lim(lnx-ln4/x-4) as x approaches 4​

Answer:

(1, 1)  (1, 2)  (1, 3) (1,4)

(1,5)  (2,1)   (2,2) (2,3)

(2,4)  (3,1)  (3,2)   (3,3)

(4,1)   (4,2) (5,1)

Step-by-step explanation:

An event is a specified set of results of a random experiment in probability theory. The number of possible outcomes that Event E has is 21.

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Let E be the event where the sum of two rolled dice is greater than or equal to 7. Therefore, the outcomes in E are represented in red in the given table below.

(1, 6)

(2, 6)

(3, 6)

(4, 6)

(5, 6)

(6, 6)

(2, 5)

(3, 5)

(4, 5)

(5, 5)

(6, 5)

(3, 4)

(4, 4)

(5, 4)

(6, 4)

(4, 3)

(5, 3)

(6, 3)

(5, 2)

(6, 2)

(6, 1)

Hence, the number of possible outcomes that Event E has is 21.

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Answer:

x f(x)

0 0

-2 -4

4 -2

You need to draw y = 2 f (x-1)

So you need to choose x so that x-1 = 0, -2, 4 then you can use the above values

New function

x-1 = 0, x = 1, y = 2 f (x-1) = 2 f(0) = 2 x 0 = 0

x-1 = -2 x = -1 y = 2 f (x-1) = 2 f(-2) = 2 x -4 = -8

x-1 = 4 x = 5 y = 2 f (x-1) = 2 f (4) = 2 x -2 = -4

So 3 points on the new graph are (1, 0) (-1, -8) and (5, -4)

Basically going from y = f(x) to y = f(x-a) where a is a constant positive number you translate (move) y = f(x) a units to the right.

y = f(x) to y = 2 f(x), you dilate f(x) with center (0,0) factor 2, so (a,b) > (2a, 2b)

So basically here you are doing both things.

So if (a,b) is on y = f(x) then after the translation (a,b) > (a+1, b) then after the dilation (a+1,b) > (2a+2, 2b)

Our graph for A was the same, but my B was a bit different. I hope this helps regardless. :)

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

Answer:

≈ 14.6%

Step-by-step explanation:

percentage increase is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase = 2.75 - 2.40 = 0.35 , then

percentage increase = [tex]\frac{0.35}{2.40}[/tex] × 100% ≈ 14.6% ( to the nearest tenth )

Answer: 20

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]

It's the sum of a geometric sequence.

Let's rewrite it a bit:

[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]

And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]

Now let's calculate the initial sum:

[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]

The time for the ball to pass the top of the building is determined as 4 s.

The time for the ball to pass the top of the building is obtained when the velocity of the ball is zero.

h = -16t² + 128t + 144

v = dh/dt

v = -32t + 128

at maximum height, v = 0

0 = -32t + 128

32t = 128

t = 128/32

t = 4 s

Thus, the time for the ball to pass the top of the building is determined as 4 s.

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After 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

We have:

An object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

When the ball pass the top of the building, h = 144 foot

Plug h = 144 foot in h= -16t² + 128t + 144

144 = -16t² + 128t + 144

[tex]\rm -16t^2+128t=0[/tex]

t = 0 or t = 8 seconds

At t = 0, initially, the ball was thrown upward.

At t = 8 seconds, the ball passes the top of the building

Thus, after 8 seconds, the ball will pass the top of the building if the object is thrown upward from the top of a 144​-foot building with an initial velocity of 128 feet per second.

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Answer:

the interior angle of a triangle = 180- 89 ( forming linear pair)

= 91°

y = 91 + 23

Y = 114° ( sum of interior angle of a triangle ls equal to its outer angle)

Answer:

114

Step-by-step explanation:

Angle A + 89 = 180 (Sum ofAngles in a straight line)

Angle A = 180 - 89 = 91

Angle B + Angle A + 23 = 180 (Sum of angles in a triangle)

Angle B + 91 + 23 = 180

Angle B = 180 - 114 = 66

Angle B + y = 180 (Sum of angles in a straight line)

66 + y = 180

y = 180 - 66 = 114

Refer to the attached picture.

Answer:

Step-by-step explanation:

I can give you the meaning of Y

Y is the vertical value in a pair of coordinates. In other words how far up or down the point is. The Y coordinate is always written second in an ordered pair of coordinates (x,y) when used. A example from the internet is:

The preimage was shifted to the image by a translation 2 units right and 2 units up, so the answer is [tex](x,y) \longrightarrow (x+2, y+2)[/tex]

Answer:

○ Length = 20 centimeters and Width = 5 centimeters

Step-by-step explanation:

Let the length = L

Then the width is L - 15

A = lw

100 = L(L - 15)

L² - 15L - 100 = 0

(L - 20)(L + 5) = 0

L - 20 = 0  or  L + 5 = 0

L = 20  or  L = -5

Since a length of a rectangle cannot be negative, we discard the solution L = -5 and keep the solution L = 20.

L = 20

width = L - 15 = 20 - 15 = 5

Answer:  ○ Length = 20 centimeters and Width = 5 centimeters

Answer:

5:11:9

Step-by-step explanation:

Change the decimal to fractions

45/10:99/10:81/10

Multiply through by the Lowest Common Factor 10

10×45/10:10×99/10:10×81/10

Which makes it

45:99:81

They have a common factor which is 9, so divide through by 9

45/9:99/9:81/9

Your answer is

5:11:9

Hope it helps

Answer:

20

Step-by-step explanation:

Answer:

20$ For the Roses

Step-by-step explanation:

Think about it like this. For each daisy (1$), the price is double for roses (2$).

Brad has a limit of 33$. And he bought 3 more daisies than roses.

If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.

(10 Daisies = 10$) + (10 Roses = 20$) = 30$

30$ + (3 Daisies = 3$) = 33$

Answer: [tex]\frac{\sqrt{113}}{7}[/tex]

Step-by-step explanation:

As X is an acute angle, all 6 trigonometric functions with an argument of X are positive.

Using the identity [tex]1+\tan^{2} X=\sec^{2} X[/tex],

[tex]1+\left(\frac{8}{7} \right)^{2}=\sec^{2} X\\\\\sec^{2} X=\frac{113}{49}\\\\\therefore \sec X=\boxed{\frac{\sqrt{113}}{7}}[/tex]

A pattern is a recurring arrangement of numbers, forms, colours, and so on.

In mathematics, a pattern is a recurring arrangement of numbers, forms, colours, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.

As per the pattern, Each figure has 3 more squares than the one before it.

Hence, the correct option is C.

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Answer: x-1

Step-by-step explanation:

Answer:

Answers are 20, 12 and 16

Step-by-step explanation:

Y=4x

for x = 5

y=4(5)

y=20

for x = 3

y=4(3)

y=12

for x = 4

y=4(4)

y=16

Answer:

X I Y

5 20

3 12

4 16

Step-by-step explanation:

since y=4 multiplied by x

so, 5x4=20

3x4=12

4x4=16

The Gross pay which Derek gets is 690 dollars.

Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages. The amount remaining after all withholdings are accounted for is net pay or take-home pay.

Here, Total hours worked by Derek = 43 hours

Rate of pay = $15 per hour

Rate of pay beyond 40 hours = $30 per hour

Now,

Rate of pay for the first 40 hours = 40 X 15 = $ 600

Since the pay rate doubles after 40 hours,

Rate of pay for the remaining 3 hours = 3 X 30 = $ 90

Gross Pay = 600 + 90 = $ 690

Thus, the Gross pay which Derek gets is 690 dollars.

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Answer:

See below

Step-by-step explanation:

She combined 3x and - 9x   incorrectly

  she should have gotten  - 6 x       not  - 12 x

The equation of the circle is [tex](x-8)^2 + (y-6)^2 = 25[/tex].

Answer:

43

Step-by-step explanation:

63-3/3=20 63-20

Answer:

mark has 18

don has 45

Step-by-step explanation:

Answer:

−135z

2

−2z
The 2 is representing Square

Step-by-step explanation:

(3z)
2

−4z+11−(12z)
2

+2z−11

Expand (3z)

2

.

3

2

z

2

−4z+11−(12z)

2

+2z−11

Calculate 3 to the power of 2 and get 9.

9z

2

−4z+11−(12z)

2

+2z−11

Expand (12z)

2

.

9z

2

−4z+11−12

2

z

2

+2z−11

Calculate 12 to the power of 2 and get 144.

9z

2

−4z+11−144z

2

+2z−11

Combine 9z

2

 and −144z

2

 to get −135z

2

.

−135z

2

−4z+11+2z−11

Combine −4z and 2z to get −2z.

−135z

2

−2z+11−11

Subtract 11 from 11 to get 0.

−135z

2

−2z

Answer:

[tex]1)\text{ Friday}\\2)\text{ }7:00\\3a)\text{ }0\\3b)\text{ }4\\3c)\text{ }0\\4a)\text{ }6\\4b)\text{ }4\\4c)\text{ }2[/tex]

Answer:

Yes, k = 1/3 and y = 1/3x

Step-by-step explanation:

[tex]\text{The given line passes through the origin, hence it has equation of the form:}\\y=kx[/tex]

[tex]\text{Therefore y varies directly as x.}The line passes through the point (3,1)}[/tex]

[tex]\text{This implies that,}[/tex]

[tex]1=k(3)\\k=\frac{1}{3}[/tex][tex]\text{Hence the constant of variation is}[/tex] ⇒ [tex]\frac{1}{3}[/tex]

The equation would be ⇒ [tex]y=\frac{1}{3} x[/tex]

The mean and the standard deviation are 233 and 208.95 respectively.

The mean of a distribution is its average, while the standard deviation is the summary of how far each data in the dataset, is to the mean.

First, we calculate the class midpoint (x) from the given intervals.

The class midpoint is the average of the intervals. So, we have:

X1 = (0+199)/2 = 99.5

X2 = (200+399)/2 = 299.5

X3 = (400+599)/2 = 499.5

X4 = (600+799)/2 = 699.5

X5 = (800+999)/2 = 899.5

X6 = (1000+1199)/2 = 1099.5

X7 = (1200+1399)/2 = 1299.5

So, the table becomes:

X values Frequency (f)

99.5 345

299.5 97

499.5 52

699.5 21

899.5 9

1099.5 8

1299.5 3

The mean of the distribution is:

This gives:

Mean = (99.5*345)+(299.5*97)+(499.5*52)+(699.5*21)+(899.5*9)+(1099.5*8)+(1299.5*3)/(345+97+52+21+9+8+3)

Mean = 124832.5/535 = 233

Therefore, Mean = 233

The standard deviation is calculated as follows:

So, we have:

Б =

√(99.5*(345-233)²+((299.5-233)² * 97)+((499.5-233)² * 52)+((699.5-233)² * 21)+((899.5-233)² * 9)+((1099.5-233)² * 8)+((1299.5- 233)² * 3)/ (345+97+52+21+9+8+3)

Standard Deviation = √(23357155.5)/535

        = √43658.23

        = 208.95

Б = 208.95

Hence, the mean and the standard deviation are 233 and 208.95 respectively.

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Answer:

there is no answer

Step-by-step explanation:

If you multiply 15^x by 15^y, the answer is 15^(x+y) so 2 plus -7 is negitive 5.

but there is no answer equal to this.

The equivalent expression will be;

⇒ 15⁻⁵

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The expression is,

⇒ (15²) × (15⁻⁷)

Now,

Since, The expression is,

⇒ (15²) × (15⁻⁷)

Hence, We solve as;

⇒ (15²) × (15⁻⁷)

⇒  15²⁻⁷

⇒ 15⁻⁵

⇒ 1 / 15⁵

Thus, The equivalent expression is,

⇒ 15⁻⁵

⇒ 1 / 15⁵

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Answer:

I think YZ 'cause the triangle is iscoceles triangle. As the two sides XY and XZ are equal the longest side is YZ.