A,B and C are points in the cartesian plane. the coordinates of A are (3,-2),BA=(4,-3)and AC=(4,9). Calculate
i. the coordinates of B and C​

Given that mean= 6.56 and standard deviation(σ)= 1.19

a) P(X ≤ 5)= ( (X-µ)/ σ) < (5- 6.56)/ 1.19)

                = 0.094946

P(X ≤ 5)= 0.95

So 0.95 proportion of the survey would think $5 is too expensive for a sandwich.

b) P(X ≥ 6.75) = ( (X-µ)/ σ) < (6.75- 6.56)/ 1.19)

                      = 0.43656

0.43656 proportion of people surveyed would be willing to pay more than $6.75 for a sandwich.

c)  P(X ≤ x)= 0.35

                 = P((x- µ)/ σ ≤ (x- 6.65)/ 1.19)

                  0.35

x= (-0.3853) (1.19) + 6.56

 = 6.1015

6.1015  is the 35th percentile for how much people are willing to pay for a sandwich.

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Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms

These were the sets of axioms that were proposed by the man David Hilbert in the 1899. They are a set of 20 assumptions that he made. He made these assumptions as a treatment to the geometry of Euclid.

These helped to create a form of formalistic foundation in the field of mathematics. They are regarded as his axiom of completeness.

Hilbert’s axioms are divided into 5 distinct groups.  He named the first two of his axioms to be the axioms of incidence and the axioms of completeness. His third axiom is what he called the axiom of congruence  for line segments. The forth and the fifth are the axioms of congruence for angles respectively.

Hence we can conclude by saying that Hilbert axioms changed Euclid's theorem by identifying and explaining the concept of undefined terms.

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complete question

Hilbert’s axiom’s changed Euclid’s geometry by _____.

1 disproving Euclid’s postulates

2 utilizing 3-dimensional geometry instead of 2-dimensional geometry

3 describing the relationships of shapes

4 identifying and explaining the concept of undefined terms

The area of the region bounded by the graphs of the given equations is 0.

To find the area of the region bounded by the graphs of the given equations y = -2x - x^2 and y = -8, we need to determine the points of intersection between the two curves.

Setting the equations equal to each other:

-2x - x^2 = -8

Rearranging and simplifying the equation:

x^2 - 2x + 8 = 0

This quadratic equation does not have real solutions. Therefore, the two curves do not intersect, and there is no region bounded by them.

As a result, the area of the region bounded by the graphs of the given equations is 0.

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An odd number cubed is an odd number.

To answer the question, we need to know what odd numbers are

Odd numbers include 1,3, 5,7... and take the general for (2n + 1) where n = 0, 1, 2...

Now, we need to show that an odd number cubed is an odd number.

So, the odd number (2n + 1) cubed is

(2n + 1)³ = (2n + 1)(2n + 1)²

= (2n + 1)(4n² + 4n + 1)

= 8n³ + 8n² + 2n + 4n² + 4n + 1

= 8n³ + 12n² + 6n + 1

= 2(4n³ + 6n² + 3n) + 1

Since (4n³ + 6n² + 3n) is an integer say k, we have that

2(4n³ + 6n² + 3n) + 1 = 2k + 1

Since 2k + 1 is an odd number, 2n + 1 is an odd number and (2n + 1)³ = 2k + 1 which is an odd number.

So, an odd number cubed is an odd number.

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Answer:

SLOPE: 1

Y-Intercept: (0,4)

Step-by-step explanation:

Answer:

m=1

Step-by-step explanation:

Answer:

12 = 4

15 5

Step-by-step explanation:

12 ÷3= 4

15 ÷3= 5

:)

Answer:

Wow, thanks :)

Step-by-step explanation:

You are just too kind :D

Answer:

MEEEEEEE

Step-by-step explanation:

I WAS ON THE TOLITE IN  CLASS AND MY CAM TURNED ON THEN MY MOM CAME IN...

2?

On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.

This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.

The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.

Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.

In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.

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Answer:

(D)3 units

Step-by-step explanation:

To find the value of a, we use the Theorem of Intersecting Secants.

Applying this to the diagram, we have:

UV X TV = RV X SV

12 X a=(5+4)*4

12a=9*4

12a=36

Divide both sides by 12

a=3 units.

The correct option is D.

By applying the Theorem of Intersecting Secants, the length of TV (a) is equal to: D. 3 units.

The Theorem of Intersecting Secants states that the product of a secant and its external secant is equal to the product of the other secant and its external secant, when two (2) secants are drawn to a circle from an exterior (outside) point:

In order to determine the length of TV (a), we would apply the Theorem of Intersecting Secants as follows:

UV × TV = RV × SV

12 × TV = (5 + 4) × 4

12TV = 9 × 4

12TV = 36

TV = 36/12

TV = 3 units.

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The equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

The expression is given as:

3/2(6x^2 - 2/3x)

Open the bracket

3/2*6x^2 - 3/2*2/3x

Evaluate the product

9x^2 - x

Hence, the equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

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In a case whereby a computer system is advertised with a 14-inch monitor. The measurement of the monitor is along the diagonal of the screen. The height of the monitor screen is 9 inches  the width of the monitor screen is 10.724 inches.

From the question, we have a diagonal (hypotenuse) of 14 inches whre the height is 9 inches.

Then using the Pythagorean Theorem, there are values for the a and c

\(9^2 + b^2 =196\\81 + b^2 = 196\\b=\sqrt{196} \\b= 10.724 inches\)

Therefore, the width of the monitor screen is 10.724 inches

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The flux through through the boundary of the rectangle is -sin(6x)/6.

According to the statement

we have given that the limits and the equation, and we have to find the flux of the given equation.

For this purpose, we know that the

Flux is a the surface integral of the perpendicular component of a vector field over a surface.

And the given equation is :

x^4 + 5,ycos(6x)

The given limits are:

0≤ x ≤ 2, 0 ≤ y ≤ 4

So, Integrate with the given imits,

\(\int\limits^2_0 \int\limits^4_0 {x^4 + 5,ycos(6x)} \, dx\)

When integrate these terms with dx and dy one by one then the equation become:

For the x:

\(\int\limits^2_0 {x^4 + 5,ycos(6x)} \, dx \\\bracket\limits^2_0 [{\frac{x^5}{5},{-ysin(6x)}}/{6]\)

And then integrate w.r.t the y.

Then the flux through the boundary become:

-sin(6x)/6.

So, The flux through through the boundary of the rectangle is -sin(6x)/6.

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Answer: y = 4

Step by step explanation:

−3y + 2 = −10y + 30

Step 1: Add 10y to both sides.

−3y + 2 + 10y = −10y + 30 + 10y

7y + 2 = 30

Step 2: Subtract 2 from both sides.

7y + 2 − 2 = 30 − 2

7y = 28

Step 3: Divide both sides by 7.

7y/7  =  28/7

y = 4

Based on the histogram to the right, the number of the  team members that are included are 18 members.

A histogram is known to be a diagram or a graph that shows the statistical information that is often used to depict the frequency of data items and this is often done in a successive numerical intervals that has equal size rectangles.

For the above question, you have to count the no of units taken on y axis and this is:

= 1+1+1+3+4+3+5

= 18 members

So, Based on the histogram to the right, the number of the  team members that are included are 18 members.

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Answer:

Angle E is equal to angle A and line VC is equal to line BT

Step-by-step explanation:

through AAS, you prove the triangle is simalar

Answer:

544

Step-by-step explanation:

EASY JUST MULTIPLY!!!

multiply your total of ways to fill the position, by how many members!

so...   272 x 2 = 544    hopes this helps!!

The other zero of the degree 4 polynomial with rational coefficients, given zeros at 8i, 0, and -2, is -8i, as complex roots occur in conjugate pairs. Therefore, the zeros are 8i, -8i, 0, and -2.

When a polynomial with rational coefficients has a complex root, it always occurs in conjugate pairs. This means that if a + bi is a root, where a and b are real numbers, then its conjugate a - bi will also be a root.

In the given problem, the complex zero 8i is present. Since it is of the form 0 + 8i, we know that its conjugate will be 0 - 8i, which is -8i. Therefore, -8i is also a zero of the polynomial.

In addition to the complex zeros, the problem states that the polynomial has zeros at 0 and -2. These are both real numbers.

Putting it all together, the zeros of the polynomial are: 8i, -8i, 0, and -2.

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There is no sufficient evidence to indicate the true standard deviation is less than 4000

What is standard deviation ?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

given that n = 16

x = 60139.7

s = 3718.06

∝ = 0.05

To test the hypothesis

H0 : = 4000

H1 :  < 4000 (claim)

test statistics

x² = ((n-1)s²) / H0²

   = (15 * 13823970.16) / (16000000)

   = 12.96

P- value = P [x² < 12.96]           DF = n-1 = 15

             = 0.3946

0.1 < P-value <0.5

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The cοοrdinates οf the center M are therefοre (-13.5, -13.5) frοm the pοints P(-16,-16) and Q(-11,-11) and the distance d(P,Q).

Cοοrdinates are a cοllectiοn οf numbers used tο describe a pοint's lοcatiοn in a space οr plane in mathematics. The first number in a pair οf cοοrdinates usually indicates the lοcatiοn alοng the x-axis, and the secοnd number indicates the pοsitiοn alοng the y-axis.

A three-dimensiοnal cοοrdinate system is prοduced by adding a z-axis tο the twο-dimensiοnal cοοrdinate system fοrmed by the x- and y-axes. In geοmetry, algebra, trigοnοmetry, and οther branches οf mathematics, cοοrdinates are frequently used.

given

We emplοy the distance algοrithm tο determine the separatiοn between pοints P and Q:

sqrt[(x₂ - x₁) + (y₂ - y₁)] Equals d(P,Q)

where pοint P's cοοrdinates are x₁ and y₁, and pοint Q's cοοrdinates are x₂ and y₂.

By entering the specified numbers, we οbtain:

sqrt[(-11 - (-16))² + (-11 - (-16))² Equals d(P,Q)

= sqrt[5² + 5²]

equals sqrt[50] = 5sqrt (2)

Therefοre, P and Q are separated by 5 sqrt(2) units.

We emplοy the midpοint methοd tο determine the midpοint's cοοrdinates:

M = [((x₁ + x₂)/2), ((y₁+ y₂)/2)]

By entering the specified numbers, we οbtain:

= [-13.5, -13.5] .5]

The cοοrdinates οf the center M are therefοre (-13.5, -13.5) frοm the pοints P(-16,-16) and Q(-11,-11) and the distance d(P,Q).

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Answer:

Is the dilation an enlargement or reduction?

Reduction

The point of dilation is about what coordinate?

0,0

What is the scale factor?

1/3

Step-by-step explanation:

The dilation is a reduction. The point of dilation is about coordinate (0,0).  The scale factor is 1/3.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

On a coordinate plane, the pre-image rectangle has points (0, 0), (6, 0), (6, -3), and (0, -3).

The image has points (0, 0), (2, 0), (2, -1), and (0, -1).

The required figure has been attached below which represents the dilation.

As we can see that the dilation is a reduction.

The point of dilation is about coordinate (0,0).

This result of dilating a given triangle with a scale factor is 1/3.

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For skewed data displays, the median is often a better estimate of the center of distribution than the mean because the former is unaffected by large numbers.

Mean refers to the average of set of two or more numbers.

Mean of a set having 'n'  numbers = \(\frac{Sum Of 'n' Numbers}{n}\)

Median refers to the middle-most value of a list of numbers, arranged either in ascending or descending order.

Median = \(\left \{ {{\frac{n}{2}^{th} term, if n = even } \atop( (\frac{n-1}{2}+\frac{n+1}{2})/2)^{th} term, if n = odd }} \right.\)

Now,

Hence, For skewed data displays, the median is often a better estimate of the center of distribution than the mean.

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Answer:

Slope. -6

Y- intercept. 180

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Step-by-step explanation:

Answer: 320x + 55

Step-by-step explanation:

The statements about this situation that are true include:

Since the number of times the website was visited had a net change of +55 and during each subsequent month, starting in the next year, the number of visits increased by 320. The expression to solve this will be:

= 320(x) + 55

= 320x + 55

where, x = number of months.

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The probability of selecting a black card first and a red card second from a standard deck of 52 playing cards without replacement is 13/51.

The probability of selecting a black card on the first draw is 26/52, or 1/2, since there are 26 black cards in a standard deck of 52 playing cards.

After the first card is drawn, there are 51 cards remaining, of which 26 are red. Therefore, the probability of selecting a red card on the second draw, given that a black card was selected on the first draw, is 26/51.

To find the probability of both events happening (selecting a black card followed by a red card), we multiply the probabilities of each event:

P(black card first, red card second) = P(black card first) × P(red card second | black card first)

P(black card first, red card second) = (1/2) × (26/51)

P(black card first, red card second) = 13/51

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When two identical rectangles are linked at one corner and drawn on coordinate axes, the resulting shape is a right-angled trapezoid.

Let's consider the coordinate axes with the origin (0,0) as the common corner of the rectangles. Suppose the length and width of each rectangle are 'a' and 'b', respectively.

The vertices of the rectangles are as follows:

Rectangle 1:

A = (0,0)

B = (0,a)

C = (b,a)

D = (b,0)

Rectangle 2:

A' = (0,0)

B' = (a,0)

C' = (a+b,0)

D' = (a+b,-b)

Connecting the corresponding vertices of the rectangles, we obtain the following trapezoid:

A--A'--B'--B--C--C'--D'

The shape formed by linking two identical rectangles at one corner on the coordinate axes is a right-angled trapezoid. The length of the longer parallel side is equal to the sum of the lengths of the two rectangles, while the length of the shorter parallel side is equal to the width of the rectangles.

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The required approximation of the number of CD's represented by the shaded sector of the circle is 850.

A circle is a shut two-layered figure wherein the arrangement of the relative multitude of center in the plane is equidistant from a given point called "focus". Each line that goes through the circle frames the line of reflection evenness. Additionally, it has rotational balance around the middle for each point.

We have,

The entire circle represents a total of 2875 CD's sold

So, we can say that shaded part is slightly more than the one-fourth of total part of the circle.

So,

2875/4 = 718 +

Thus, approx 850 CD's are sold.

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The correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores. This suggests that as study times increase, there is a tendency for test scores to also increase. However, the relationship is not extremely strong.

The correlation coefficient, denoted by 'r', ranges from -1 to 1. A positive value indicates a positive relationship, meaning that as one variable increases, the other tends to increase as well. In this case, the correlation coefficient of 0.49 indicates a moderate positive relationship between study times and test scores.

It's important to note that the correlation coefficient of 0.49 falls between 0 and 1, closer to 1. This suggests that there is a tendency for test scores to increase as study times increase, but the relationship is not extremely strong. Other factors may also influence test scores, and the correlation coefficient does not imply causation.

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