what is the slope of (-3,4) (-2,0)

Answer:

The  t-statistic is \(t = 0.6956\)

Step-by-step explanation:

From the question we are told that

     The population mean is  \(\mu = 22 \ minutes\)

       The standard deviation is  \(s = 7.043\)

       The  given data is  23, 35, 17, 30, 20, and 19.

Generally the sample mean is mathematically evaluated as

      \(\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}\)

     \(\= x =24\)

The t-statistic is mathematically evaluated as

       \(t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }\)

=>   \(t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }\)

=>   \(t = 0.6956\)

Answer: 0.70

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

We have the sum of first n terms of an AP,

Sn = n/2 [2a+(n−1)d]

Given,

36= 6/2 [2a+(6−1)d]

12=2a+5d ---------(1)

256= 16/2 [2a+(16−1)d]

32=2a+15d ---------(2)

Subtracting, (1) from (2)

32−12=2a+15d−(2a+5d)

20=10d ⟹d=2

Substituting for d in (1),

12=2a+5(2)=2(a+5)

6=a+5 ⟹a=1

∴ The sum of first 10 terms of an AP,

S10 = 10/2 [2(1)+(10−1)2]

S10 =5[2+18]

S10 =100

This is the sum of the first 10 terms.

Hope it will help.

\(\sf\underline{\underline{Question:}}\)

If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.

$\sf\underline{\underline{Solution:}}$

$\space$

$\sf\underline\bold\red{||Step-by-Step||}$

$\sf\bold{Given:}$

$\space$

$\sf\bold{To\:find:}$

$\space$

$\sf\bold{Formula\:we\:are\:using:}$

$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$

$\space$

$\sf\bold{Substituting\:the\:values:}$

→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$

→ $\sf{36 = 3[2a+(6-1)d]}$

→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$

$\space$

$\sf\bold{Again,Substituting \: the\:values:}$

→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$

→ $\sf{255=8[2a + (16-1)d]}$

:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$

→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$

$\space$

$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$

→ $\sf{10=20}$

→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$

$\space$

$\sf\bold{Putting \: d=2\: in \:equation - 1:}$

→ $\sf{12=2a+5\times 2}$

→ $\sf{a = 1}$

$\space$

$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$

$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$

$\mapsto$ $\sf{5(2\times1+9\times2)}$

$\mapsto$ $\sf\bold\purple{5(2+18)=100}$

$\space$

$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$

_____________________________

Answer:

Step-by-step explanation:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)

Lets look at the derivative part:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)

\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)

Substituting in eq(1), we have:

\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)

Answer:

4x+10+2x-1=9x-15;

6x+9=9x-15;

6x-9x=-15-9;

-3x=-24;

3x=24;

from which

x=24:3=8

Then:

DF=9x-15=(9×8)-15=72-15=57

Was this helpful

Answer:

5216.844

Step-by-step explanation:

Let x be the fourth number.

We know that the sum of the four numbers is 20500:

2341.578 + 10690 + x + 2341.578 = 20500

Simplifying and solving for x:

x = 20500 - 2341.578 - 10690 - 2341.578

x = 5216.844

Answer:22

Step-by-step explanation:27-5

In order to simplify the expression

y² + 11y - 6y + y²,

we just have to add the terms with the same unkowns or combine like terms

terms with y: +11y and -6y

terms with y²: +y² and +y²

Now, we combine like terms:

terms with y: +11y - 6y = 5y

terms with y²: +y² + y² = 2y²

Then

y² + 11y - 6y + y²

= 2y² + 5y

Answer: y² + 11y - 6y + y² = 2y² + 5y

Answer:

If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.

Step-by-step explanation:

Answer:

Thanks

Step-by-step explanation:

and also check out the language

Answer: 8 (5+x)

Step-by-step explanation:

Answer:

The equation of the line with a slope of 2 and a y-intercept of 4 in the slope-intercept is:

Hence, option 'A' is correct.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

In our case, we are given

substituting m = 2 and b = 4 in the slope-intercept form of the line equation

y = mx+b

y = 2x + 4

Therefore, the equation of the line with a slope of 2 and a y-intercept of 4 in the slope-intercept is:

Hence, option 'A' is correct.

Answer:

4.53 x 11 = 49.83

Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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Answer: 5/6

Step-by-step explanation:

2 and 1/2 = 2.5

2.5 / 3 = 5/6 = 0.8333333

don't u have a calculator?

The sum of three consecutive numbers for 150 is 49,50,51.

Three consecutive numbers:  x+(x+1)+(x+2)

x+x+1+x+2= 150

3x+3 = 150

3x = 150-3

3x= 147

X = 147/3

49 =x

But we also need to find (x+1) and (x+2)

49+1= 50

49+2= 51

49+50+51 = 150

The three consecutive numbers are 49,50,51.

Meaning: Numbers that follow one another numbers sequentially are known as consecutive numbers. The difference between any two numbers is always 1. A series of numbers' mean and median are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.

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Diane plans to arrive at 7:30 A.M.

Time is a notion that is used to quantify the length and progression of occurrences. It is a key aspect of how things work and can be expressed in terms of hours, minutes, seconds, and other time intervals. Time helps us schedule, coordinate, and comprehend the sequence of events in our daily lives. It also enables us to arrange and synchronize activities.

If we take the assumed intended arrival time of 8:00 A.M. and deduct Diane's anticipated arrival time of 30 minutes, we get the intended arrival time.

Therefore, Diane plans to arrive at 7:30 A.M.

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Answer:

Divide by P

Step-by-step explanation:

i = P x M

divide by P to get M alone, which means you have to do it to both sides

i/P = M

Answer:

He was an Anti-federalist

Step-by-step explanation:

Answer:

Anti-federalist

Step-by-step explanation:

The Federalists, led by Secretary of Treasury Alexander Hamilton, wanted a strong central government, while the Anti-Federalists, led by Secretary of State Thomas Jefferson, advocated states' rights instead of centralized power.

Answer:

Well on my end i got 47.12, with pi included

Step-by-step explanation:

The surface area of the cylinder with the diameter 2cm and height 15cm  is \(100.48 \; cm^2\)

Calculation to find Surface area of cylinder:

Given the diameter of the cylinder is 2cm and height  15cm

Formula :

The surface area of the cylinder =\(2\pi r^2+2\pi rh\)

where 'r' is the radius and 'h' is the height of the cylinder

Diameter = 2cm

\(radius =\frac{diameter }{2} =\frac{2}{2} =1\)

radius = 1cm and height is 15 cm

the value of pi is 3.14

Substiute all the values

\(SA = 2\pi r^2+2\pi rh\\SA=2(3.14)(1)^2+2(3.14)(1)(15)\\SA=6.28+94.2\\SA=100.48 cm^2\)

The surface area of the cylinder with the diameter 2cm and height 15cm  is \(100.48 \; cm^2\)

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An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Using equations, the time for the main engine 14.4 seconds and 21.6 seconds for the auxiliary engine

Let's call the time each engine takes to consume its allotted fuel supply as "t₁" for the main engine and "t₂" for the auxiliary engine.

From the first piece of information, we know:

t₁ = (2/3)t₂

From the second piece of information, we know that the combined fuel consumption time for both engines is 36 seconds:

t₁ + t₂ = 36

Now we can substitute the first equation into the second:

t₁ + (2/3)t₂ = 36

Combining like terms:

t₂ = 21.6

Finally, substituting t₂ back into the first equation:

t₁ = (2/3)(21.6) = 14.4

So the main engine alone could be fired for 14.4 seconds and the auxiliary engine alone could be fired for 21.6 seconds.

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Given the graph of the function

We will check the discontinuity of the function at x = -3

So, as shown in the graph :

as the function reach to x = -3 from the right and the left , the value of the function = -1

But at x = -3 , the function does not have a value

So, there is a discontinuity at x = -3, but can be removed if f(-3) = -1

So, the answer is : option A

There is a discontinuity that can be removed by defining f(-3) = -1

Answer:

C.) y = 3(x - 3)(x - 7)

For the function:

Writing equation:

y = a(x - h)² + k

15 = a(8 - 5)² - 12

15 = 9a - 12

9a = 15 + 12

9a = 27

a = 3

So the equation is:

y = 3(x - 5)² - 12

y = 3(x² - 10x + 25) - 12

y = 3x² - 30x + 63

y = 3(x - 3)(x - 7)

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

X¹= -2 + 2√33

X²= -2 - 2√33

Step-by-step explanation:

X × (X+2) = 32

X² + 2X = 32

X² + 2X - 32= 0

Δ=132

X= -2 ± 2√33

X¹= -2 + 2√33

X²= -2 - 2√33

(You can change the 2√33 to 11,5 if you want to)

The minimum profit occurs at L = 0, where Q = 0.

To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).

We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.

Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.

Testing for critical points:Q = L²\(e^{(0.01L)\)

Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)

= 0(2L + 0.01L²) \(e^{(0.01L)\)

= 0L (critical point) or 200 \(e^{(0.01L)\)

= 0 (extraneous, ignore)

2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)

The only critical point is at L = 0.

Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)

= \(2e^{(0)\) = 2Since Q''(0) > 0,

The critical point at L = 0 is a minimum.

Therefore, there is no value of L that maximizes the profit.

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The values of L that will maximize the profit are 0 and -200

From the question, we have the following parameters that can be used in our computation:

\(Q = L\²e^{0.01L\)

Differentiate the function

So, we have

\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)

Set the equation to 0

\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)

Cross multiply

\(L \cdot (L + 200) \cdot e^{0.01L} =0\)

When expanded, we have

L = 0, L + 200 = 0 and \(e^{0.01L} =0\)

When solved for L, we have

L = 0 and L = -200

Hence, the values of L are 0 and -200

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