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Part 1
Arrivals to a bank automated teller machine​ (ATM) are distributed according to a Poisson distribution with a mean equal to per minutes. Complete parts a and b below.

Answer:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.

Substitute the center and radius into the formula to create an equation of the circle:

[tex]\implies (x+8)^2+(y-4)^2=25[/tex]

The y-value of any point on the x-axis is zero.

Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:

[tex]\implies (x+8)^2+(0-4)^2=25[/tex]

[tex]\implies (x+8)^2+(-4)^2=25[/tex]

[tex]\implies (x+8)^2+16=25[/tex]

[tex]\implies (x+8)^2+16-16=25-16[/tex]

[tex]\implies (x+8)^2=9[/tex]

[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]

[tex]\implies x+8=\pm3[/tex]

[tex]\implies x+8-8=\pm3-8[/tex]

[tex]\implies x=-8\pm3[/tex]

[tex]\implies x=-11, x=-5[/tex]

Therefore:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

The fraction of person that represents a degree is 1/4

A Π chart is a type of representation used in showing data representing the parts sometimes in degrees.

Π charts are made in circle and use the features of circle

Considering the problem at hand, the total number of workers in the office is 90

The total angle of a circle is 360

if 90 person is equivalent to 360 then one person would be

1 person = 360 / 90

1 person = 4 degrees

therefore 1 degree will be 1/4 person

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The value of sin(x/2)= √(1-√11/6)/2

The value of cos(x/2)=√(1+√11/6)/2

The value of tan(x/2) = 5/6/(√(1+√11/6)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.

In trigonometry, sin( x/2)= √(1-cosx)/2

cos( x/2)= √(1+cosx)/2

tan( x/2)=sinx/1+cosx

if sin (x) = 5/6

this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is

a= √(6^2-5^2)

a= √36-25

a= √11

therefore if cos x= √11/6

sin(x/2)= √(1-√11/6)/2

cos(x/2)= √(1+√11/6)/2

tan(x/2)=5/6/(√(1+√11/6)

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The pairs of numbers given, (1, 2) is not a solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y= 2x+1 /3

Now, First value of x = 0

y= 2(0)+1 /3

y= 1/3

i.e., (0, 1/3)

and, Second value of x = 1

y= 2(1)+1 /3

y= 5/3

i.e., (1, 5/3)

and, Third value of x = 4

y= 2(4)+1 /3

y= 9/3

y=3

i.e., (4, 3)

Hence, from the pairs of numbers given, (1, 2) is not a solution.

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In the given equation we get the following values:

M = 2

C = 5

Given, we have the equation:

Y = 2x + 5

we are asked to determine the following values of m and c.

The given equation is in the form of slope intercept form.

slope intercept form is given as:

y = mx+c

hence :

M = 2 and

C = 5

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. This relationship will be the equation of a straight line:

hence we get the required values.

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Answer:

AAS

Step-by-step explanation:

let us say that angleDAB is 60 then angleADB is 30

due to the presence of line DB we can also say that angleDCB is 60 and angle CBD is 30

Step-by-step explanation:

okok

Answer:

Below

Step-by-step explanation:

4  3/10   * 3 =   43/10 * 3 = 129 / 10 =  12 9/10 miles

When talking about a number line, the farther right the digit moves, the large the number. The farther left it goes, the smaller the number.

For example, 81 would be to the right of 80. And 79 would be on the left. The larger the negative number, the smaller it is. So -70 is smaller than -20.

I hope this helps!

Answer:

162

Step-by-step explanation:

12²+6² ÷ 2

= 144 + 36 ÷ 2

= 144 + 18

= 162

The value of tan 30° after using trigonometric ratio  is  [tex]\frac{1}{\sqrt{3} }[/tex] .

What is trigonometric ratio?

 There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan30°

Now ,Tan 30 degrees in radians is written as

=>tan (30° × π/180°)

=> [tex]\frac{1}{\sqrt{3} }[/tex]

Therefore the value of tan30° is  [tex]\frac{1}{\sqrt{3} }[/tex] .

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Answer: The answer to this question would be: 5 days

In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.

From the description, you can get an equation of each price which would look like this(x=number of day rent):

cost1= 110 + 46x

cost2= 70 + 54x

Then, the days when the price same would be:

cost1 = cost2

110 + 46x= 70+54x

110-70= 54x - 46x

40= 8x

x=5

Step-by-step explanation:

Answer:

Step-by-step explanation:

a.

f(d)=11(1.01^d

d=6.97 days

b.

t

f(c) represents the size of algae after c days

c.

f(2)=11(1.01)^2

f(7)=11(1.01)^7

[tex]rate=\frac{f(7)-f(2)}{7-2} \\=\frac{11(1.01)^7-11(1.01)^2}{5} \\=\frac{11[(1.01)^7-(1.01)^2]}{5} \\\approx 0.0104 ~mm[/tex]

According to the growth function, the population be in 2050 will be 10,635

Growth function:

The growth function refers the pattern of data that shows greater  increases with passing time, creating the curve of an exponential  function.

Given,

In 1965, the population of a certain town was 2010. In 1995, the population was 3620.

Here we need to find the population in 2050.

While we looking into the given problem, let us consider,

P refers the final population

A refers the the starting population, and

x refers the time passed

Now,  we need to determine the value of the growth factor n and it can be calculated using the information for the years 1965 and 2010.

Here we know that, in 1965, the population of a certain town was 2010. In 1995, the population was 3620.

And the value of x is 30

So, it can be written as,

=> 3620 = 2010eⁿˣ³⁰

=> 3620/2010  = e³⁰ⁿ

=> 362/201 = e³⁰ⁿ

Here by applying ln to both sides of the equation:

⇒ln(362/201) = ln(e³⁰ⁿ)

By, using the laws of logarithms:

=> 30n = ln(362) - ln(201)

=> n = [ln(362) - ln(201)] / 30

=> n = 0.0196

Here we have to use this information to determine P in 2050.

Here the value of A will still be 2010, but x will be 85 years.

Here we have to apply these values then we get,

=> P = 2010e⁰°⁰¹⁹⁶ˣ⁸⁵

=> P = 2010e¹°⁶⁶⁶

=> P = 2010 x 5.2909

=> P = 10635

Therefore, there are 10635 in 2050.

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The values of the variables a, b and c are; a = 5/19, b = -160/19, c = 960/19

We are given the quadratic function formula as;

p(t) = at² + bt + c

Thus, the equation is now;

p(t) = at² + bt + 0

p(t) = at² + bt

From the graph, we see that when x = 8, y = 0. Thus;

p(8) = a(8²) + 8b + c = 0

64a + 8b + c = 0   ------(1)

From the graph, we know that the axis of symmetry is;

x = -b/2a

Thus;

16 = -b/2a

b = -32a  -----(2)

From the graph, we see that when x = 5, y = 15. Thus;

p(8) = a(5²) + 5b + c = 0

25a + 5b + c = 15   ------(3)

Put -32a for b in eq 1 and 3 to get;

64a + 8(-32a) + c = 0  

-192a + c = 0   ------(4)

25a + 5(-32a) + c = 15

-135a + c = 15   ------(5)

Subtract eq 4 from eq 5 to get;

192a - 135a = 15

57a = 15

a = 15/57

a = 5/19

Thus;

b = -32(5/19) = -160/19

-135(5/19) + c = 15

15 + (675/19) = c

c = 960/19

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The difference in the cost of all 30 pens between two shops is,

£1.05

Given, Eve is going to buy 30 pens from either shop A or shop B.

Shop A: pack of 10 pens for £2

Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.

So, the cost of 30 pens from the shop A is,

as, a pack of 10 pens is of £2

1 pen = 2/10

30 pens = £6

Now, the cost of 30 pens from the shop B is,

as, a pack of 5 for £1.10

1 pen = 1.10/5 = £0.22

also buy 1 and get 1 at half price.

So, 2 pens = 0.22 + 0.11 = £0.33

Therefore, 30 pens = £4.95

So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.

Hence, the difference in the cost of all 30 pens between two shops is,

£1.05

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The standard score (z-score) of the given sample is -20.

Given,

[tex]u[/tex] = 35

[tex]o[/tex] = 9

n = 60

x = 32

To calculate standard score (z-score) use formula,

[tex]z=\frac{x-u}{\frac{o}{n} }\\\\z=\frac{32-35}{\frac{9}{60} }\\\\z=\frac{-3}{0.15}\\ \\z=-20[/tex]

Thus, the standard score(z-score) of given sample mean is -20.

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Answer:

It is not a solution

Step-by-step explanation:

put in (-9,-5) in for x and y

9(-9)+4(-5)=10

-81-20=10

-101=10

This is false so (-9,-5) is not a solution to the equation 9x+4y=10

Answer:

-3/22

Step-by-step explanation:

Hope this helps!

Answer: [tex]-\frac{3}{22}[/tex]

Step-by-step explanation:

To find the product, multiply the two fractions:

[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]

Answer:x^4+6

Step-by-step explanation:

you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4  and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)

The solution set is X ∈{1, -7}

The set of values that satisfy a given set of equations or inequalities is known as a solution set. For example, the solution set for a set of polynomials over a ring is the subset on which the polynomials all vanish (evaluate to 0).

Given that 3(x+3) – 12 = 0

We have to find the solution set

3(x+3) – 12 = 0

3(x+3) = 12

X+3 = ±4

X + 3 = 4 or x + 3 = -4

X = 1 or x = -7

X ∈{1, -7}

Therefore the solution set is X ∈{1, -7}

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Every second, 44 megabytes of files will be transferred to her hard drive.

The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.

The function is below

F = 38 + 6t   ....(i)

To determine the number of megabytes of files transferred to her hard drive every second

Substitute the value of t = 1 in the equation (i), and solve for F

F = 38 + 6(1)

F = 38 + 6

F = 44

So the number of megabytes of files = 44

Therefore, every second, 44 megabytes of files will be transferred to her hard drive.

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Answer:

  28 mph

Step-by-step explanation:

Given that a car moving 36 mph takes 7 hours for a trip, you want to know the speed if the trip takes 9 hours.

The speed and time vary inversely for the same distance. If the time goes up by a factor of 9/7, the speed will go down by the inverse factor: 7/9.

  7/9 × 36 mph = 28 mph

The speed of the car is 28 mph for the 9-hour trip.

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Answer:

y-2

Step-by-step explanation:

The simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

What is a radical expression?

An nth root of a number x is a number r that, when multiplied by n, equals x, where n is a positive integer, also known as the degree of the root. Degree 3 roots are referred to as cube roots, while degree 2 roots are known as square roots.

We have,

k² = 17

The variable in this non-linear equation needs to be separated. This is achieved by exponentiating both sides by the reciprocal of the exponent of the variable, which in our example is equal to 1/2.

[tex](k^{2} )^{\frac{1}{2} } = 17^{\frac{1}{2} }[/tex]

[tex](k^{2} )^{\frac{1}{2} } = -17^{\frac{1}{2} }[/tex]

[tex]k= 17^{\frac{1}{2} }[/tex]

[tex]k = -17^{\frac{1}{2} }[/tex]

Hence, the simplest form of radicals is  [tex]k \ \epsilon \ \{17^{\frac{1}{2}} ,-17^{\frac{1}{2} } \}[/tex]

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The value of the unknown angle x would be 43 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.

The unknown angle is x which needs to find.

Therefore, applying trigonometry;

Sin x = perpendicular/hypotenuse

Sin x = 6/10

Sin x = 3/5

Sin x = 0.6

x = Sin inverse (0.6)

x = 43 degrees.

Hence, the value of the unknown angle x would be 43 degrees.

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