Please see the attached

Answer:

The quotient is

[tex]8 {x}^{2} + 15x - \frac{1}{8} [/tex]

and the remainder is

[tex] \frac{63}{64} [/tex]

The equation of the line AB,with slope of -1/2 is  y = (-1/2)x + 7/2. We then use the dot product to show that the direction vectors of the lines AB and AC are orthogonal, and the coordinates of point C is (6,7).

In an orthonormal frame (o; i; j), the points A and B are given as A(3;1) and B(1;2), and the line (AC) is given by the equation 2x-y-5=0.

To determine the equation of line (AB), we need to find the slope (or gradient) of the line passing through A and B. We can find this by using the formula

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

where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the values of A and B, we get

slope = (2 - 1) / (1 - 3) = -1/2

Now that we have the slope, we can use the point-slope form of a line to find the equation of line (AB). Let (x,y) be any point on the line, then we have

y - 1 = (-1/2)(x - 3)

Simplifying, we get

y = (-1/2)x + 7/2

So the equation of line (AB) is y = (-1/2)x + 7/2.

To show that the direction vectors AB and AC of the lines (AB) and (AC) are orthogonal, we need to find the direction vectors of these lines and show that their dot product is zero. The direction vector of a line is just the vector that "points" in the direction of the line. To find it, we can take any two points on the line and subtract their coordinates to get a vector.

For line (AC), we can take A and C as two points on the line. Since we don't know the coordinates of C yet, we can solve the equation of line (AC) for x to get

x = (y + 5) / 2

Now substituting x by the above expression in the coordinates of point A we get

C((y + 5)/2, y)

Thus, the direction vector of line (AC) is

AC = C - A = ((y + 5)/2 - 3, y - 1) = (y/2 - 7/2, y - 1)

Similarly, we can take A and B as two points on the line (AB) to get the direction vector of line (AB):

AB = B - A = (1-3, 2-1) = (-2, 1)

Now, the dot product of AB and AC is

AB · AC = (-2)(y/2 - 7/2) + (1)(y - 1) = -y + 7

We can see that the dot product is zero when y=7. Hence, direction vectors AB and AC are orthogonal at point C(3,7).

To determine the coordinates of C, we substitute y=7 in the equation of line (AC) we obtained earlier

2x - y - 5 = 0

2x - 7 - 5 = 0

2x = 12

x = 6

Therefore, C has coordinates (6,7).

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The surface area of the triangular prism is approximately 44.29 square millimeters.

What is surface area?

Surface area is the total area that the surface of a three-dimensional object covers. It is a measure of the amount of space that the surface of an object occupies. Surface area is usually measured in square units such as square meters, square centimeters, square inches, or square feet.

What is the area?

The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.

The area of a plane figure is the space enclosed by its boundary.

According to the given information:

To find the surface area of a triangular prism, we need to add up the area of all the faces. A triangular prism has three rectangular faces and two triangular faces.

Let's start by finding the area of the triangular faces. The base of the triangular prism is a right triangle with base 4 millimeters, height 4 millimeters, and hypotenuse 5.7 millimeters. We can use the Pythagorean theorem to find the missing side:

[tex]a^2 + b^2 = c^2\\4^2 + 4^2 = 5.7^2[/tex]

16 + 16 = 32.49

32 = 32.49 - 0.49

32 = 32

So the missing side has length [tex]\sqrt{(5.7^2 - 4^2)} =3.69 millimeters.[/tex] This is the base of each triangular face.

The height of the triangular prism is 3 millimeters, so the height of each triangular face is also 3 millimeters.

The area of each triangular face is:

(1/2) × base × height

= (1/2) × 3.69 × 3

≈ 5.54 square millimeters

So the total area of the two triangular faces is:

2 × 5.54= 11.08 square millimeters

Now let's find the area of each rectangular face. The length of each rectangular face is the same as the base of the triangular face, which is 3.69 millimeters. The width of each rectangular face is the height of the triangular prism, which is 3 millimeters.

The area of each rectangular face is:

length × width

= 3.69 × 3

≈ 11.07 square millimeters

So the total area of the three rectangular faces is:

3 × 11.07

= 33.21 square millimeters

To find the surface area of the triangular prism, we add up the area of all five faces:

11.08 + 33.21

= 44.29 square millimeters

Therefore, the surface area of the triangular prism is approximately 44.29 square millimeters.

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The median is the accurate reflection of the data

501, 900, 971, 977, 1071

The mean would be

summation of the values

mean = 884

The median is the value that occurs in the middle = 971

The median would be more accurate reflection of the data. 501 is an outler. This is what caused us to have a mean that is c loser to 884. Hence we have 971 the median to be more accurate reflection of the data

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The probability of rolling a 4 on a single throw of a fair 6-sided die is 1/6, since there is only one way to roll a 4 and there are 6 equally likely outcomes in total.

The probability of rolling an even number on a single throw of a fair 6-sided die is 3/6, or 1/2, since there are three even numbers (2, 4, and 6) out of six possible outcomes.

To find the probability of rolling a 4 or an even number on a single throw, we can add the probabilities of these two events:

P(4 or even) = P(4) + P(even) - P(4 and even)

where P(4 and even) is the probability of rolling a 4 and an even number on the same throw. Since there is only one outcome (rolling a 4), which is not even, this probability is 0.

Therefore:

P(4 or even) = P(4) + P(even) - P(4 and even)

             = 1/6 + 1/2 - 0

             = 2/3

So the probability of rolling a 4 or an even number on a single throw of a 6-sided die is 2/3.

If the die is thrown 2 times, the probability of rolling a 4 or an even number on both throws is the product of the probabilities of rolling a 4 or an even number on each throw:

P(4 or even on both throws) = P(4 or even) × P(4 or even)

                           = (2/3) × (2/3)

                           = 4/9

Therefore, the probability of rolling a 4 or an even number on both throws of a 6-sided die is 4/9.

Answer:

Step-by-step explanation:

decimal: 0.44444444444

fraction: 4/9

Answer:

All lines are parallel.

Step-by-step explanation:

Get each equation in Slope-Intercept form:

  1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]

  2. No change

  3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]

Notice:

a. All slopes are -4/3

b. All y-intercepts are different

A set of data that could be represented by the box-and-whisker plot include the following: D.

The median of the set of data is equal to 10.

In Mathematics and Statistics, a box-and-whisker plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set (2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28), the five-number summary for the given data set include the following:

Minimum (Min) = 2.

First quartile (Q₁) = 16.

Median (Med) = 10.

Third quartile (Q₃) = 25.5.

Maximum (Max) = 28.

In conclusion, we can logically deduce that the median of the data set is 10 and it has no outlier.

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The valid row-operation which needs to be performed on the given matrix to get "1" in position of row1 and column1 are "R₁ → 2R₁ + R₂" and then "R₁ → R₁/2".

The "row-operation" is a type of matrix operation that involves swapping, scaling, or adding rows in a matrix. These operations are used to transform a matrix into a more reduced form.

The Augmented matrix on which we have to perform the "row-operation" is

⇒ [tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex],

To get "1" in first row and first column,

The first row-operation is R₁ → 2R₁ + R₂

We get,

⇒ [tex]\left[\begin{array}{ccc}7\times 2-12&-4\times 2+7&8\times 2-13\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}14-12&-8+7&16-13\\-12&7&-13\end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{ccc}2&-1&3\\-12&7&-13\end{array}\right][/tex],

The second , row-operation to get a "1", is R₁ → R₁/2,

We get,

⇒ [tex]\left[\begin{array}{ccc}2/2&-1/2&3/2\\-12&7&-13\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}1&-0.5&1.5\\-12&7&-13\end{array}\right][/tex].

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The first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

= n(E) / n+S)

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Thus, the first blank will be filled by Option A: Total Number of Possible Outcomes. The second blank will be filled by Option B: Number of Winners

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Drag tiles to fill in the blanks to complete the expression that could be used to predict the number of winners of a game. Tiles may be used once or not at all. A)Total Number of Possible Outcomes B)Number of Winners C)Number of Unfavorable Outcomes D)Number of Games P(event) = Number of Favorable Outcomes _________________________ ????????????????????????????? = ????????????????????????????? _________________________ 11 Total Number of Contestants

Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.

Solving for x, we have:

3(2x - 8) = 4425

6x - 24 = 4425

6x = 4451

x = 741.83

Rounding to the nearest whole number, we have x = 742.

Therefore, x = 742.

Answer:

We can use the formula for compound interest to calculate the amount and interest:

A = P * (1 + r/n)^(n*t)

I = A - P

Where:

P = Principal = $15,300

r = Rate = 8% = 0.08

n = Compounding frequency per year = 4 (since it is compounded quarterly)

t = Time period = 6 years

Plugging in the values, we get:

A = 15,300 * (1 + 0.08/4)^(4*6) = $23,659.28

I = 23,659.28 - 15,300 = $8,359.28

Therefore, the amount after 6 years is $23,659.28 and the interest earned is $8,359.28.

I hope this helps.

Answer:

x = [tex]\frac{5u+4y}{2-6z}[/tex]

Step-by-step explanation:

2(x - 2y) = 6xz + 5u ← distribute parenthesis on left side

2x - 4y = 6xz + 5u ( add 4y to both sides )

2x = 6xz + 5u + 4y ( subtract 6xz from both sides )

2x - 6xz = 5u + 4y ← factor out x from each term on the left side

x(2 - 6z) = 5u + 4y ← divide both sides by (2 - 6z)

x = [tex]\frac{5u+4y}{2-6z}[/tex]

It will take approximately 6.24 years to have enough money for the down payment saved.

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where:

A = the amount of money we want to have (in this case, $35,000)

P = the initial amount we have (in this case, $20,000)

r = the annual interest rate (in this case, 12%)

n = the number of times interest is compounded per year (let's assume it's compounded monthly, so n = 12)

t = the number of years we're investing for (this is what we want to find)

Substituting the values we know:

$35,000 = $20,000(1 + 0.12/12)^(12t)

Simplifying:

1.75 = (1 + 0.01)^(12t)

Taking the natural logarithm of both sides:

ln(1.75) = 12t ln(1.01)

Dividing both sides by 12 ln(1.01):

t = ln(1.75) / (12 ln(1.01))

Using a calculator:

t ≈ 6.24 years

Therefore, it will take approximately 6.24 years to have enough money for the down payment saved.

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Answer:

11-2x not 13x

Step-by-step explanation:

\(6-2)x + (5-4)x does = 13x

If there were parentheses as in the 2nd line, everything else is correct

the mistake is going from

6-2x + 5-4x to

(6-2x) + (5-4)x

PEMDAS is the order of operations. P for parentheses 1st, Multiplication 3rd, addition 4th, subtraction 5th

(there are no exponents or division or parentheses, so it's just M, A and S that apply)

combine like terms, 2x-4x =-2x

combine the constant terms 6+5 = 11

6-2x +5-4x = 11-2x

The mistake was assuming parentheses when they aren't there.

correct answer is 11-2x not 13x

Answer:

35%

(I replaced the 1st digit by a and the second digit by b)

The percent of the area that is not covered is 80 percent

In mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².

area of tent

= (10 - 0) * (6 - (-3))

= 90

The area of the campsite would be:

(25 - (-5) x (10 - (-5))

= 450

Then the area would be 450 - 90

= 360

the percentage that is not covered by tent = 360 / 450 x 100

= 80 percent

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If the line passes through the point (2,8) that cuts off the least area from the first quadrant, the slope is 8/3 and the y-intercept is 0.

To find the equation of the line that passes through the point (2, 8) and cuts off the least area from the first quadrant, we need to first determine the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

We can use the point-slope form of the equation of a line to find the slope. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Plugging in (2, 8) as the point, we get:

y - 8 = m(x - 2)

Next, we want to minimize the area that the line cuts off in the first quadrant. Since the line passes through the origin (0, 0), the area cut off by the line in the first quadrant is equal to the product of the x- and y-intercepts of the line.

We can express the x-intercept in terms of y by setting y = 0 in the equation of the line and solving for x:

0 - 8 = m(x - 2)

x = 2 + 8/m

The y-intercept is simply the y-coordinate of the point where the line intersects the y-axis, which is given by:

y = mx + b

8 = 2m + b

b = 8 - 2m

We can now express the area cut off by the line as:

A = x*y

A = (2 + 8/m)*8 - (8 - 2m)*2/m

A = (16 + 64/m) - (16 - 4m)/m

A = 64/m + 4m/m

To minimize the area, we can take the derivative of A with respect to m and set it equal to zero:

dA/dm = -64/m² + 4/m² = 0

64 = 4

m = 8

Plugging m = 8 into the equation for the x-intercept, we get:

x = 2 + 8/8 = 3

So the equation of the line is y = 8x/3.

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Answer:

x= 3 cm

Explanation:

I am bad at it

The conclusion on the null hypothesis is B. Reject H₀ because the P-value is less than or equal to a.

It is posited that the mean pulse rate for a specific grouping of adult males equals 76 bpm as set forth by the null hypothesis. In its place, an alternative hypothesis suggests this figure does not reflect actuality.

At a given significance level identified by alpha = 0.05, rejection of the null hypothesis requires us to identify a P-value lesser than or equal to 0.05.

The P-value determined within the question happens to be below such a threshold at 0.0075, which results in the rejecting of the null hypothesis.

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The exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

A manufacturer earned $55 per hour of labor when it opened.

Each year the manufacturer earns an additional 7% per hour.

Since the manufacturer earns an additional 7% per hour each year, the amount earned per hour can be represented as follows:

[tex]A(t) = 55(1 + 0.07)^t[/tex]

where t is the number of years after the plant opened. T

This can be simplified as function:

[tex]A(t) = 55(1.07)^t[/tex]

Therefore, the exponential function that gives the amount A(t) that the plant earns per hour t years after it opens is [tex]A(t) = 55(1.07)^t[/tex]

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Answer:

Step-by-step explanation:

8+(6-3)-9

The first action is addition in parentheses

(6-3) = 3

The second action is addition and then subtraction, you can subtract first and then add, it makes no difference because the answer will be the same in all cases

8 + 3 - 9 = 11 - 9 = 2

Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by

[tex]A=P(1+r/n)^{nt}[/tex]

where P = Principal, r = annual rate of interest, n = the number of times interest is compounded per year & t = time in years.

The given principal is $1600 for 11 years & amount is $2400 compounded quarterly.

To find the rate of interest compounded quarterly for 11 years substitute the given values in the above formula i.e

[tex]2400=1600(1+r/4)^{11*4}[/tex]

r=3.70%.

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Answer: w = –27i + 35j

Step-by-step explanation:

Answer: e

Step-by-step explanation:

Answer:Valid

Step-by-step explanation:

Answer:  (5, -1)

Step-by-step explanation:

format:  f(x)

in  f(5)=-1       x=5

also sometimes f(x) is called y so  y= -1

put into ordered pair format

(5, -1)

234 2/5 is equivalent to 1172/5.

234 2/5 is a mixed number, which means it is a combination of a whole number and a fraction.

To convert it to an improper fraction, we need to multiply the whole number by the denominator of the fraction and add the numerator.

The result becomes the new numerator, and the denominator stays the same.

In this case, we have:

234 2/5 = (234 x 5 + 2) / 5

= 1172/5

Therefore, 234 2/5 is equivalent to 1172/5 as an improper fraction.

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The height of the larger cone is 71.13 meters

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

Using the above as a guide, we have the following:

Scale factor = h1/h2

So, we have

h1/h2 = √(1883/7352)

substitute the known values in the above equation, so, we have the following representation

36/h2 = √(1883/7352)

So, we have

h2 = 36 * √(7352/1883)

Evaluate

h2 = 71.13

Hence, teh height is 71.13

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