.3}{6.4}\)

z = -0.67

\(z = \frac{26.7-23.3}{6.4}\)

z = 0.53

P(19.9<X<26.7) = P(z<0.53) - P(z< -0.67)

P(19.9<X<26.7) = 0.7019 - 0.2514

P(19.9<X<26.7) = 0.4505

(c) x=36.4

\(z = \frac{36.4-23.3}{6.4}\)

z = 2.05

P(X>36.4) = P(z>2.05) = 1 - P(z<2.05)

P(X>36.4) = 1 - 0.9798

P(X>36.4) = 0.0202

(d) Events are unusual if probability is less than 5% or 0.05. So, part (c) has an unusual event.

The probability will be:

(a) 0.2038

(b) 0.4046

(c) 0.0203

(d) Event in part (c) is unusual.

According to the question,

Let,

(a)

The z-score for X=18 will be:

→ \(z = \frac{X- \mu}{\sigma}\)

      \(= \frac{18-23.3}{6.4}\)

      \(= -0.828\)

So,

The probability will be:

→ \(P(X<18) = P(z < -0.828)\)

                     \(= 0.2038\)

(b)

The z-score for X=19.9 will be:

→ \(z = \frac{X -\mu}{\sigma}\)

     \(= \frac{19.9-23.3}{6.4}\)

     \(= -0.531\)

The z-score for X=26.7 will be:

→ \(z = \frac{X -\mu}{\sigma}\)

      \(= \frac{26.7-23.3}{6.4}\)

      \(= 0.531\)

So,

The probability will be:

→ \(P(19.9 < X< 23.3) = P(-0.531 < z< 0.531)\)

                                   \(= 0.4046\)

(c)

The z-score for X=36.4 will be:

→ \(z = \frac{X -\mu}{\sigma}\)

     \(= \frac{36.4-23.3}{6.4}\)

     \(= 2.047\)

So,

The probability will be:

→ \(P(X > 36.4 )= P(z > 2.047)\)

                       \(= 0.0203\)

(d)

Just because it's probability value is less than 0.05, so that the events is "part c" is unusual.

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