Find and interpret the z-score for the data value given.
The value 86 in a dataset with mean 101 and standard deviation 19
Round your answer to two decimal places.
The value is i 5.3
standard deviations
below
the mean.

Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

[tex]\frac{14}{2}[/tex] [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

Given:

0.145t² + 0.019t + 5.5 = 0

Using almighty formula or quadratic formula

t=-b±√b²-4ac/2a

Where:

b²=19²

a=145

c=5500

Let plug in the formula

t=-19±√19²- 4(-145) (5500)/2(-145)

t=-19±√361+(3,190,000)/-290

t=-19±√3,190,361/-290

t=-19±1,786.158/-290

Hence,

-19-1,786.158/-290; -19+1,786.158/-290

t=6.2; 6.09

Therefore If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

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Main Answer:

The required value of PB is 21.

An equation is a mathematical statement with an equal symbol between two expressions that have equal values.

Given: If A-P-B and if AP=2x-9, AB=32, and PB=1.5x+6.

To find: Find PB.

According to the question,

AP + PB = AB

On putting the given values, we get,

(2x-9)+(1.5x+6) = 32

2x - 9 +1.5x + 6 = 32

3.5x - 3 = 32

3.5x = 32+3

3.5x= 35

x=10

Now, we will substitute the value of x=10 in the equation, we get,

PB= 1.5x+6

PB= 1.5 × 10 + 6

PB=15 + 6

PB=21

Final Answer:

The simplified value of PB = 1.5x + 6 is 21.

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45 because it's 45 and I'm smart with a PhD in maths

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Then the expression will be given as

⇒ 470(32 - n)

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

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The number of lines located on plane A using the given diagram are 4.

As given in the question,

Number of lines located on plane A are as follow:

Point outside the plane A are T, W, S

Points located on plane A are as follow:

V, M, N, P

Lines formed by located points V, M, N, P on plane A

VM, VN, VP and MP

Therefore, number of lines located on plane A using the given diagram are 4.

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The value of x so that the equation based on a and b has a solution is x = -7/5

  An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

  Equations can be graphed, they are used to model many problems and theories.

     As we can see, we have the following equation:

(a + 2)b + 13 = 5x

  and we have the values of the coefficients a and b, and these are:

   We substitute these values in the equation:

(a + 2)b + 13 = 5x

(18 + 2)-1 + 13 = 5x We solve the equation

(20)-1 +13 = 5x

-20 + 13 = 5x

5x = -7

x = -7/5

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Answer:

last one is the correct one

Mark please

Add or subtract.Simplify where possible.

[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6}[/tex] =  [tex]\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]

How the given expression is simplified?

[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6} \\\\\text{On taking LCM of the denominator}\\\\\frac{4}{x^{2}-36} +\frac{x^{2}+6x }{x^{2}-36}\\\\\frac{4+x^{2}+6x}{x^{2}-36}\\\\\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]

What is simplification?

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Answer:

Step-by-step explanation:

A. The common factor of the expression is 5[tex]x^{3}[/tex]y

B. In order to find a common factor, you find the prime factor. In this case, the biggest number that goes evenly into 40 and 25 is 5.

C. Divide the original problem by the common factor  5[tex]x^{3}[/tex]y

that gives you  5[tex]x^{3}[/tex]y(8x[tex]y^{2}[/tex]-5)

Hope this helps!

When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. The height of Kara's building is 186.6 ft.

In math, height can be defined as the vertical distance from the top to the base of the object. Height is the distance between an object's highest and lowest points.

The measurement of an object's height from the base to the top is known as the height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Mount Everest's summit serves as an illustration of height.

Ignoring the height of Kara,

h = 50 tan 75°

substituting the value of tan 75°, we get

= 50 × 3.7321

Height of building = 186.6 ft.

Therefore, the approximate height of Kara's building is 186.6 ft.

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Answer:

6?

Step-by-step explanation:

24=10x-6x

24=4x

6=x

Step-by-step explanation:

Given that

To find

So, according to the question

we have,

         (0,40) and (15,70)

We have to find the equation of line

So, we know that

               y = mx + c, ---------------(1)

From graph,

           c = 40 and

           m = slope (we have to find it)

We kwon the slope of any two point

      m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

        x₁ = 0 , and y₁ = 40

        x₂ = 0 , and y₂ = 40        

So,

      m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

      m = [tex]\frac{70-40}{15-0}[/tex]

      m = [tex]\frac{30}{15}[/tex]

      m = 2

Now putting the all values in equation (1)

We will get,

               y = mx + c, ---------------(1)

               y = 2x + 40

Answer:

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If the tire says P235/65R17, the diameter of your wheel will be 17 inches.

The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.

It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.

It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.

In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.

In conclusion, it is 17 inches.

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Answer: 1 ) other angle = 32.0°

2 ) A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Step-by-step explanation for first picture:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

x + 58° = 90°

x = 90° - 58°

x = 32.0°

Step-by-step explanation for second picture:

( number on x line, number on y line )

A = ( 2, -2 )

B = ( -2, 5 )

C = ( -4, 2 )

reflection

A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Answer : second option

Answer:

C,D, and E

Step-by-step explanation:

-29/4 is an improper fraction version of -7 1/4

-7- 1/4 = -7 1/4

-(7 + 1/4) is -29/4

Just make -29/4 into a mixed number, which is -7 1/4

Answer:

Step-by-step explanation: the answer is the last 3 ones because if you add them together, you get -7 1/4.  Remember that -(number) = -1(number). So, -(1) = -1(1).

The number 6 comma 107 comma 200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex].

Scientific notation is used to represent a very large number or a very small number in Simple way.

Steps to find scientific Notation of a number

Step (i) Move the decimal point until a number between 1 and 10 is created.

Step (ii) Count the number of times the decimal is moved .

Step (iii) If the decimal is moved n times then multiply the term by n times of 10.

In the given question

the number 6107200.

Step (i) We will move the decimal 6 place towards left.

number becomes 6.107200

Step (ii) The decimal is moved 6 place towards left.

Step (iii) we will multiply by [tex]10^{6}[/tex].

[tex]=6.1072*1000000[/tex]

So , the number becomes [tex]6.1072*10^{6}[/tex]

Therefore , the number 6107200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex]

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Angle 213.7°  the bearing of D from towns  A, B, C and D .

What is an angle in math?

The bearing of B from D is angle ADB, which is

∠ADB = arctan(30/45) ≈ 33.7°

The bearing of D from B is that angle plus 180°, so is

180° +33.7° = 213.7°

We use angle ADB because the reference direction for bearings is North.

The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).

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In the given sequence, the next term is obtained by multiplying the next term by (-1), hence it is a geometric sequence with r = 1. The next two terms are 3, -3.

Arithmetic sequence.

In a arithmetic sequence, the next term = the previous term + common difference. Or mathematically:

a(n) = a(n-1) + d

or d = a(n) - a(n-1) for all n

Where d = common difference.

Geometric sequence.

In a geometric sequence,  the next term = the previous term x common ratio. Or mathematically:

a(n) = a(n-1) . r

or r = a(n)/a(n-1) for all n

Where r = common ratio

The sequence given:

           3,-3,3,-3, . . . . .

In this sequence:

a(1) = 3

a(2) = -3

a(3) = 3

a(4) = -3

The next two terms means a(5) and a(6). We already have a(4) = -3. Hence,

a(5) = a(4) . r = -3. (-1) = 3

a(6) = a(5) . r = 3. (-1) = -3

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Answer:

I would say y=3x+6

Step-by-step explanation:

The inequality that can be used to determine the maximum number of outfit she can purchase is 55.17oo  ≤ 117.47.

The first step is to determine which inequality sign would be used.

The following are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The sign that would be used is the less than or equal to sign- ≤  . This is because Audrey cannot spend more than her budget.

The next step is to determine the total cost of items bought:

Total cost = $295.33 + (17.86 x 3) + 33.62 = $382.53

Now determine the amount of money she has left : $500 -  $382.53 = $117.47

(Total amount spent on outfit) amount left

(oo x $55.17)  ≤ 117.47

55.17oo  ≤ 117.47

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Answer:

$6.95

Step-by-step explanation:

Kole: $ 6.50

His sister : $6.50+$0.40

= $6.90

Half of his sister: $6.90/2 =$3.45

$10-($6.50 +$3.45)

=$10-$3.05

=$6.95

The geometric mean between pair of numbers 4√3 and 10√3 is 10.95

We know that for a sequence of numbers x1, x2, . . . , xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 4√3 and 10√3

We need to find the geometric mean between pair of numbers, 4√3 and 10√3.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{4\sqrt{3}\times 10\sqrt{3} } \\\\\Pi=\sqrt{4\times 10 \times \sqrt{3}\times \sqrt{3} } \\\\\Pi=\sqrt{40 \times 3 } \\\\\Pi=\sqrt{120}\\\\ \Pi=2\sqrt{30}\\\\\Pi=10.95[/tex]

Therefore, the geometric mean between pair of numbers 4√3 and 10√3 is 10.95

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This sequence follows the rules of Arithmetic Progression

Arithmetic Progression is an example of mathematical sequences. In this sequence, the next term is generated by adding the previous term to a fixed number which is called 'Common Difference'. This is generally represented by 'd'. It is calculated by subtracting any two consecutive terms in the sequence.

We can generally find out any term of the given statement. The  [tex]n^{th}[/tex] term of a sequence is calculated by adding the previous term to the common difference. The formula to calculate the [tex]n^{th}[/tex] term of an Arithmetic Progression is :

                     =>  [tex]a_{n} = a_{n-1} + d[/tex]

Here, n = No. of term, [tex]a_{n-1}[/tex] = previous term, and d = common difference

In the given sequence, 5,22,39,56......

Each term is separated by a common difference 'd'

Calculating d = a2-a1   => d = 22-5 => d = 17

Every term has a common difference of 17 so this is an Arithmetic Sequence

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