If y=2x-1, what is the value of x in terms of y?

A)y/2-1
B)y/2+1/2
C)y/2-1/2
D)y/2+1

Answer:

  y = 2(x +3)² -1

Step-by-step explanation:

You want the vertex form of the equation y = 2x² +12x +17.

The vertex form of the equation is ...

  y = a(x -h)² +k² . . . . . . where (h, k) is the vertex and 'a' is a scale factor

The equation can be converted to vertex form by the following steps.

The equation you want is ...

  y = 2(x +3)² -1

Answer:

Rewrite the equation in vertex form.

[tex]{y = 2(x+3)^{2}}-1[/tex]

Use the vertex from, [tex]{y = a(x-h)^{2} + k[/tex], to determine the values of [tex]{a, h, }[/tex] and [tex]k[/tex]

[tex]a = 2\\h = -3\\k = -1[/tex]

Find the vertex [tex](h, k).[/tex]

[tex](-3, -1)[/tex]

By using the division algorithm to divide 116 by 3 will be 38.

The given integers a and b are 116 and 3 respectively.

Let q be the counter variable and r be the variable to store the new dividend after each loop.

Division algorithm,

If a<b

return 0;

else

q = 0;

r = a;

repeat

q = q+1;

r = r-b;

until r<b;

return q, r;

Working:

116 is not less than 3, implies

r = 116 -3 = 113

q = 0+1=1

Repeating until we get q = 38, r = 2 = a

2<3, hence returns q = 38, r =2

The question is incomplete, the complete question is:

use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.

(a) q = 39   (b) q =32   (c) q = 38

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The n expressed in terms of r and p is n=r/p.

How to solve the word problems?

Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:

You must frequently create two distinct linear equations in two variables in order to solve these issues.

So, it is expressed as:

r=pn

n=r/p

Hence, The n expressed in terms of r and p is n=r/p.

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The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:

3.58 years.

The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.

The rates for each town are given as follows:

Considering the initial population, the exponential functions for the population of each town after t years are given as follows:

Kingsfield will have a larger population than Queensville when:

[tex]7500(1.2)^t > 32000(0.8)^t[/tex]

Hence:

[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]

(1.5)^t > 4.27

tlog(1.5) > log(4.27)

t > log(4.27)/log(1.5)

t > 3.58 years.

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The inverse of the function shown is (x + 5).

What is the inverse of the function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Coordinates of the given line are (8,3) and (-2,-7)

The function of the given graph for two points form is

[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]

or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]

or, y - 3 = x - 8

or, y = x -8 + 3 = x - 5

y = x - 5

To find the inverse, replace x with y and y with x then, we get

x = y - 5

y = x + 5

[tex]f^{-1}[/tex] = x + 5

Hence, the inverse of the function shown is (x + 5).

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Observed that 7 is a divisor of 14, 21 and 28.

So in effect:

[tex]\bold{14 = 7 * 2}[/tex]

[tex]\bold{21 = 7 * 3}[/tex]

[tex]\bold{28 = 7 * 4}[/tex]

Thus, adding member by member the previous equalities, we would have:

[tex] \bold{14 + 21 + 28 = 63 = 7 * 2 + 7 * 3 + 7 * 4}[/tex]

Taking out the common factor of 7 in the previous expression, we will have:

[tex] \bold{4 + 21 + 28 = 7 * 9}[/tex]

I mean:

[tex] \bold{14 + 21 + 28 = 7 * 9}[/tex]

That is to say, that 7 is a divisor of the sum [tex]\bold{14 + 21 + 28}[/tex] since it is contained exactly 9 times in said sum.

For the function f(x)=4x²-3x-16 then value of f(-2) is 6.

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=4x²-3x-16.

f of x equal to four times of x square minus three times of x minus sixteen.

We need to find the value of f(-2).

We need to replace the value of x with -2.

f(-2)=4(-2)²-3(-2)-16.

=4(4)+6-16

=16+6-16

=6

Hence, the value of f(-2) is 6 for the function f(x)=4x²-3x-16.

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Billy has already saved 25% of the total cost.

What is percentage?

A percentage in mathematics is a number or ratio that may be stated as a fraction of 100.In determining a percentage of a number, we should first divide it by 100 before multiply the outcome by 100. As a result, the proportion refers to a part per 100. The word "percent" refers to a fraction of one hundred. The letter "%" stands for it.

Given that, the cost of the DVD is $64.

He saved $16 for the DVD.

The percent of saving

= Saving amount/ cost of DVD × 100%

= (16/64) × 100%

= 0.25 × 100%

= 25%.

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Answer:775 cents

Step-by-step explanation:

31 * .25 = $7.75 dollars

convert to cents

100 cents per dollar

The value of number 31 quarters into cents would be, 775 cents.

Given that,

Change the number 31 quarters into cents.

Used the formula for the relation between quarters and cents, that is,

1 quarters = 25 cents

Now, change the number 31 quarters into cents as,

1 quarters = 25 cents

31 quarters = 31 × 25 cents

= 775 cents

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The value of y when X value is -1 would be = -5

The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.

From the given equation:

(x-2)²/16 - (y-4)²/9 = 1

Take X = -1 and substitute X for -1 into the given equation,

(-1-2)²/16 - (y-4)²/9 = 1

9/16 - (y-4)²/9 = 1

(y-4)²/9 = 9/16- 1

(y-4)²/9 = -7/16

Cross multiply

(y -4)² = 9(-7)/16

y²+16 = -63/16

16(y²+16) = -63

16y²+256 = -63

16y² = -319

y² = -319/16

y² = -20

y= -√20

y = -4.5

y = -5

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In linear equation, 187 tickets do they need to sell.

What is a linear equation ?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.        

                                           The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." This is the basis for its designation as a "linear equation."

The drama club wants to raise at least $1500. They have already received donations of $565 so the amount left till target is:

= 1500 - 565

= $935

Tickets are being sold at $5 so the number of tickets needed to get to $935 is

= 935/5

= 187 tickets

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The probabilities for this problem are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the commute times are given as follows:

[tex]\mu = 25, \sigma = 6.1[/tex]

The probability that the time is more than 31 minutes is one subtracted by the p-value of Z when X = 31, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (31 - 25)/6.1

Z = 0.98

Z = 0.98 has a p-value of 0.8365.

1 - 0.8365 = 0.1635 = 16.35%.

The probability that the time is less than 8 minutes is the p-value of Z when X = 8, hence:

Z = (8 - 25)/6.1

Z = -2.79

Z = -2.79 has a p-value of 0.0026.

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The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

What is an equation of a circle?

A circle can be characterized by its centre's location and its radius's length.

Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 2²

        (x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.

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a. You would expect 3.5 of those in the sample to name chocolate.

b. The probability exactly four of those in the sample name chocolate is 0.2438.

c. The probability four or more name chocolate is 0.5829..

a. If 35% of people in the general population indicate that chocolate is their favorite flavor of ice cream, then we would expect 35% × 10 = 3.5 people in a sample of 10 to name chocolate as their favorite flavor. Since we cannot have a fractional number of people, we can round this down to 3 people.

b. The probability that exactly 4 people in a sample of 10 name chocolate as their favorite flavor can be calculated using the binomial distribution. The probability of each individual event (i.e., a person naming chocolate as their favorite flavor) is 0.35, and there are 10 total events. The probability of exactly 4 successes (people naming chocolate as their favorite flavor) is given by the formula:

(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])

Where "choose" denotes the binomial coefficient, and the exponent indicates the number of times each event occurs. Plugging in the values, we get:

(210) × (0.0036125) × (0.274625) = 0.2438

So the probability that exactly 4 people in the sample name chocolate as their favorite flavor is approximately 0.2438.

c. To calculate the probability that 4 or more people in the sample name chocolate as their favorite flavor, we can use the same formula as above, but sum the probabilities for each possible number of successes greater than or equal to 4. For example, the probability of 4 successes is given by:

(10 choose 4) × ([tex]0.35^4[/tex]) × ([tex]0.65^6[/tex])

The probability of 5 successes is given by:

(10 choose 5) × ([tex]0.35^5[/tex]) × ([tex]0.65^5[/tex])

And so on. Summing the probabilities for each possible number of successes greater than or equal to 4, we get:

0.2438 + 0.1933 + 0.1047 + 0.0380 + 0.0081 = 0.5829

So the probability that 4 or more people in the sample name chocolate as their favorite flavor is approximately 0.5829.

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The final function  after the transformations are applied to the graph of y =√x is y = 2√(x - 5) +1.

What is transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Rule of transformation:

g(x) = c f(x+a) + b

If c > 1, then f(x) vertically starched by c factor. If 0< c < 1, then f(x) vertically compressed by c factor.

If a>0, then f(x) is shifted horizontally a unit right side. If a<0, then f(x) is shifted horizontally a unit left side.

If b>0, then f(x) is shifted vertically b unit upward. If a<0, then f(x) is shifted vertically b unit downward.

Putting c = 2, a = -5, b = 1, and f(x) = √x

y = 2√(x - 5) +1

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It is true, we have to find the surface area of the triangular prism we have to find  a piece of information that is missing.

In the given question we have to find the surface area of the triangular prism.

We have to follow the some step to find the surface area of the triangular prism.

Step 1: Calculate the values of b(1), b(2), and b(3), the triangle base's three sides. Additionally, calculate the values of h, the triangle base's height, and l, the prism's length (the length between the bases).

Step 2: Use the formula for calculating the area of a triangle (A=1/2bh), where b is one of b(1), b(2), or b(3), to determine the area of a triangular base (whichever one is perpendicular to h). Given that this region contains two triangle bases, multiply the result by two.

Step 3: Multiply the perimeter of a base triangle by the prism's length to find the area of its rectangular sides: A=(b(1)+b(2)+b(3))l.

Step 4: Combine the outcomes from steps 3 and 4. This is the surface area of the triangular prism.

Since the question is not clear so I have write the step to find the area of  triangular prism. Using this method we can find the area of  triangular prism.

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The number of sections that are most likely on each color on the spinner are

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

Number of times the spinner is spun = 50 times

The outcomes are

Number of sections = 10

The section of each color is then calculated as

Color = Color outcomes/Number of times * Number of sections

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

Red = 19/50 * 10 = 3.8

Green = 11/50 * 10 = 2.2

Black = 4/50 * 10 = 0.8

Orange = 16/50 * 10 = 3.2

Approximate

Red = 4

Green = 2

Black = 1

Orange = 3

The above represents the possible sections

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The equation for the line graphed in slope-intercept form is y = 2/9x + c

The equation of a line is represented as;

y = mx + c

Where;

From the graph shown, we can see that;

The intercept, c = 2

The formula for slope is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Now, substitute the values

Slope, m = 3 - 1/5 -(-4)

Subtract the numerators

Slope, m = 2/ 5 - (-4)

expand the bracket

Slope, m = 2/9

Now, substitute the values into the formula for the equation of a line, we have;

y = 2/9x + c

Hence, the equation is y = 2/9x + c

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(a) The Absolute minimum value is -3/2 and maximum value is 3.

(b) We have global minima at x = 4/9 and global minimum value at x = −4/27.

(c) Global maximum value of function is 2.72 and minimum value of function is 0.37.

a) Given function as:

f(x,y)=x2-y2-2xy-2x

The triangular region described by the vertices (1,0),(0,1) and (-1,0) can be described by the straight lines :

a) Straight line joining (1,0) and (0,1) i.e y= 1-x

b) Straight line joining (0,1) and (-1,0) i.e y= 1+x

c) Straight line joining (-1,0) and (1,0) i.e the x axis where y=0

When y=0, we have, x^2-2x

Now, df/dx=0 for maxima / minima

2x-2=0

X=1

Also, d^(2)f/dx^(2)=2>0 and df/dx<0 for x<1

So, we have minimum value = 12−2×1=−1

and maximum value = (−1)2−2×−1=3

When y=1+x, we have ,

f(x,y)=x^2−(1+x)^2−2x(1+x)−2x

df/dx=2x−2(1+x)−2x−2(1+x)−2

=−6−4x<0, for  x>−3/2

Hence f(x,y) is always decreasing function in the interval x=[-1,0] , with minimum

=f(0,1)

=02−12−2×0×1−2×0

=−1

Maximum value = f(-1,0)

=(−1)2−02−2×−1×0−2×−1

=1−0+2

=3

When y= 1-x, we have,

f(x,y)=x^2−(1−x)^2−2x(1−x)−2x

df/dx=2x+2(1−x)+2x−2(1−x)−2

=4x−2>0,for x>1/2

Hence at x=1/2,we have df/dx=0 which is global minima point since

d2(f)/dx2=4>0

So, minimum value for y = 1- x

=f(1/2,1/2)

=1/22−1/22−2×1/2×1/2−2×1/2

=−1/2−1=−3/2

Maximum value in the interval [ 0 1] shall be

=max(f(0,1).f(1,0))

=max(−1,−1)=−1

So, considering all points on this triangle , we have absolute maximum

= max(f(x,y) for y=0, f(x,y) for y=1+x, f(x,y) for y=1-x)

=max(3,3,−1)

=3

Absolute minimum considering all points on the triangle

= min(f(x,y) for y=0, f(x,y) for y=1+x, f(x,y) for y=1-x)

=min(−1,−1,−1.5)

=−3/2

b) Given g(x,y)=x+xy−2y2

When y=x0.5, we have,

g(x,y)=x+x^1.5−2x

=x^1.5−x

For the domain x = [0 , 1], we have ,

dg/dx=1.5×x^0.5−1=0

x=4/9

d^2(g)/d^x2=0.75x0.5>0 for x=4/9

Hence, we have global minima at x = 4/9 and global minimum value

=(4/9)1.5−49

=8/27−4/9

=−4/27

Global maximum = max(g(0,0),g(1,1))

=max(0,0)

=0

c) Given h(x,y)=exp⁡(xy)

When (x/2)^{2}+y^{2}=1, we have

y=(1−x^{2}/4)^0.5

So, h(x,y) = [tex]\text{exp}\left(x(1-\frac{x^{2}}{4})^{0.5}\right)[/tex]

Now,dh/dx=[tex]\text{exp}\left(x(1-\frac{x^{2}}{4})^{0.5}\right) \times ((1-\frac{x^2}{4})^{0.5}+0.5x\times\frac{-x/2}{(1-x^2/4)^{0.5}}[/tex]

For maxima / minima , we mush have ,

dh/dx=0

[tex](1-\frac{x^2}{4})^{0.5}+0.5x\times\frac{-x/2}{(1-x^2/4)^{0.5}}[/tex]5=0

[tex](1-x^2/4)^{0.5}-0.25 \frac{x^2}{(1-x^2/4)^{0.5}}[/tex]=0

[tex]1-x^2/4-0.25x^2[/tex]=0

1−x^2/2=0

x = 1.41,−1.41

In the range [-1.41,1.41], we always have dh/dx>0

At x=20.5and x=−20.5, we have

y=(1−x2/4) 0.5

=(1−24)0.5

=120.5,−120.5

Global maximum value of function

=f(20.5,1/20.5)

=exp(1)

=2.72

Global minimum value of function

=f(20.5,−1/20.5)

=exp(−1)

=(0.37)

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Answer:

Read explanation :)

Step-by-step explanation:

Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.

Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.

Your Welcome Hope This Helps You.

Answer:

yeah what is the question or awnser

Step-by-step explanation:

The given p-series 1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent as the value of is equal to 3/4 ⇒p < 1.

As given in the question,

Given p-series is equal to :

1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

As value of 1³ = 1 and fourth root of 1³ is equal to 1.

We can substitute 1 = (1 /fourth root of 1³) which is equal to

= (1/ [tex]\sqrt[4]{1^{3} }[/tex] ) + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex])

Apply nth formula we get,

= [tex]\sum\limits^\infty_0 {\frac{1}{\sqrt[4]{n^{3} } } }[/tex]

⇒ p = 3/4

And 3/4 < 1

⇒ p < 1

⇒P-series is divergent.

Therefore, as the value of p =3/4<1 the given series  1 + (1/[tex]\sqrt[4]{2^{3} }[/tex]) + (1/[tex]\sqrt[4]{3^{3} }[/tex]) + (1/ [tex]\sqrt[4]{4^{3} }[/tex])+ (1/ [tex]\sqrt[4]{5^{3} }[/tex]) is divergent.

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Answer:

5[tex]\sqrt{3}[/tex]i

Step-by-step explanation:

[tex]\sqrt{-5(5)(3)}[/tex]  You can pull out a 5 and you are left with [tex]\sqrt{-1}[/tex] and [tex]\sqrt{3}[/tex].

The [tex]\sqrt{-1}[/tex] = 1

5[tex]\sqrt{3}[/tex] i

Answer: [tex]5\sqrt{3} i[/tex]

Step-by-step explanation:

The square root of -75 is not a real number, because it is not possible to find a real number that when squared results in a negative number.

In mathematics, the square root of a number is defined as the number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. Similarly, the square root of 9 is 3, because 3 x 3 = 9.

However, it is not possible to find a real number that, when squared, results in a negative number. This is because any real number multiplied by itself is always positive, regardless of whether the original number was positive or negative. For example, the square of -2 is 4, because    (-2) × (-2) = 4, which is a positive number.

Double however, complex numbers are used to represent numbers that have a non-zero imaginary component, such as the square root of -1. Complex numbers are written in the form a + bi, where a and b are real numbers and i represents the imaginary unit.

Therefore, the square root of -75 can be written in simplified form as  [tex]5\sqrt{3} i[/tex], where [tex]i[/tex] is the imaginary unit. This represents a complex number with a real component of 0 and an imaginary component of [tex]5\sqrt{3}[/tex].

The null hypothesis cannot be rejected.

Given that,

A study is done to determine the average cost difference between utilizing two different statistical tools to analyze data. 15 data sets are used to do this. Each program performs an analysis on each, and the cost of the analysis is noted.

To test if cost is same, we test mean difference of scores =0

H0: d=0

H0: d != 0

z0 = 0-(-05467) / 0.039976

= 1.367

z score for alpha = .05 is 1.96

Since, z0 < z score, we cannot reject the null hypotheses

Therefore, the null hypothesis cannot be rejected.

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Survey research method is used to  do researchers use to systematically collect data from respondents through questionnaires or interviews.

It can be used for descriptive, exploratory, or explanatory research. This method is best suited for studies that have individual people as the unit of analysis. Although other units of analysis, such as groups, organizations or dyads, are also studied using surveys, such studies often use a specific person from each unit as a “key informant” or a “proxy” for that unit, and such surveys may be subject to respondent bias if the informant chosen does not have adequate knowledge or has a biased opinion about the phenomenon of interest. For instance, Chief Executive Officers may not adequately know employee’s perceptions or teamwork in their own companies, and may therefore be the wrong informant for studies of team dynamics or employee self-esteem.

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The probability that the mean height x is between 68 and 70 inches is found as 37.28%.

The z-score is written as follows:

z = (x - μ)/σ

In which,

x =  between 68 and 70 inches.

μ = mean 69 inches

σ = standard deviation 6 inches

Put the values in the formula,

Probability that the mean height x is between 68 and 70 inches

P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)

P(68 < x < 70) = (-0.16) < z < (0.16)

P(68 < x < 70) = 0.4364 - 0.0636

P(68 < x < 70) = 0.3728

P(68 < x < 70) = 37.28%

Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.

To know more about the z score, here

https://brainly.com/question/15333077

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