The First National Bank of Wilson has 600 checking account customers. Recent sample of 50 of these customers show 29 have a visa card with the bank. Construct the 90% confidence interval for the proportion of checking account customers who have a visa card with the bank. (Use a Z distribution table0

Answer:

True

Step-by-step explanation:

We know that sales of store 1 and store 2 will be two independent sample and given that weeky sales are normally  distributed therefore we can use indepedence means method.

That is to say, we are affirming that what they say is correct therefore the correct answer is "true".

Answer:

V = 512 ft^3

Step-by-step explanation:

The volume of a prism is length * width * height

V = 8*8*8

V = 512 ft^3

The volume of a rectangular prism is lwh.

V=lwh

V=8*8*8

V=8^3

V=512

Answer:

The statement translate to 'Every square has three sides'

Step-by-step explanation:

Since P(x) is an open sentence and the domain for x is the set of all squares, its means that whatever that is applicable to one square also applicable to others

Answer:

Step-by-step explanation:

Time = distance/speed

Considering the first stage,

Speed = 20km/hr

Distance = 5km

Time = 5/20 = 0.25 hour

Considering the second stage,

Speed = 10km/hr

Distance = 5km

Time = 5/10 = 0.5 hour

Considering the third stage,

Speed = 25km/hr

Distance = 5km

Time = 5/25 = 0.2 hour

Considering the third stage,

Speed = 20km/hr

Distance = 5km

Time = 5/20 = 0.25 hour

Therefore, the time it took the biker to complete the race is

0.25 + 0.5 + 0.2 + 0.25 = 1.2 hours

Answer:

c. number of items - discrete; total time - continuous

Step-by-step explanation:

The question is incomplete due to the lack of the following options:

to. number of items - continuous; total time - discrete

b. number of items - continuous; total time - continuous

c. number of items - discrete; total time - continuous

d. number of items - discrete; total time - discrete

Knowing this, the type of variables recorded by managers of the home improvement store are,

c. number of items - discrete; total time - continuous

Discrete variables are those that are well defined and in the finite set of values and continuous variables are variables that can take a value between any of the other two values.

Complete question:

Consider a binomial experiment with n = 20 and p = .70.

A. Compute f(12).

B. Compute f(16).

C. Compute P(x≥ 16).

D. Compute P(x≤15).

E. Compute E(x).

F. Compute Var(x).

Answer:

a) 0.1144

b) 0.1304

c) 0.2375

d) 0.7625

e) 14

f) 4.2

Step-by-step explanation:

Given:

n = 20

p = 0.70

q = 1 - p ==>  1 - 0.70 = 0.30

a) Use the formula:

[tex] P(x) = CC\left(\begin{array}{ccc}n\\x\end{array}\right) p^x q^(^n^-^x^) [/tex]

Thus,

[tex]P(12) = C\left(\begin{array}{ccc}20\\12\end{array}\right) (0.7^1^2) (0.3^(^2^0^-^1^2^) )[/tex]

[tex] = 125970*0.0138*0.00006 [/tex]

[tex] = 0.1144 [/tex]

b) [tex]P(16) = C\left(\begin{array}{ccc}20\\16\end{array}\right) 0.7^1^6 (0.3^(^2^0^-^1^6^))[/tex]

[tex] = 4845 * 0.0033 * 0.0081 [/tex]

[tex] = 0.1304 [/tex]

c) Compute P(x≥16):

P(x ≥ 16) = P(16) + P(17) + P(18) + P(19) + P(20)

[tex]= C\left(\begin{array}{ccc}20\\16\end{array}\right) 0.7^1^6 (0.3^(^2^0^-^1^6^)) + C\left(\begin{array}{ccc}20\\17\end{array}\right) 0.7^1^7 (0.3^(^2^0^-^1^7^) ) + C\left(\begin{array}{ccc}20\\18\end{array}\right) 0.7^1^8 (0.3^(^2^0^-^1^8^)) + C\left(\begin{array}{ccc}20\\19\end{array}\right) 0.7^1^9 (0.3^(^2^0^-^1^9^)) + C\left(\begin{array}{ccc}20\\20\end{array}\right) 0.7^2^0 (0.3^(^2^0^-^2^0^))[/tex]

[tex] = 0.1304 + 0.0716 + 0.0278 + 0.0068 + 0.0008 = 0.2375 [/tex]

d) P(x ≤ 15):

= 1 - P(x ≥ 16)

= 1 - 0.2375

= 0.7625

e) E(x): use the formula, n * p.

= n*p

= 20 * 0.7

= 14

f) Var(x)

Use the formula: npq

npq = 20 * 0.7 * 0.3

= 4.2

σ

Answer: the slope is 2

Step-by-step explanation:

2x-y=16

-y=16-2x

y=2x-16

Answer:

Tangent

Step-by-step explanation:

if the angle in question is the bottom of the ladder and the ground, then tangent is opposite over adjacent... or 12/5

Hope this is right

Answer: -6

Step-by-step explanation: The slope of a line is rise divided by run. This is shown by the equation (y2-y1) / (x2-x1) = slope of a line.

For this specific line you can plug in two points such as (2,-4) and (1,2)

[2-(-4)] / (1-2) = -6

Hope this helps :)

Answer:

The area of the original piece of paper is 60cm

Answer:

the answer is 60

hope it helps :D

Step-by-step explanation:

Answer:

  height = 10.5 cm (for open-top container)

Step-by-step explanation:

The area of the base is ...

  A = πr²

The lateral area is ...

  A = 2πrh

We want the ratio of these to be 1:6, so we have ...

  πr²/(2πrh) = 1/6

  6πr² = 2πrh . . . cross multiply

  h = 3r . . . . . . . divide by 2πr

  h = 3(3.5 cm) = 10.5 cm

The height is 10.5 cm.

Answer:

4 because 6th floor has no office

Answer:

5 floors

Step-by-step explanation:

Fewer than 80 makes it 0-79

So,

0-79 => 5 floors

Answer:

A) 715 ways

B) 715 ways

C) (1/715)

Step-by-step explanation:

This is a permutation and combination problem.

Since we want to select a number of people from a larger number of people, we use combination as the order of selection isn't important now.

A) How many different ways can the officers be appointed?

There are 4 officer positions.

There are 13 people in total.

We want to select 4 people from 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

B) How many different ways can the committee be appointed?

Number of committee members = 4

Total number of people available = 13

Number of ways to select 4 people from 13 = ¹³C₄ = 715

C) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

Selecting a group of the youngest candidates is just 1 amongst the total number of ways the 4 committee members can be picked,

Hence, the required probability = (1/715)

Hope this Helps!!!

Answer:

[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]

Step-by-step explanation:

[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]

hope this helps you

brainliest appreciated

good luck! have a nice day!

Answer:

8 nickels, 5 dimes and 7 quarters

Step-by-step explanation:

Each nickel is $0.05, each dime is $0.10 and each quarter is $0.25.

So, if we have n nickes, d dimes and q quarters, we can write the system of equations:

[tex]n + d + q = 20\ (eq1)[/tex]

[tex]0.05n + 0.1d + 0.25q = 2.65\ (eq2)[/tex]

[tex]7n + 5d + 20q = 221\ (eq3)[/tex]

If we multiply (eq2) by 140 and (eq1) by 7, we have:

[tex]7n + 14d + 35q = 371\ (eq4)[/tex]

[tex]7n + 7d + 7q = 140\ (eq5)[/tex]

Now, making (eq4) - (eq3) and (eq5) - (eq3), we have:

[tex]9d + 15q = 150\ (eq6)[/tex]

[tex]2d - 13q = -81\ (eq7)[/tex]

Multiplying (eq7) by 4.5, we have:

[tex]9d - 58.5q = -364.5\ (eq8)[/tex]

Subtracting (eq6) by (eq8), we have:

[tex]73.5q = 514.5[/tex]

[tex]q = 7[/tex]

Finding 'd' using (eq6), we have:

[tex]9d + 15*7 = 150[/tex]

[tex]9d = 150 - 105[/tex]

[tex]d = 5[/tex]

Finding 'n' using (eq1), we have:

[tex]n + 5 + 7 = 20[/tex]

[tex]n = 8[/tex]

So we have 8 nickels, 5 dimes and 7 quarters.

Answer:

One solution

Step-by-step explanation:

12x+6=5x

7x+6=0

7x=-6

x=-6/7

Only one solution. Hope this helps!

Answer:

THEREFORE THE CONFIDENCE INTERVAL from the Z table = ±1.645

Step-by-step explanation:

Confidence level = 95% = 0.95

compound 1

Number of samples ( n1 ) = 243

Average brake life ( x1 ) = 37866 miles

standard deviation ( ∝ ) = 4414 miles

compound 2

number of samples ( n2 ) = 268

Average brake life ( x2 ) = 45789 miles

standard deviation ( ∝ ) = 2368 miles

Determine the 95% confidence interval for the true difference between average lifetimes

significance level (β) = 1 - confidence level = 1 - 0.95 = 0.05

standard error = [tex]\sqrt{\frac{\alpha1^2 }{n1} + \frac{\alpha2^2}{n2} }[/tex]    = [tex]\sqrt{}[/tex]( 4414^2/243) + (2368^2/268) =

critical value = 0.05/2 =Z 0.025 = 1.645

THEREFORE THE CRITICAL VALE from the Z table = ±1.645

Answer:

The boat is approaching the dock at a speed of 3.20 ft/s when it is 4 feet from the dock.

Step-by-step explanation:

The diagram of the situation described is shown in the attached image.

The distance of the boat to the dock along the water level at any time is x

The distance from the person on the dock to the boat at any time is y

The height of the dock is 5 ft.

These 3 dimensions form a right angle triangle at any time with y being the hypotenuse side.

According to Pythagoras' theorem

y² = x² + 5²

y² = x² + 25

(d/dt) y² = (d/dt) (x² + 5²)

2y (dy/dt) = 2x (dx/dt) + 0

2y (dy/dt) = 2x (dx/dt)

When the boat is 4 ft from dock, that is x = 4 ft,

The boat is being pulled at a speed of 2 ft/s, that is, (dy/dt) = 2 ft/s

The speed with which the boat is approaching the dock = (dx/dt)

Since we are asked to find the speed with which the boat is approaching the dock when the boat is 4 ft from the dock

When the boat is 4 ft from the dock, x = 4 ft.

And we can obtain y at that point.

y² = x² + 5²

y² = 4² + 5² = 16 + 25 = 41

y = 6.40 ft.

So, to the differential equation relation

2y (dy/dt) = 2x (dx/dt)

when x = 4 ft,

y = 6.40 ft

(dy/dt) = 2 ft/s

(dx/dt) = ?

2 × 6.40 × 2 = 2 × 4 × (dx/dt)

25.6 = 8 (dx/dt)

(dx/dt) = (25.6/8) = 3.20 ft/s.

Hope this Helps!!!

Answer:

We can call the variable e. "more than" is denoted by > so the inequality is e > 40. To graph it, draw a circle on the tick mark that has 40 underneath it but don't fill in the circle. Then, draw a continuous line to the right of the circle and draw an arrow at the end of it to show that it goes on forever.

Answer:  D) 8 inches

====================================================

Work Shown:

Refer to the diagram below.

A = 50 degrees

B = unknown

C = 80 degrees

-----

For any triangle, the three angles always add to 180

A+B+C = 180

50+B+80 = 180

B+130 = 180

B = 180-130

B = 50 degrees

Since angles B and C are the same measure, their opposite sides are the same length. Triangle ABC is isosceles. Therefore, a = x = 8

Answer: D) 8 inches.

Step-by-step explanation: The triangle has three angles: two were given (50º and 80º) and the other one can be calculated (50º). Therefore, this triangle is an isosceles triangle, it has one base and two congruent sides. Since the one side is 8in, then the other missing side must also be 8in according to the Isosceles Triangle Theorem.

Answer:

2√62

Step-by-step explanation:

248 | 2

124 | 2

62 | 2

31 | 31

1

248 = 2³·31

√248 = √2²·2·31 = 2√62

Answer:

57.6 km per hr

Step-by-step explanation:

Let us assume the horizontal distance between the ship is constant = x

= 70 Km

The ship A sails south at 40km/h is denoted as 40t

The Ship B sails north at 20 km/h is denoted as 20t

Now the vertical distance separating the two ships is

=  20t + 40t

= 60t

And, the Distance between the ship is changing

[tex]D^2 = y^2 + x^2[/tex]

As x is constant

[tex]\frac{\partial x}{\partial t}$ = 0[/tex]

Now differentiating

[tex]2D \frac{\partial D}{\partial t}$ = 2y $\frac{\partial y}{\partial t}$[/tex]

The distance between two ships is at 4

So,  

vertical distance is

[tex]= 60\times 4[/tex]

= 240

And, the horizontal distance is 70

[tex]D = \sqrt{240^2 + 70^2} = 250[/tex]

[tex]2 \times 250 \frac{\partial D}{\partial T}$ = 2 \times 240 \times 60[/tex]

So, the distance between the ships is  57.6 km per hr

Answer:

2. A) LNM-ONP

3. B) HI

4. A) GH AND HI

Step-by-step explanation:

2. corresponding sides of similar triangle are proportional  and corresponding angles are congruent

3. it seems that triangles are 45-45-90 so GH correspondents with HI

4. JH is geometric mean of line segment making hypotenuse

so JH = [tex]\sqrt{GH*HI}[/tex]

Answer:

18

Step-by-step explanation:

4 - (-5) + 04 - (- 5)+0

Negative times negative cancels.

4 + 5 + 4 + 5 + 0

Add the terms.

9 + 9 + 0

= 18

Answer:

Step-by-step explanation:

4-(-5)+04-(-5)+0

4+5+04+5+0

14+04

if you meant 0.4 then, it would be 14.4

if you mean 04 then, it would be 18

Answer:

[tex]a.\ P(x) = - 0.002x^2+3.8x-40[/tex]

b. 320

[tex]c.\ P'(x) = -0.004 x + 3.8[/tex]

d. 3.76

Step-by-step explanation:

Given that:

Revenue function:

[tex]R(x) = 6x[/tex]

Cost Function:

[tex]C(x) = 0.002x^2+2.2x+40[/tex]

We know that,

Answer a: Profit = Revenue - Cost

[tex]\Rightarrow P(x) = R(x) - C(x)\\\Rightarrow P(x) = 6x - (0.002x^2+2.2x+40)\\\Rightarrow P(x) = - 0.002x^2+3.8x-40[/tex]

Answer b:

P(100) = ?

Putting value of x as 100 in above equation:

[tex]P(100) = - 0.002\times 100^2+3.8 \times 100-40\\\Rightarrow P(100) = -20+380 -40\\\Rightarrow P(100) = 320[/tex]

Answer c:

P'(x) = ?

Differentiating the equation [tex]P(x) = - 0.002x^2+3.8x-40[/tex]

[tex]P'(x) = -2 \times 0.002 x^{2-1} + 3.8 + 0\\P'(x) = -0.004 x + 3.8[/tex]

Answer d:

P'(100) = ?

Putting x = 100 in equation [tex]P'(x) = -0.004 x + 3.8[/tex]

[tex]P'(100) = -0.004 \times 100 + 3.8\\P'(100) = -0.4 + 3.8\\P'(100) = 3.76[/tex]

Answer:

-18/3x - 9

Step-by-step explanation:

-9(2/3x + 1)

Expand.

-18/3x + -9

Answer:

The correct answer to the following question will be "0.19".

Step-by-step explanation:

So that the above seems to the right answer.

Reflect over y-axis,reflect over the X axis ,rotate 180°

Option D is the correct option.

Explanation:

Let's take point A which is (4,-1)

Reflection over y- axis will make this point (4,1)

Then, reflection over X axis will make this point (4,-1)

After rotation of 180 degree we will get (-4,1) .

Please see the attached picture....

Hope it helps...

Good luck on your assignment...

Answer:  d) reflect over the x-axis, reflect over y-axis, rotate 180°

Step-by-step explanation:

A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.

Reflection over the x-axis changes the sign of the y-coordinate

Z = (x, y)    →    Z' = (x, -y)

Reflection over the y-axis changes the sign of the x-coordinate

Z' = (x, -y)    →    Z'' = (-x, -y)

Rotation of 180° changes the signs of both the x- and y-coordinates

Z'' = (-x, -y)   →     Z''' = (x, y)

Answer:

Y = -X - 7

Step-by-step explanation:

y-y1 =m(x-x1)

y-(-2)= -1(x-(-5)

y+2 = -1(x+5)

Solve for y

subtract 2 from both sides

y=-x-5-2

Y = -x-7