4 to the 4th power equals 256. Explain how to use that fact to more quickly evaluate 4 to the 5th power.

Answer:

The answer is below

Step-by-step explanation:

Given that:

Mean (μ) = 3 ounces. standard deviation (σ) = 0.15, sample size (n) = 13 and confidence (C) = 98%

α = 1 - C = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01.

The z score of 0.01 (α/2) corresponds to the z score of 0.49 (0.5 - 0.01) which from the normal distribution table is 2.33.

The margin of error (E) is:

[tex]E=z_{0.01}*\frac{\sigma}{\sqrt{n} } = 2.33*\frac{0.15}{\sqrt{13} }=0.1\\[/tex]

The confidence interval = μ ± E = 3 ± 0.1 = (2.9, 3.1)

The confidence interval is between 2.9 ounce and 3.1 ounce

you can imagine this as a venn diagram. the "or" event would consist of everything in both sides and the middle of the venn diagram because you can choose form either event x or event y.

the "and" event would consist of everything in the middle of the venn diagram because you choice must be a part of both event x and event y.

the complement of an event is just everything that is not included in the event. for example, in a coin flip, the complement of heads is tails. in a dice roll, the complement of {1,2} is {3,4,5,6}

so if you come across these just think "either or" or "both and." and remember that the complement is everything excluding what is listed.

i apologize if this does not help, im not that great at explaining things

Answer:

C. surface area of 5 rectangular prisms.

Step-by-step explanation:

The table in the given figure as shown above has a rectangular flat top that has a solid shape of rectangular prism.

It also has 4 legs that are also rectangular in shape. The legs are rectangular prisms.

To determine the quantity of paint Kimberly would need, she needs to make use of the surface area of the table.

The surface area of the table = surface area of the top + surface area of the 4 legs = surface area of 5 rectangular prisms.

Answer:

C

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ \ \ $82,092 \ \ \ }[/tex][tex]\large\boxed{\sf \ \ \ \$82,092 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

At the beginning we have $49,000

After the first year we get 49,000*(1+3.5%)=49,000*1.035

After n years we get

   [tex]49,000\cdot1.035^n[/tex]

So in 15 years it comes

   [tex]49,000\cdot1.035^{15}=82,092.09...[/tex]

rounded to the nearest dollar is $ 82,092

Hope this helps

Answer:

x = 0

Step-by-step explanation:

[tex]4+9(3x-7)=-42x-13+23(3x-2)\\4+27x-63=-42x-13+69x-46\\27x+4-63=-42x+69x-13-46\\27x-59=25x-59\\2x-59=-59\\2x=0\\x=0[/tex]

Step-by-step explanation:

5q+8p=775

q + p = 125

5q + 8q = 775

-5q -5q = -625

3q = 150

q = 50 premium

q + 50 = 125

q = 75 quick

Correct answer is

A: 5x+8y=775 and x+y =125

Next Answer is

50 premium car washes

75 Quick Car Washes

Answer:

It is the first graph

Step-by-step explanation:

Just got it right on the test review :)

Inequalities help us to compare two unequal expressions. The graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The given inequality can be solved as,

[tex]\dfrac29(x+3) > 4(\dfrac59)\\\\\dfrac{2x+6}{9} > \dfrac{20}{9}\\\\2x + 6 > 20\\\\2x > 20 - 6\\\\x > \dfrac{14}{2}\\\\x > 7[/tex]

Hence, the graph shows that all the values of x that satisfies the given inequality are x>7. Thus, the correct option is A.

Learn more about Inequality:

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Answer:

c

Step-by-step explanation:

Answer:

Null hypothesis: u = 8.8 liters

Alternative hypothesis: u < 8.8 liters

Step-by-step explanation:

The null hypothesis is always opposite to Tue alternative hypothesis and is the default hypothesis.

In this case study, the null hypothesis is that the average American consumes 8.8 liters of alcohol per year: u = 8.8

The alternative hypothesis is that does the average American consumes less than 8.8 liters of alcohol per year: u < 8.8 liters

Answer:

90 degree EFC. and. BMC

across fc/ma

across ec/ab

Answer: A. [tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B. Minimum distance between them  = 18.61 feet.

C. After 28.76 seconds Sven and Rudyard are closest.

Step-by-step explanation:

A) Let (0,0) be the intersection point.

Then, Initial Location of Sven (0,190).

Speed of Sven = 7 feet per second

Then, position of Sven after t seconds = (0,190-7t)  [speed = distance x time]

Similarly, Initial position of Rudyard= (130,0)

Speed of Rudyard = 4 feet per second

Position after t seconds = (130-4t,0)

Distance d between Sven and Rudyard t seconds after they start walking:

[tex]d=\sqrt{(190-7t)^2+(130-4t)^2}[/tex]

B) Let [tex]d(t)=\sqrt{(190-7t)^2+(130-4t)^2}\\[/tex]

[tex]d'(t)=2(190-7t)(-7)+(2)(130-4t)(-4)\\\\=130t-3700[/tex]

Put d'(t)=0

[tex]130t-3700=0\\\\\Rightarrow\ t=\dfrac{3700}{130}\approx28.46\ sec[/tex]

Minimum distance :

[tex]d(28.46)=\sqrt{(190-7(28.46))^2+(130-4(28.46))^2}\\\\=\sqrt{346.154}\approx18.61\ feet[/tex]

Hence, the minimum distance between them  = 18.61 feet.

c) After 28.76 seconds Sven and Rudyard are closest.

Answer:

The highest number on a die is 6. when we roll out two die the total sum cannot be more that 12. and each sum having the same probability of showing up.

The outcome of our experiment can be 2,3,4,5,6,7,9,10,11 or 12.

Step-by-step explanation:

Statistical experiment can be simply stated as the likelihood of an an event to occur or not.

Answer:

Step-by-step explanation:

The perimeter of a rectangle is expressed as 2(L+B) where;

L is the length and B is the breadth of the triangle.

P = 2(L+B)

68 = 2(L+B)

L+B = 68/2

L+B = 34

L = 34 - B ... 1

Area of the rectangle A = LB... 2

Substituting equation 1 into 2 will give;

A = (34-B)B

A = 34B-B²

To maximize the area of the triangle, dA/dB must be equal to zero i.e

dA/dB = 0

dA/dB = 34 - 2B = 0

34-2B = 0

2B = 34

Dividing both sides of the equation by 2 we will have;

B = 34/2

B = 17

Substituting B = 17 into equation 1 to get the length L

L = 34-17

L = 17m

This shows that the rectangle with maximum area is a square since L = B = 17m

The dimension of the rectangle is Length = 17m and Breadth = 17m

The dimensions are 17m and 17m.

The perimeter of a rectangle is given as:

= 2(length + width)

Since in their case, the lengths have same values, this will be:

Perimeter = 2(l + l)

Perimeter = 4l

4l = 68

L = 68/4

L = 17m

Therefore, the dimensions are 17m and 17m.

Read related link on:

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Answer:

The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Step-by-step explanation:

GIven that :

[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid  can be calculated as follows:

[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]

[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]

[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Answer:

16 Years

Step-by-step explanation:

Given:

D=165 feet and the frequency of the motion is 1.6 revolutions per minute.

Solution:

The radius is half of the diameter.

The radius of the wheel is 82.5 feet.

[tex]T=\frac{1}{1.6} \text{ minutes}[/tex]

As we know: [tex]\omega=\frac{2\pi}{T}[/tex]

Substitute the value of T in the above formula.

[tex]\omega=\frac{2\pi}{\frac{1}{1.6}}\\\omega=3.2\pi[/tex]

If the center of the wheel is at the origin then for [tex]t=0[/tex] the rest position is [tex]-a[/tex].

This can be written as:

[tex]h(t)=-a\cos(\omega t)\\h(t)=-82.5cos(32.\pi t)[/tex]

The actual height of the rider from the ground is:

[tex]h(t)=\text{ Initial height from bottom}+\text{ radius}-82.5\cos(3.2\pi t)\\h(t)=15+82.5-82.5\cos(3.2\pi t)\\h(t)=97.5-82.5\cos(3.2\pi t)[/tex]

The required equation is [tex]h(t)=97.5-82.5\cos(3.2\pi t)[/tex].

Answer:

Hey there!

The circumference of a circle is [tex]\pi(d)[/tex], where d is the diameter, and [tex]\\\pi[/tex] is a constant roughly equal to 3.14.

The diameter is 16, so plugging this into the equation, we get 3.14(16)=50.24.

The circumference of the circle is 50.24 yards.

Hope this helps :)

Answer:

The answer is 1 - 16b.

Step-by-step explanation:

You have to collect like-terms :

[tex]1 - 5b - b - 8b - 2b[/tex]

[tex] = 1 + b( - 5 - 1 - 8 - 2)[/tex]

[tex] = 1 + b( - 16)[/tex]

[tex] = 1 - 16b[/tex]

Answer:

The answer is

Step-by-step explanation:

1 – 5b + – b + – 8b – 2b can be written as

1 - 5b - b- 8b - 2b

Subtract the like terms

That's

We have the final answer as

1 - 16b

Hope this helps you

A.  The graph of the function is high on the extreme left side, and low on the extreme right side.

The graph has no "start" or "end".  It's defined for all 'x' between negative and positive infinity.  So no matter how far left or right you go, there's always a 'y' for whatever 'x' you're at.

But it's guaranteed that once you get far enough left (negative x), the first term -x³ will definitely be positive, and will become more and more positive as you go farther left.

And similarly, once you get far enough right (positive x), the first term,   -x³ will definitely be negative, and it'll become more and more negative as you go farther right.

So, except for some wiggling within a short distance either side of the origin, if you look at this graph from 10 miles away, f(x) comes out of the sky  on the left side, and it heads down into the salt mine on the right side.

Answer:

guys omg the answer is A its not a scam guys

Step-by-step explanation:

Answer:

Largest integer in the interval [−∞, 31] is 31.

Step-by-step explanation:

Given the interval: [−∞, 31]

To find: The largest integer in this interval.

Solution:

First of all, let us learn about the representation of intervals.

Two kind of brackets can be used to represent the intervals. i.e. () and [].

Round bracket means not included in the interval and square bracket means included in the interval.

Also, any combination can also be used.

Let us discuss one by one.

1. [p, q] It means the interval contains the values between p and q. Furthermore, p and q are also included in the interval.

Smallest p

Largest q

2. (p, q) It means the interval contains the values between p and q. Furthermore, p and q are not included in the interval.

Smallest value just greater than p.

Largest value just smaller than q.

3. [p, q) It means the interval contains the values between p and q. Furthermore, p is included in the interval but q is not included in the interval.

Smallest value p.

Largest value just smaller than q.

4. (p, q] It means the interval contains the values between p and q. Furthermore, p is not included in the interval but q is included in the interval.

Smallest value just greater than p.

Largest value q.

As per above explanation, we can clearly observe that:

The largest integer which belongs to the following interval: [−∞, 31] is 31.

Answer:

C : A salesperson earns $50 plus $10 for every $100 of merchandise he sells.

Step-by-step explanation:

If a salesperson earns $50 plus $10 for every $100 of merchandise he sells, the rate of change is 100. The linear equation is T = 50 + 100h, where T is the total amount he earns and h is the number of $100 in merchandise he sells.

The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.

It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.

Let's check all the options, then we have

A: You drive from Colorado to Texas. In the first 4 hours, you cover 240 miles, and in the second 5 hours, you cover another 240 miles. It is an example of a linear function but the slope gets changed after 2 hours.

B: The money you put in the bank earns 5% Interest. This means that the bank pays you 5% of the amount of the money kept in the bank each year. It is an example of the exponential function.

C: A salesperson earns $50 plus $10 for every $100 of merchandise he sells. It is an example of a linear function.

D: The number of bacteria doubles every hour.  It is an example of the exponential function.

The example that represents the constant rate will be a salesperson who earns $50 plus $10 for every $100 of merchandise he sells. Then the correct option is C.

More about the average rate change link is given below.

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Answer:

10 units²

Step-by-step explanation:

The shape is a triangle.

The area can be found by multiplying the base (in units) with height (in units) divided by 2.

base = 4 units

height = 5 units

[tex]\frac{4 \times 5}{2}[/tex]

[tex]\frac{20}{2} =10[/tex]

surface area of a equilateral by hand a 140.4 cm and 9cm

Hey there! :)

Answer:

(-6, -7)

Step-by-step explanation:

Given the equations:

y = -1/6x - 8

y = 2x + 5

When graphed, we get a solution, or point of intersection, at (-6, -7). This is the point at which the two equations are equal to each other. This can even be proven:

-7 = -1/6(-6) - 8

-7 = 1 - 8

-7 = -7

----------------------

-7 = 2(-6) + 5

-7 = -12 + 5

-7 = -7

Thus, proving graphically and algebraically, the solution is at (-6, -7).

Answer:

see below.

Step-by-step explanation:

1st row has four small boxes

2nd row has three big boxes

big box 1 has no items ragged in it.

big box 2 has small box 1 and also small box 1 dragged into it.

big box 3 has small box 3 and small box 4 dragged into it.

Answer:

Inventory turnover ratio is 3.74

explanation:

Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.

Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold

= $35,500 / $9500

= 3.74

Answer:

(-2,-1), (2,1), (4,2)

Step-by-step explanation:

This is how I did it: (took me like a minute)

Draw a graph or get graph paper. You could also probably find a graph online that you can write on.  (remember to label)

Now mark two points of the line. So for this question you could use (0,0) and (2,1).

Now draw a line connecting both points.

Finally you can check whether the points are on the line or are not.

Hope this helps!

Answer:

12.04

Step-by-step explanation:

Well to solve for the unknown side "c" we need to use the Pythagorean Theorem formula,

[tex]a^2 + b^2 = c^2[/tex]

We already have a and b which are 8 and 9 so we plug them in.

[tex](8)^2 + (9)^2 = c^2[/tex]

64 + 81 = c^2

145 = c^2

c = 12.04 rounded to the nearest hundredth.

Thus,

the unknown side is about 12.04.

Hope this helps :)

Answer:

x=-7, y= -20

Step-by-step explanation:

2x - y =6

x - y = 13

when I subract (x-y =13 ) from (2x-y =6)

2x -y =6

-x +y=-13

______________

x = -7

substitute x=-7 in the second equation

-7 - y =13

-y = 13 +7

-Y = 20

Y=-20

x=-7, y= -20

Answer:

x= -7/6

y= -25/3

Step-by-step explanation:

2x-y =6

4 x-y =13

Firstly, 4x-y=13(-)  =>> - 4x+y=-13

Then we make the sum and result 6x= -7. Result x= -7/6.

We need to find y. So:  

-y= 6-2x =>>  y= -6 +2x =>> y= -6 +2*(-7/6) =>> y= -6-7/3 =>> y=(-18-7)/3 =>>y= -25/3

Answer:

D. (0, 7).

Step-by-step explanation:

Moving from (4,3) to (2, 5) we move 2 to the left; 2 - 4 = 2 then 2 up 3 + 5 = +2.

So the point C is 2-2, 5+2 = (0, 7).