solve for x to the nearest tenth y completing the square: x^2-5x+7=0​

Answer:

C. If Sally does not play basketball, then She is not 6 feet tall

Step-by-step explanation:

Represent the two statements with p and q

Given

p = Sally is 6 feet tall

q = Sally plays basketball

Required

Determine the contrapositive

For a statement

\(p\ -> q\)

Meaning; If p then q

The contrapositive is:

\(\¬q -> \¬p\)

Meaning: If not q, then not p

Hence;

Option C answers the question

Answer:

He got 16 incorrect

Step-by-step explanation:

Answer:

fraction: 3/4

percent: 75%

Step-by-step explanation:

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

The value of g(h(10)) is 2√2. the correct option is A.

Given that the functions are g(x)=√x-4 and h(x)=2x-8.

A function is defined as the relationship between a set of inputs where each input has an output.

Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.

h(10)=2(10)-8

h(10)=20-8

h(10)=12

Now, we will find g(h(10)) where h(10)=12.

By substituting h(10)=12 in g(h(10)), we get

g(h(10))=g(12).

Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get

g(12)=√(12-4)

g(12)=√8

g(12)=2√2

Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.

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Answer:

Rotation then Transition C on Edge.

Step-by-step explanation

Because im smart like that

The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4

\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   \(10^{-5}\)  and P(Z > 4) = 2.8665 x  \(10^{-5}\) .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  \(10^{-5}\)  + 2.8665 x  \(10^{-5}\)  = 5.7330 x  \(10^{-5}\)

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  \(10^{-5}\)  = 5.73 (rounded to the nearest whole number).

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Answer: b) $60.56 per year of age

Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.

Regression line is a line graph that best fits the data. Like any other line, its formula is given by

y = mx + b

with

m being the slope

b the y-intercept

The slope of the line, correlation and standard deviations of the two variables have the following relationship:

\(m=r\frac{S_{y}}{S_{x}}\)

where

r is correlation

\(S_{y}\) is standard deviation for the y data

\(S_{x}\) is standard deviation for the x data

For our problem:

r = 0.34

\(S_{y}=\) 2850

\(S_{x}=\) 16

Calculating

\(m=0.34(\frac{2850}{16})\)

m = 60.56

Slope for the regression line of annual income per year of age is 60.56.

There's a constant increase of 8 seats per row.

Therefore, if we were to model the situation with the equation of a line, the slope would be 8.

Using the

Answer:

Step-by-step explanation:

answer C looks good  

Answer:

option c is answer

Step-by-step explanation:

as we can see r^2 =(d/2)^2

r^2=(6/2)^2

r^2=36/4=9

A=πr^2

A=9π

Answer:

8

Step-by-step explanation:

scince it has the lines that mean that it will always be positive.

Answer:

8

Step-by-step explanation:

Have a nice day!

The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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c=170/30 is the equation that represents the number of calories,c, burned per min.

A division is a process of splitting a specific amount into equal parts.

Given that Tarmu run 30 min and burned 170 calories

We need to find the equation that represents the number of calories, c, burned per min.

To find the calories burned in each minute we have to divide one hundred seventy by thirty.

c=170/30

c=5.66 cal/min

Hence, c=170/30 is the equation that represents the number of calories,c, burned per min.

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Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

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Answer:

$64.8

Step-by-step explanation:

hihihihihihihihihihihihihi

Answer:

Step-by-step explanation:

I think jhonnu

Answer:

-3 is the answer.

Step-by-step explanation:

=2(-1+3)-7

=2(2)-7

=4-7

=-3

Hope it will help you :)

Answer:

Refer to the step-by-step explanation, please follow along very carefully. Answers are encased in two boxes.

Step-by-step explanation:

Given the following function, find it's derivative using the definition of derivatives. Evaluate the function when θ=1, 11, and 3/11

\(p(\theta)=\sqrt{11\theta}\)

\(\hrulefill\)

The definition of derivatives states that the derivative of a function at a specific point measures the rate of change of the function at that point. It is defined as the limit of the difference quotient as the change in the input variable approaches zero.

\(f'(x) = \lim_{{h \to 0}} \dfrac{{f(x+h) - f(x)}}{{h}}\)\(\hrulefill\)

To apply the definition of derivatives to this problem, follow these step-by-step instructions:

Step 1: Identify the function: Determine the function for which you want to find the derivative. In out case the function is denoted as p(θ).

\(p(\theta)=\sqrt{11\theta}\)

Step 2: Write the difference quotient: Using the definition of derivatives, write down the difference quotient. The general form of the difference quotient is (f(x+h) - f(x))/h, where "x" is the point at which you want to find the derivative, and "h" represents a small change in the input variable. In our case:

\(p'(\theta) = \lim_{{h \to 0}} \dfrac{{p(\theta+h) - p(\theta)}}{{h}}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h}\)

Step 3: Take the limit:

We need to rationalize the numerator. Rewriting using radical rules.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11(\theta + h)} - \sqrt{11\theta} }{h} \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11\theta + 11h} - \sqrt{11\theta} }{h}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h}\)

Now multiply by the conjugate.

\(p'(\theta)= \lim_{h \to 0} \dfrac{\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} }{h} \cdot \dfrac{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} } \\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{(\sqrt{11}\sqrt{\theta+h} - \sqrt{11}\sqrt{\theta} )(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )} \\\\\\\)

\(\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11h}{h(\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} )}\\\\\\\Longrightarrow p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\)

Step 4: Simplify the expression: Evaluate the limit by substituting the value of h=0 into the difference quotient. Simplify the expression as much as possible.

\(p'(\theta)= \lim_{h \to 0} \dfrac{11}{\sqrt{11}\sqrt{\theta+h} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta+(0)} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{\sqrt{11}\sqrt{\theta} + \sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11}\sqrt{\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\\\\\\\Longrightarrow p'(\theta)= \dfrac{11}{2\sqrt{11\theta} }\)

\(\therefore \boxed{\boxed{p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta} }}}\)

Thus, we have found the derivative on the function using the definition.

It's important to note that in practice, finding derivatives using the definition can be a tedious process, especially for more complex functions. However, the definition lays the foundation for understanding the concept of derivatives and its applications. In practice, there are various rules and techniques, such as the power rule, product rule, and chain rule, that can be applied to find derivatives more efficiently.\(\hrulefill\)

Now evaluating the function at the given points.  

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}; \ p'(1)=??, \ p'(11)=??, \ p'(\frac{3}{11} )=??\)

When θ=1:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(1)= \dfrac{\sqrt{11} }{2\sqrt{1}}\\\\\\\therefore \boxed{\boxed{p'(1)= \dfrac{\sqrt{11} }{2}}}\)

When θ=11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(11)= \dfrac{\sqrt{11} }{2\sqrt{11}}\\\\\\\therefore \boxed{\boxed{p'(11)= \dfrac{1}{2}}}\)

When θ=3/11:

\(p'(\theta)= \dfrac{\sqrt{11} }{2\sqrt{\theta}}\\\\\\\Longrightarrow p'(\frac{3}{11} )= \dfrac{\sqrt{11} }{2\sqrt{\frac{3}{11} }}\\\\\\\therefore \boxed{\boxed{p'(\frac{3}{11} )= \dfrac{11\sqrt{3} }{6}}}\)

Thus, all parts are solved.

Answer:

42,069

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Circle equation standard form

(x-h)^2 + ( y-k)^2 = r^2       h, k is the center

All are centered at 0,0    

radii are  sqrt(225)  = 15    sqrt 49 = 7      and    sqrt 178

Answer: C) 24

Step-by-step explanation:

first we take down the information given to us

sports shop sells rackets in

4 different weights

2 types of strings

3 grip sizes

Now to get the number of different rackets they could sell, you simply take the  multiplication of the number of racket gripe sizes, the types of strings and different weights they sell

so

4 * 2 * 3 = 24

therefore the sport shop could sell up to 24 different rackets .

Answer:

24

Step-by-step explanation: got it right on my test

Answer:

Obtuse - over 90°

Acute - less than 90°

Right - 90°

Straight - 180°

1. Obtuse

2. Acute

3. Right

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Answer:

(-1/7 ; 0)

Step-by-step explanation:

the line intercepts the x axis when y = 0

7x + 0 = -1

7x = - 1

7/7 x = -1/7

x = -1/7

Answer:

The x intercept is -1/7

( -1/7 , 0)

Step-by-step explanation:

To find the x intercept, set y =0 and solve for x

7x+7y = -1

y =0

7x+7(0) = -1

7x +0 = -1

7x = -1

Divide by 7

7x/7 = -1/7

x = -1/7

The x intercept is -1/7

( -1/7 , 0)

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1