The weight of full-Russian Blue cat can be described by a Normal distribution with a mean of 11 pounds and a standard deviation of 1.3 pounds. (One of the largest breeds of cat is the Maine Coon cat which can weigh 25 pounds!)
a) Kitty has a full-grown Russian Blue cat that weighs 7.9 pounds. What is the z-score for this dog? (Express your answer to one decimal place.)
b) The answer to part a should be negative. Explain what the fact that the z-score is negative tells us about that cat.
Pls break it down
c) We know that there are two criteria for determining if a data value is an outlier. Using the three standard deviations criterion, is this data value an outlier. Be sure to explain your answer.

Answer:

1.) positive

2.) negative

3.) zero

4.) undefined

5.) zero

6.) positive

7.) positive

8.) undefined

9.) negative

The universal set is U={a,b,c,d,e,f,g,h}.

(i) The complement of A={a,b,c} is U\A={d,e,f,g,h}.

(ii) The complement of B={d,e,f,g} is U\B={a,b,c,h}.

(iii) The complement of C={a,c,e,g} is U\C={b,d,f,h}.

(iv) The complement of D={f,g,h,a} is U\D={b,c,d,e}.

In set theory, the complement of a set A is defined as the set of all elements that are not in A but are in the universal set U. In other words, it is the set of all elements in U that do not belong to A.

For example, if U = {1,2,3,4,5} and A = {1,3,5}, then the complement of A, denoted as A', is {2,4}. This is because A' contains all the elements in U that are not in A.

Similarly, for the sets given in the question, the complements can be found as follows:

(i) A' = {d,e,f,g,h}

(ii) B' = {a,b,c,h}

(iii) C' = {b,d,f,h}

(iv) D' = {b,c,d,e}

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Answer:

the usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. ... This give a geometric justification that the area of a circle really is "pi r squared".Jan 29, 2008

Step-by-step explanation:

The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

For the triangles SAT and SAO in this problem, we have that:

The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.

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Answer: bus driver

Step-by-step explanation:

Given: Earning of bus driver =  1600 dollars per month

Earning of  manager  = 6800 dollars per month

Amount donated by bus driver = 1200 dollars

Amount donated by manager = 4500 dollars

Percentage of amount donated by bus driver = \(\dfrac{1200}{1600}\times100 \%=\dfrac{3}{4}\times100\%=75\%\)

Percentage of amount donated by manager = \(\dfrac{4500}{6800}\times100 \%\approx66.18\%\)

Clearly, 75> 66.18

So, bus driver donated  higher percentage of money.

The area of the heptagon is  24. 2 square units

To determine the area of the shape which is a heptagon, we have that;

A = 1/2)nsr.

Such that the parameters of the formula are written as;

From the information given, we have that;

n = 7

s = 2. 77

r = 2. 5

Substitute the values, we have that;

Area = 1/2 × 2. 5 × 2. 77 × 7

Multiply the values, we get;

Area = 1/2 × 48.475

Divide the values

Area = 24. 2 square units

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Answer:

19

Step-by-step explanation:

The triangle with sides a and b and angle c is added as an attachment

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

Triangles with the following properties

Side lengths = a and b

Angle between the side lengths = C

The above parameters mean that

Also, the other angles and sides can be derived from the above parameters

So, we have

Next, we construct the triangle

See attachment for the triangle

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Answer:

Step-by-step explanation:

2.25 foot

Answer:

2 feet, 4 inches.

Step-by-step explanation:

The guy above only gave feet.

Answer:

5 miles

Step-by-step explanation:

The Pythagoras theorem : a² + b² = c²

where a = length = 4

b = base= 3

c = hypotenuse

4² + 3²

16 + 9 = 25

√25 = 5

The remainder when 101⁴⁸⁰⁰⁰⁰⁰⁰²³ is divided by 35 is 12.

Now, let's look at how we can use the Chinese Remainder Theorem to compute 101⁴⁸⁰⁰⁰⁰⁰⁰²³ mod 35. First, we need to express 35 as a product of prime powers:

=> 35 = 5 x 7.

Then, we can consider the congruences 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ a (mod 5) and 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ b (mod 7), where a and b are the remainders we want to find.

Since 101 is not divisible by 5, we have 101⁴ ≡ 1 (mod 5). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁴)¹²⁰⁰⁰⁰⁰⁰⁰⁵ ≡ 1 (mod 5).

This means that a = 1.

Since 7 is a prime number, φ(7) = 6, so we have 101⁶ ≡ 1 (mod 7). Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ (101⁶)⁸⁰⁰⁰⁰⁰⁰⁰³ ≡ 1 (mod 7).

This means that b = 1.

Now, we need to find a number that is equivalent to 1 modulo 5 and 1 modulo 7. This number is

=> 1 x 7 x 1 + 5 x 1 x 1 = 12.

Therefore,

=> 101⁴⁸⁰⁰⁰⁰⁰⁰²³ ≡ 12 (mod 35).

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Answer:

13 ig

Step-by-step explanation:

Answer:

its 13. 6 7 8 9 10 11 12 13. ............

Answer:

The equality is not true.

Step-by-step explanation:

\((4^2 +24) = |(3 - 7) - 16|\)

\((16 +24) = |(3 - 7) - 16|\)

\(40 = |(3 - 7) - 16|\)

\(40 = |(- 4) - 16|\)

\(40 = |-20|\)

\(40 = 20\)

But

\(40 \neq 20\)

Answer:

8cx - 22ac - 15bx + 45ab +18ax - 6bc.

Step-by-step explanation:

(8c-9b)(x-5a)+(3x+3c)(6a-2b)

= 8c (x-5a) -9b(x-5a) + 3x(6a-2b) + 3c(6a-2b)

= 8cx - 40ac -9bx + 45ab + 18ax - 6bx + 18ac - 6bc

Combining like terms:

=  8cx - 22ac - 15bx + 45ab +18ax - 6bc.

Answer:

8cx + 45ab + 18ax - 2bc - 15bx - 22ac

Step-by-step explanation:

The Taylor polynomials T2(x) and T3(x) for f(x) = 2sin(x) centered at a = r/2 are T2(x) = r - (x-r/2)² and T3(x) = r - (x-r/2)² + (x-r/2)³/3.

To find the Taylor polynomials T2(x) and T3(x) for f(x) = 22sin(x) centered at a = r/2, we need to find the values of the function and its derivatives at x = a and substitute them into the Taylor polynomial formulas.

First, we find the values of f(x) and its derivatives at x = a = r/2:

f(a) = 22sin(a) = 22sin(r/2)

f'(x) = 22cos(x)

f'(a) = 22cos(a) = 22cos(r/2)

f''(x) = -22sin(x)

f''(a) = -22sin(a) = -22sin(r/2)

f'''(x) = -22cos(x)

f'''(a) = -22cos(a) = -22cos(r/2)

Using these values, we can now write the Taylor polynomials:

T2(x) = f(a) + f'(a)(x-a) + f''(a)(x-a)²/2

T2(x) = 22sin(r/2) + 22cos(r/2)(x-r/2) - 22sin(r/2)(x-r/2)²/2

T2(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)²

T3(x) = T2(x) + f'''(a)(x-a)³/6

T3(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)² - 11cos(r/2)(x-r/2)³/3

Therefore, the Taylor polynomials T2(x) and T3(x) for f(x) = 22sin(x) centered at a = r/2 are:

T2(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)²

T3(x) = 22sin(r/2) + 11cos(r/2)(x-r/2) - 11sin(r/2)(x-r/2)² - 11cos(r/2)(x-r/2)³/3

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Answer:

You would find it in the 1st quadrant (top-right) on the y axis

Hope this helps

The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

Answer:

\(684\:\mathrm{cm^2}\)

Step-by-step explanation:

The area of any triangle is equal to \(A=\frac{1}{2}\cdot a\cdot b\cdot \sin C\), where \(a\) and \(b\) are two sides of a triangle and \(C\) is the angle between them.

Plugging in given values, we have:

\(A=\frac{1}{2}\cdot 27\cdot 82\cdot \sin 162^{\circ}=\boxed{684\:\mathrm{cm^2}}\)

Answer:

342

Step-by-step explanation:

see image

Answer:

y=x-2

Step-by-step explanation:

Line them up on a graph and then use each answer choice and see which matches which would be y=x-2

Answer:

Options (B), (D) and (E)

Step-by-step explanation:

In the figure attached, a triangle has been given with interior angles x, y and z and exterior angle as w.

By the exterior angle theorem,

"Exterior angle formed by extending one side of a triangle is equal to the opposite two interior angles."

Therefore, x° + y° = w°

Since measure of angle w is equal to the sum of two angles x and y,

So, w° > x°

Similarly, w° > y°

Therefore, Options (B), (D) and (E) are the correct options.

Answer:

(1, 4)

Step-by-step explanation:

im assuming that the point is h(1) = 4

this point is basically just h(x) = y

1 is your x

4 is your y

you plot it at the point (1, 4)

Based on the coupon rate on this corporate bond and the face value, the yield on the bond is 15.2%.

The number of periods is missing so we shall assume a maturity period of one year.

The rate can be found using an Excel worksheet or a financial calculator.

Using an Excel worksheet, the relevant function is the RATE function and the following details will be needed:

Nper = 1 year

Pmt = 6% x 5,000

= $300

Pv = (5,000 * 0.92)

= $4,600

Pv = -4600 because it should be negative.

Fv = $5,000

The yield you will get is 15.2% as shown in the attached image.

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Answer:

Shane=x

Abha=y

x+y>=2000

x-y=178 Which leads to x=178+y ..... #1

hence by substitution in the inequality

178+2y>=2000

2y>=2000-178

2y>=1822

y>=911 ......in #1

x>=178+911

x>=1089

Solutions x>=1089 & y>=911

The points are K(0, 6), L(-8, 0), J(9, 4).

Given that is a coordinate plane with Points K, L, J we need to determine the location of the points,

So,

You require the point's coordinates, which are made up of an x-coordinate (horizontal) and a y-coordinate (vertical), in order to label it on a coordinate plane.

So, Point K is at 6 units upwards from the origin so the point (0, 6) the x-intercept is zero.

Point L is 8 units vertically left side so the point is (-8, 0) here the y-intercept is zero.

Point J is 9 units vertically right side and 4 units upwards so the point is (9, 4).

Hence the points are K(0, 6), L(-8, 0), J(9, 4).

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The triangles that are right triangles are triangles A and E using the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse(the longest side) is equal to the sum of the squares of the other two sides. 

For triangle A:

the long side (√5)² = 5

the sum of the other sides is

(√3)² + (√2)² = 5

For triangle B:

the long side (√5)² = 5

the sum of the other sides is

(√3)² + (√4)² = 7

For triangle C:

the long side 6² = 36

the sum of the other sides is

4² + 5² = 41

For triangle D:

the long side 7² = 49

the sum of the other sides is

5² + 5² = 50

For triangle E:

the long side 10² = 100

the sum of the other sides is

8² + 6² = 100

Therefore, the triangles that are right triangles are triangles A and E using the Pythagoras rule.

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The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.

The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.

1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.

2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).

  Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.

3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.

  The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.

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Answer:

16 units²

Step-by-step explanation:

Volume:

v = s³

64 = s³

Take the cube root of both sides

4 = s

Area:

a = s²

a = 4²

a = 16 units²

Answer:

\(\huge\boxed{\bf\:1}\)

Step-by-step explanation:

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\)

Take \(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }\) & factorise it at first.

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}\)

Now factorise the next set : \(\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\).

\(\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}\)

Now, multiply the two simplified results.

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}\)

\(\rule{150pt}{2pt}\)