If A=(-7,8,1) and B(8,7,7), find ||AB||. Round to 3 decimal places

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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The value of p is 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

Given that

Point A(p8,4p+5) is located on a line that connects M(-2,-5) and N(1,-10).

The equation of line that passing through points  M and N,

Use the formula of equation of line,

y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)

y-(-5) = (-10+5/1+2)(x-(-2))

⇒ y+5 = -5/3(x+2)

⇒5x+3y +25 = 0    (1)

Since, line passes through point  A(p−8,4p+5), so this point A will satisfy the equation (1)

5(p-8)+3(4p+5)+25 = 0

⇒ 17p = 0

⇒ p = 0

The value of p is 0.

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Answer:

Answer: C. f(x) = 2x²+x+6

Using the Empirical Rule, it is found that:

a) 2.5% of adult males are under 64 inches tall.

b) 81.5% of adult males are between 64 and 73 inches tall.

It states that, for a normally distributed random variable, approximately:

For item a, we have that 64 is two standard deviations below the mean, hence, considering the symmetry of the normal distribution:

2.5% of adult males are under 64 inches tall.

As shown by the first graph at the end of the answer.

For item b, we have that 64 is two standard deviations below the mean, while 73 is one above, hence, considering the symmetry of the normal distribution:

P = 0.5 x 95 + 0.5 x 68 = 81.5%.

As shown by the two blue sections, plus the left brown section, in the second graph.

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Answer:

Part A

The expression for the total amount of money Liz and Andy makes selling necklaces at the fair is

The total amount they both make from selling necklaces = 8·L + 8·A

Part B

The total amount they both make from selling jewelries = 35 + 8·L + 8·A

Step-by-step explanation:

The amount at which Liz and Andy sells necklaces = $8

The amount Andy makes selling bracelets = $35

Part A

The total amount of necklaces Liz sells = L

The total amount of necklaces Andy sells = A

The expression for the total amount of money Liz and Andy makes selling necklaces at the fair, 'N', is given as follows;

N = 8·L + 8·A

Part B

The expression for the total amount of money Liz and Andy makes selling jewelries at the fair, 'J', is given as follows;

J = 35 + 8·L + 8·A

By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Answer:

6^4  = 1296

Step-by-step explanation:

6 to the power of 4

The given statement is FALSE.

Given statement;

When practicing statistics in real life, it is not very important to check the necessary assumptions of a statistical procedure to effectively carry out and use the results.

The above-mentioned statement is FALSE.

→ We are aware that checking assumptions is crucial when applying statistics in daily life because failing to do so will prevent us from receiving fair answers to our statistical queries or drawing valid inferences. To use the good process and appropriate statistical distributions while utilizing statistics in daily life, it is crucial to examine assumptions.

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

Explanation:

a)

The formula for calculating the length of an arc is expressed as

Length of arc = θ/360 x 2πr

where

θ is the angle subtended at the center of the circle.

r is the radius of the circle

From the information given,

diameter = 5(length of each metal spoke)

r =diameter/2 = 5/2 = 2.5

Recall, the total angle in the circle is 360 degrees. There are 8 partitions. Angle between consecutive spokes is

360/8 = 45. Thus,

θ = 45

Length of are between consecutive spokes = 45//360 x 2 x π x 2.5

Length of are between consecutive spokes = 5π/8

b) The formula for calculating the area of a sector is expressed as

area of a sector = θ/360 x πr^2

By substituting the values,

area of a sector = 45/360 x π x 2.5^2

Area of sector = 25π/32 square inches

Answer:

59.3 °

Step-by-step explanation:

its trigonometry

so you have the

opposite side= 43.5

and the adjacent side = 24.8

if you use SOH CAH TOA you will find that to find y you need to use TOA as tou have the opposite and adjacent.

to find the angle (tan) you need to do tue opposite / adjacent

tan^-1 (43.5/25.8)

= 59.3 to 1 d.p.

you need to use tan^-1 as you are finding the missing angle

A residual plot is a scatterplot in which the residuals (vertical distances between the predicted and actual values) are plotted against the independent variable. A residual is defined as the difference between the predicted value (based on the regression equation) and the actual value.

Residual plots are a valuable tool for checking the adequacy of the model. It helps us check whether the assumptions of linearity, independence, equal variance, and normality are met or not.

The most basic way to create a residual plot is to plot the residuals against the fitted values. If the points in the residual plot are randomly scattered around the horizontal axis, then the assumption of linearity has been met.

If the points show a pattern, such as a curved line, then the assumption of linearity has been violated.To create a residual plot, follow these steps:

Step 1: Estimate the regression equation and obtain the predicted values (ŷ) and residuals (e). ŷ = b0 + b1X

Step 2: Plot the residuals on the vertical axis and the independent variable (X) on the horizontal axis

.Step 3: Look for patterns in the residual plot. If the points are randomly scattered around the horizontal axis, then the assumptions of linearity, independence, equal variance, and normality are met. If there is a pattern, such as a curved line, then the assumptions have been violated. A residual plot can be used to detect outliers, influential observations, and nonlinearity.

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The equation that represents the cost, c, of n sets is c = 63.74n

from the question, we have the following parameters that can be used in our computation:

Each volleyball set costs $63.74.

Let the total number of sets be n

So we have

Cost of n = 63.74 * n

This gives

c = 63.74n

Hence, the equation is c = 63.74n

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Answer:

-0.25 units

Step-by-step explanation:

144x^2 - 72x + 9 = 0

common factor: 9

16x^2 - 8x + 1 = 0

(4x + 1)^2 = 0

4x +1 = 0

4x = -1

x = -0.25 units

Answer:

Step-by-step explanation:

Volume = Bh

Turn the shape so the trapezoid is on the bottom/base

h=18   for overall shape

B = area of base, trapezoid

B = 1/2 (b₁ + b₂) h  

b₁ = 11

b₂ = 25

h = 24   for trapezoid

B = 1/2 (11 + 25)(24)

B = 432

V = Bh

V = (432)(18)

V= 7776 in³

Answer: you forgot to put how much she uses to make one! Put it in the comments of this answer and I’ll solve it =)

Step-by-step explanation:

Answer:

\(k = 1\)

\(P(x > 3y) = \frac{2}{3}\)

Step-by-step explanation:

Given

\(f \left(x,y \right) = \left{ \begin{array} { l l } { k , } & { 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x } & { \text 0, { elsewhere. } } \end{array} \right.\)

Solving (a):

Find k

To solve for k, we use the definition of joint probability function:

\(\int\limits^a_b \int\limits^a_b {f(x,y)} \, = 1\)

Where

\({ 0 \leq x} \leq 2,0 \leq y \leq 1,2 y \leq x }\)

Substitute values for the interval of x and y respectively

So, we have:

\(\int\limits^2_{0} \int\limits^{x/2}_{0} {k\ dy\ dx} \, = 1\)

Isolate k

\(k \int\limits^2_{0} \int\limits^{x/2}_{0} {dy\ dx} \, = 1\)

Integrate y, leave x:

\(k \int\limits^2_{0} y {dx} \, [0,x/2]= 1\)

Substitute 0 and x/2 for y

\(k \int\limits^2_{0} (x/2 - 0) {dx} \,= 1\)

\(k \int\limits^2_{0} \frac{x}{2} {dx} \,= 1\)

Integrate x

\(k * \frac{x^2}{2*2} [0,2]= 1\)

\(k * \frac{x^2}{4} [0,2]= 1\)

Substitute 0 and 2 for x

\(k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1\)

\(k *[ \frac{4}{4} - \frac{0}{4} ]= 1\)

\(k *[ 1-0 ]= 1\)

\(k *[ 1]= 1\)

\(k = 1\)

Solving (b): \(P(x > 3y)\)

We have:

\(f(x,y) = k\)

Where \(k = 1\)

\(f(x,y) = 1\)

To find \(P(x > 3y)\), we use:

\(\int\limits^a_b \int\limits^a_b {f(x,y)}\)

So, we have:

\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {f(x,y)} dxdy\)

\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 {1} dxdy\)

\(P(x > 3y) = \int\limits^2_0 \int\limits^{y/3}_0 dxdy\)

Integrate x leave y

\(P(x > 3y) = \int\limits^2_0 x [0,y/3]dy\)

Substitute 0 and y/3 for x

\(P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy\)

\(P(x > 3y) = \int\limits^2_0 y/3\ dy\)

Integrate

\(P(x > 3y) = \frac{y^2}{2*3} [0,2]\)

\(P(x > 3y) = \frac{y^2}{6} [0,2]\\\)

Substitute 0 and 2 for y

\(P(x > 3y) = \frac{2^2}{6} -\frac{0^2}{6}\)

\(P(x > 3y) = \frac{4}{6} -\frac{0}{6}\)

\(P(x > 3y) = \frac{4}{6}\)

\(P(x > 3y) = \frac{2}{3}\)

Answer:

44

Step-by-step explanation

4c + d

this is an expression and since they provided c and d it is easy to solve

c = 9 and d = 8. You need to plug in c and d into the expression to solve the problem.  

4(9) + (8)

4 times 9 is 36 so it leaves you with 36 + 8

36 + 8 = 44

I hope this helps but basically the concept is just plugging in the numbers in place of the variables. For future problems plug in the numbers given where the variables are.

Answer:

the correspond answer to this is y=6 (2,6)

Step-by-step explanation:

Answer: y = 4

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

3 = (10 - y1)/(4 - 2)

3(4 - 2) = 10 - y1

3(2) = 10 - y1

6 = 10 - y1

-y1 = -4

y = 4

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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The variables are as follows:

x = 4

y = 4.8

The lengths of the sides of the kites are 4.5 and 6.8 units.

A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.

The non vertex angles are congruent.

Therefore,

x + 0.5 = 2x - 3.5

2x - x = 0.5 + 3.5

x = 4

y + 2 = 2y - 2.8

2y - y = 2 + 2.8

y = 4.8

Hence,

length of one pair = 4 + 0.5 = 4.5 units

length of the other pair = 4.8 + 2 = 6.8 units

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The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer:

39 divided by 8 is equal to 4 with a remainder of 7.

The quotient is the number of times the divisor goes into the dividend. In this case, 8 goes into 39 4 times with a remainder of 7.

The remainder is the number that is left over after the divisor has been divided into the dividend. In this case, 7 is left over after 8 has been divided into 39.

Here is the long division of 39 by 8:

```

39 / 8

4

32

7

```

Step-by-step explanation:

The quotient of 39 divided by 8 is 4, and the remainder is 7.

We have,

When performing long division, we divide the dividend (39) by the divisor (8) to find the quotient and remainder.

  4

--------

8 | 39

  - 32

    ---

     7

Here's how the long division process works for 39 divided by 8:

-We start by dividing the first digit of the dividend (3) by the divisor (8). Since 3 is less than 8, we can't divide it evenly, so we move to the next digit (9).

- We now have 39 as the remaining portion of the dividend. We divide 39 by 8. The largest multiple of 8 that fits into 39 is 4. We place the quotient, which is 4, above the line.

- We multiply the quotient (4) by the divisor (8), which gives us 32. We subtract 32 from 39, which leaves us with a remainder of 7.

- Since there are no more digits to bring down from the dividend, and the remainder (7) is less than the divisor (8), we stop the division process.

Therefore,

The quotient of 39 divided by 8 is 4, and the remainder is 7.

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:

Time = (100 x (Amount - Principal)) / (Principal x Rate)

In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:

Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years

Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.

Step-by-step explanation: