a large company states in its promotional literature that 74% of its employees have college degrees. assume this claim is true. if 3 employees are selected at random from this company, what is the probability that at least 1 of the selected employees will not have a college degree?

The first statement is false and the second statement is true.

Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen. There are two types of random variables.

A random variable that takes a finite number of possible values can be defined as a Discrete random variable. A random variable that takes an infinite number of possible values can be defined as a Continuous random variable. A continuous random variable consists of only continuous values.

Continuous random variables are defined at intervals of values. Continuous random variables are represented by the area under a curve.

⇒  The number of cars that go through the drive-in window at a local bank each hour.

The number of cars can be counted and can be an integer like 10, 20,100 etc.

∵ The number of cars is countable it is not an example of a continuous random variable        

⇒ The high daily temperature in Anchorage.

High daily temperature can be an integer or function like 60°, 120° etc

∵ The high daily temperature is an example of a continuous random variable.

Therefore, The number of cars that go through the drive-in window at a local bank each hour is not an example of a continuous random variable and The high daily temperature in Anchorage is an example of a continuous random variable.

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The complete question is

Using the relationship of permutation and combination, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.

What is Permutation?

The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.

What is Combination?

Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situations. The combination is the taking together of n items, k at a time, without repetition. The words k-selection or k-combination with repetition are frequently used to describe combinations when repetition is permitted.

In the given question:

To proof:

[tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex].

Let's Proof the relation:

Using the basic relation of permutation and combination, we have;

[tex]$\begin{aligned}(n-r+1){ }^n P_{r-1} &=(n-r+1) \frac{n !}{(n-r+1) !} \\ &=(n-r+1) \frac{n !}{(n-r+1)(n-r) !} \\ &=\frac{n !}{(n-r) !}={ }^n P_r \end{aligned}$[/tex]

Hence, Proved.

Therefore, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.

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The use of prime factorization to find the exponents of the given numbers gives  625 = 5⁴, 343 = 7³, 216 = 6³,  169 = 13², 256 = 4⁴; 256 =  2⁸ and 729 = 9³; 729 = 3⁶

When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2

An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴

Thus, you can use prime factorization to find the exponent of the given numbers as follows:

625 as a power of 5

625 = 5×5×5×5 = 5⁴

343 as a power of 7

343 = 7×7×7 = 7³

216 as a power of 6

216 =  6×6×6 = 6³

169 as a power of 13

169 = 13×13 = 13²

256 as a power of 4; as a power of 2

256 = 4×4×4×4 = 4⁴

256 = 2×2×2×2× 2×2×2×2 = 2⁸

729 as a power of 9; as a power of 3

729 = 9×9×9 = 9³

729 = 3×3×3×3×3×3 = 3⁶

Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and  729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively

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Based on the information, the person traveled 117.8 feet by the Ferris wheel.

Circumference = π×diameter

Keep the values in formula and perform multiplication to find the circumference of the wheel

Circumference = 50π

On 1 complete revolution of 360 degrees, the distance covered = 50π

So, revolution of 270 degrees, the distance covered will be = (50π/360) × 270

Performing multiplication and division on Right Hand Side of the equation

The distance traveled = 117.8 feet

Hence, the person travelled 117.8 feet.

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Answer:

4 students for newspapers & 3 students for magazines are needed for the deliveries to be made in a day.

Step-by-step explanation:

According to the question,

So, In 8 hours each student can deliver:

35 × 8 = 280 newspapers

50 × 8 = 400 magazines

To find out minimum number of students needed to work we need to divide work done by each student in 8 hours by total deliveries to be made.

[tex] \therefore[/tex]

For Newspapers:

875/280 = 3.125

So, by rounding of the figure we will need 4 students to deliver newspapers as each student can work only for 8 hours.

For magazines:

1200/400 = 3

3 students are needed to deliver magazines.

The UCLR (Upper Control Limit) and LCLR(Lower Control Limit) are 2.22 and 0 respectively.

Given that,

At five soups that were chosen at random, average temperatures were recorded. X-bar and r-bar positions were 45.25 degree and 1.05 degree, respectively.

To find : UCLR (Upper Control Limit) and LCLR (Lower Control Limit)

R-bar = 1.05 Degrees

X-bar = 45.25 Degrees

Sample Size , n=5

D3=0

D4=2.114

3 Sigma control limits of Range Chart

LCLR = D3*R-bar = 0*1.05 =0

UCLR =D4*R-bar = 2.114*1.05 = 2.22

The UCLR (Upper Control Limit) and LCLR (Lower Control Limit) are therefore 2.22 and 0, respectively.

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After using proportion method 325 calories will she get if she drinks the larger 20 oz. size.

What is proportion?

 Ratio and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers. The ratio and proportion are important building blocks for understanding the numerous ideas in science and mathematics. Numerous challenges in daily life can be solved with proportion, including those in business when handling transactions or in the kitchen, among other situations. It creates a relationship between two or more quantities and aids in comparing them.

Here 16 oz medium size has 260 calories.

Then

=> [tex]\frac{size of coffee}{ calories}[/tex]

=>[tex]\frac{16}{260}=\frac{20}{x}[/tex]

=>x=[tex]\frac{20*260}{16}[/tex]

=> x = 325

Hence 325 calories will she get if she drinks the larger 20 oz. size.

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1. No This survey does not mean that cell phones are good for your health.

2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.

When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.

A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.

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complete question

A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.

a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no

b. What might best explain the strong correlation (as a lurking variable)?

Select one:

_____ Percent of young people

____ General economic conditions of the country

____ Percent of pop. living in cities

Answer:

-24

Step-by-step explanation:

b²-2ac

⇒Plug in the values given in places and simplify.

[tex]=(-4)^{2} -2(-4)(-5)\\=16-2(20)\\=16-40\\=-24[/tex]

-24 is the answer after substitution of the known values.

Answer:

  see the attachment

Step-by-step explanation:

You want a graph of the given figure reflected over the line y = 1/3x +1.

The given line of reflection can be written in general form as ...

  y = 1/3x +1

  3y = x +3 . . . . . . multiply by 3

  x -3y +3 = 0 . . . . subtract 3y

This is in the general form ...

  ax +by +c = 0

where a=1, b=-3, c=3.

The line of reflection is the perpendicular bisector of the segment joining a point (x, y) with its reflection (x', y').

Using the formula in the second attachment, we find the reflection

  (x1, y1) ⇒ (x, y)

satisfies ...

  (x -x1)/a = (y -y1)/b = -2(ax1 +by1 +c)/(a² +b²)

or ...

  x = -2a/(a²+b²)·(ax1 +by1 +c) +x1

  y = -2b/(a²+b²)·(ax1 +by1 +c) +y1

Using the known values for a, b, c, we have ...

  x = -2(1)/(1² +(-3)²)·(x1 -3y1 +3) +x1 = (1/5)(4x1 +3y1  -3)

  y = -2(-3)/10·(x1 -3y1 +3) +y1 = (1/5)(3x1 -4y1 +9)

Rewriting the mapping in more conventional terms, we have ...

  (x, y) ⇒ ((4x +3y -3)/5, (3x -4y +9)/5)

It is convenient to let a spreadsheet do the repetitive tedious math. The third attachment shows the application of this mapping to the coordinates of the figure's vertices (clockwise from bottom).

__

Additional comment

The figure showing the reflected polygon was created by a geometry program using its "reflect over a line" feature.

The equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9

The first point = (-7, -5)

The second point = (2, 3)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line m = (3- (-5) / (2 - (-7))

= (3 + 5) / (2 + 7)

= 8 / 9

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

The point = (2,3)

Substitute the values in the equation

y - 3  = (8/9)(x - 2)

y - 3 = (8/9)x - 16/9

y = (8/9)x - 16/9 + 3

y = (8/9)x - 11/9

Hence, the equation of the line that passes through the points (-7,-5) and (2, 3) is y = (8/9)x - 11/9

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Triangle AEM is congruent to triangle DEN by SAS congruence criterion.

What do you mean by congruence of triangle?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. The sign of congruence is’ ≅’. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle.

In triangle AEM and triangle DEN

AE = DE (Given)

ME = NE (As In triangle MEN , angle M = angle N and sides opposite to equal angles are equal)

angle MEA = angle NED (Vertically opposite angles)

Triangle AEM ≅ Triangle DEN (By SAS congruence criterion)

Therefore, both the trinagles are congruent by SAS congruence criterion.

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The point that preserves the function is (0, 9), so the correct option is D.

A function is a relationship that maps elements from a set (domain) into another set (range).

Such that each element in the domain is mapped into only one element of the range.

In the graph of the function we can see the points:

(-7, 4)

(-3, -3)

(2, 9)

(3, -8)

(5, 7)

(9, 3)

So the inputs {-7, -3, 2, 3, 5, 9} are already used and we can't use them anymore, the correct option then is:

D (0, 9)

Which has the only input that is not already graphed on the function's graph.

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A) 1,100 hours is equal to approximately 104days in Saturn.

B) You need to know how hours make 1day in Saturn. i.e 10 hours 34minutes or 10.567hours.

From the question note that the number of hours in one day is different for each planet.

Hence for Saturn;

1 day =  10hours.34minutes

X day   =1,100 hours

Note; 34 minutes in hours will be:

60 minutes  =1hour

34/60      =0.567hour

Thus;

10hours.34minutes   =   10hours +0.567hour

                                   =10.567hours

To find the number of days in 1,100 hours, we cross multiply;

X day  * 10.567hours =1,100 hours * 1 day

       X day  =     1,100 hours * 1 day

                               10.567hours

       X day    =104.1  ≈ 104 days

Therefore, you need to know the number of hours that makes a day in Saturn.i.e 10 hours 34minutes or 10.567hours.

.  Again, 1,100 hours is equal to approximately 104days in Saturn.

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The  line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.

The equation of a line can be described as follows:

y = mx + b

where

Therefore, the line passes through  (7, –2) and (8, q) with a slope of - 5.

Hence, let's find q.

y = - 5x + b

Let's find y-intercept

-2 = -5(7) + b

b = -2  + 35

b = 33

Therefore,

y = -5x + 33

Hence, let's find q.

y = -5(8) + 33

q = -40 + 33

q = -7

Therefore, q = - 7

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The value of x and y is 7 and -2 respectively.

The equations to solve are -

On adding equations 1 and 2 we get ,

3y = -6

y = -2

Putting the value of y in equation 1,

⇒ x - 2(-2) = 11

⇒ x + 4 = 11

⇒ x = 7

Hence ,the value of x and y is 7 and -2 respectively.

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Answer:

Step-by-step explanation:

f(x)=5x2+xf(x)=5x2+xWrite f(x)=5x2+xf(x)=5x2+x as an equation.y=5x2+xy=5x2+xInterchange the variables.x=5y2+yx=5y2+ySolve for yy.Tap for more steps...y=−1−√1+20x10y=-1-1+20x10y=−1+√20x+110y=-1+20x+110Replace yy with f−1(x)f-1(x) to show the final answer.f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110Verify if f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110 is the inverse of f(x)=5x2+xf(x)=5x2+x.Tap for more steps...f−1(x)=−1−√1+20x10,−1+√20x+110f-1(x)=-1-1+20x10,-1+20x+110

Answer:

Bag a, by 85 grams!

Step-by-step explanation:

1) Work out the weight of bag a

1 banana is 140 grams so to find out 8 you have to multiply them

140 x 8 = 1120

Bag a = 1120 grams

2) Work out the weight of bag b

1 pineapple weight 345 grams so to find out 3 you have to multiply them just like above

345 x 3 = 1035

Bag b = 1035

3) Find the difference

Bag a is 1120 grams and bag b is 1035

To find out out by how much you just have to subtract them

1120 - 1035 = 85

Hope this helps, have a great day!

Answer: y=3x-5

Step-by-step explanation:

This was the answer i got after solving

Hope that helped :)

Screenshot is the proof of the answer btw :)

Check the picture below.

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]

let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.

The equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936

A circle is a form made up of all points on a plane that are at the same distance from the center. In other words, it is the curve that a moving point in a plane creates to keep its distance from a specific point constant. The radius is the separation between any point on a circle and its center. The radius must typically be a positive integer. Degenerate cases include circles with displaystyle r=0 and r=0. Unless otherwise stated, this article discusses circles in Euclidean geometry, specifically the Euclidean plane.

A circle is a straight forward closed curve that splits the plane into its inner and outside. In regular use, the

The equation of a circle is given as,

(x-a)²+(y-b)=r²

Here, the center of the circle is (a ,b) and r is the radius of the circle

The circle's center can be located first. The middle point of the line segment serves as the center of the circle since the two locations from the issue are the endpoints of a diameter.

Given two end points, how do you calculate a line's midpoint? You may use the formula below.

M=((x1+x2)/2, (y1+y2)/2)

Here, M denotes the mid-point

The points are taken as (x1, y1), (x2, y2)

M=((17-13)/2, (-3+3)/2)

M=(2,0)

Now, the center of the circle is (2,0)

We have to calculate the distance

d= √(x₁-x₂)²+(y₁-y₂)²

d= √(17+13)²+(-3-3)²

d=√900+36

d=√936

Therefore, the radius of the circle is √936

Now, the equation of the circle is,

(x-2)²+(y-0)²= (√936)²

(x-2)²+y²=936

Therefore, the equation of the circle with diameter endpoints of (17, -3) and(-13,3) is (x-2)²+y²=936

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Answer:

3/4,. it's means for every 4 games there's a $3 fee

Step-by-step explanation:

3/4

it's means for every 4 games there's a $3 fee

Answer:

5.68 ft

Step-by-step explanation:

12 inches = 1 feet

[tex]68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet[/tex]

Answer:

P(x) = (x - 3)(x + 3)(x + 2)(x - 1)

Answer:

Step-by-step explanation:

Solution:To write a polynomial in standard form, simplify and then arrange the terms in descending order.Expand ( x2 − 9 )( x + 2 ) using the FOIL Method.Simplify each term.

Answer:

0

Step-by-step explanation:

[tex]m=\frac{-21-(-21)}{-14-36}[/tex]

Answer: slope = 0  

Step-by-step explanation:

slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0

It's a horizontal line

Answer: D

Step-by-step explanation: Took the test

Answer:

C

Step-by-step explanation:

If you look at a number line, you can see that numbers with greater values are to the right of numbers with smaller values.

-8 is to the left of -7 on a number line so it is not greater

9 is to the right of 3 on a number line so it is not smaller

0 is to the right of -3 on a number line so it is greater

And lastly, 0 is to the left of 4 on a number line so it is not greater

Answer:

the shorter leg = 9mm

the longer leg = 12mm

the hypotenuse is 15mm

Step-by-step explanation:

x^2 +(x+3)^2 =(x+6)^2

x^2 + x^2 + 6x +9=x^2 + 12x +36

x^2-6x-27=0

(x+3)(3-9)=0

x=-3 (impossible) ... or x=9

The margin of error with 80% confidence interval is 2.099

Given that,

A straightforward random sample of 25 observations is taken from a population that is normally distributed and has a standard deviation of 8.2.

To find : The margin of error with 80% confidence

Margin of Error : The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

Here we have

n=25,σ=8.2

For 80% confidence interval, the critical value of z is 1.28. So requried margin of error is

ME=[tex]Z_{c}\cdot \frac{\sigma}{\sqrt{n}}[/tex]=1.28[tex]\cdot \frac{8.2}{\sqrt{25}}[/tex]=2.0992

Thus, with 80% confidence, the error margin is 2.099.

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