What is the value of the expression below?​

Thus, the p-value is greater than 0.10 (the significance level α), indicating that there is not enough evidence to support the alternative hypothesis.

To find the p-value, we need to calculate the test statistic and compare it to the critical value.

Given:

Sample 1: sample size (n1) = 22, variance (\(s_{1}^2\))

= 8, mean (x1(bar))

= 51

Sample 2: sample size (n2) = 20, variance (\(s_{2}^2)\)

= 11, mean (x2(bar))

= 50.5

To calculate the test statistic, we can use the formula for the difference in means:

t = (x1(bar) - x2(bar)) / √((\(s_{1}^2\)/n1) + (\(s_{2}^2\)/n2))

Substituting the given values:

t = (51 - 50.5) / √((8/22) + (11/20))

  = 0.5 / √(0.3636 + 0.55)

  = 0.5 / √0.9136

  ≈ 0.53

Now we need to find the degrees of freedom. For independent samples with equal variance, the degrees of freedom (df) can be calculated using the formula:

df = n1 + n2 - 2

Substituting the given values:

df = 22 + 20 - 2

  = 40

With α = 0.10, the critical value for a one-tailed test (upper tail) with 40 degrees of freedom is 1.684.

Now, we can determine the p-value. Since the alternative hypothesis is μ1 - μ2 > 0, we are conducting an upper-tailed test.

The p-value is the probability of obtaining a test statistic as extreme as the one observed (t = 0.53) under the null hypothesis.

By comparing the test statistic to the critical value, we can determine the conclusion:

Since the test statistic (0.53) is less than the critical value (1.684), we fail to reject the null hypothesis.

Therefore, the conclusion is: "We don't have enough evidence to conclude that the difference in means is > 0; therefore, H0 is not rejected."

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Answer:

x = (y + 26)/5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

y + 6 = 5(x - 4)

Step 2: Distribute

y + 6 = 5x - 20

Step 3: Isolate x

y + 26 = 5x

Step 4: Isolate variable x

(y + 26)/5 = x

Step 5: Rewrite

x = (y + 26)/5

Answer:

y = 5x - 26

Step-by-step explanation:

Since x is the independent variable, you have to solve for y.

y + 6 = 5(x-4)

Now distribute:

y + 6 = 5x - 20

subtract the 6 from both sides

y + 6 - 6 = 5x - 20 - 6

y = 5x - 26

To find the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3, we first need to compute the derivative of the function.

f(x) = ln(4sec(x))
f'(x) = (1/sec(x)) * (4sec(x)) * tan(x) = 4tan(x)
Next, we use the arc length formula:
L = ∫ [a,b] √[1 + (f'(x))^2] dx
Substituting in the values, we get:
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
We can simplify this by using the identity 1 + tan^2(x) = sec^2(x):
L = ∫ [0,π/3] √[1 + (4tan(x))^2] dx
 = ∫ [0,π/3] √[1 + 16tan^2(x)] dx
 = ∫ [0,π/3] √[sec^2(x) + 16] dx
 = ∫ [0,π/3] √[(1 + 15cos^2(x))] dx
 = ∫ [0,π/3] √15cos^2(x) + 1 dx
Using the substitution u = cos(x), we get:
L = ∫ [0,1] √(15u^2 + 1) du
This can be solved using trigonometric substitution, but the details are beyond the scope of this answer. The final result is:
L = 4/3 * √(15) * sinh^(-1)(√15/4) - √15/2
Therefore, the length of the graph of f(x)=ln(4sec(x)) for 0≤x≤π/3 is approximately 3.195 units.

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C = 4.2919, so that Prob(miu - C< x <= miu + C) = 0.3.

In probability theory, X-N(0,4) represents a random variable X that follows a normal distribution with mean (miu) equal to 0 and standard deviation (sigma) equal to 4. We are asked to find the value of C such that the probability of X falling within the interval (miu - C, miu + C) is 0.3.

To solve this problem, we need to find the value of C such that the probability of X being greater than miu - C and less than or equal to miu + C is 0.3. This can be represented mathematically as:

Prob(miu - C < X <= miu + C) = 0.3

In a standard normal distribution, the area under the curve within a certain number of standard deviations from the mean is given by the cumulative distribution function (CDF). Since the mean of our distribution is 0 and the standard deviation is 4, we need to find the value of C such that the CDF at miu + C minus the CDF at miu - C is equal to 0.3.

By using statistical software or a standard normal distribution table, we can find the z-scores corresponding to the cumulative probabilities of (0.65, 0.85). These z-scores represent the number of standard deviations from the mean. Multiplying the z-scores by the standard deviation of 4 gives us the values of C.

After performing the calculations, we find that C is approximately equal to 4.2919 when rounded to four decimal places.

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Answer:

289 yards

Step-by-step explanation:

All you have to do is 1156 yards divided by 4 to get a grand total of 289 yards per side  

Answer:

4m+5=12

Step-by-step explanation:

4(3)+5#12

right hand side is not equal to left hand side

Answer: 4m+5=12

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

2x-5x+20=-7+5x-21

-3x-5x=-7-21-20

-8x=-48

x=6

Answer:

x=6

Step-by-step explanation:

2x-5x+20=5× -28

-3x+20=5x-28

-8x=-48

x=6

check:

2x-5(2)=-30-28

12-10=2

2=2

Step-by-step explanation:

please mark me as brainlest

Answer:

can you make it so its not green and easier to read please and thank you and once you do that then maybe i can try to help you

Step-by-step explanation:

Answer:

We get -2 < r < 3

Corresponding to the fourth choice

The fourth number line is the correct option

Step-by-step explanation:

-2 < 3r+4 < 13

We have to isolate r,

subtracting 4 from each term,

-2-4< 3r + 4 - 4 < 13 - 4

-6 < 3r < 9

divding each term by 3,

-6/3 < r < 9/3

-2 < r < 3

so, the interval is (-2,3)

or, -2 < r < 3

this corresponds to

The fourth choice (since there is no equality sign)

Answer:

I thinks it 3/10

Step-by-step explanation:

m=slope, so use the formula m=y2-y1/x2-x1 you get 3/10.

Hope this helps!

Answer:

$66.62

Step-by-step explanation:

10.25 x 6.5 = 66.625

Answer:

15

Step-by-step explanation:

Given that a1 = 6

an =  3 + 2(an-1),

Substitute n = 2 into the formula

a2 = 3 + 2(a1)

a2 = 3 + 2(6)

a2 = 3+12

a2 = 15

Hence the second term of the sequence is 15

Step-by-step explanation:

for the perimeter you have to say two brackets live plus height plus with plastic

Answer:

There is overwhelming evidence that human activities, especially burning fossil fuels, are leading to increased levels of carbon dioxide and other greenhouse gases in the atmosphere, which in turn amplify the natural greenhouse effect, causing the temperature of the Earth's atmosphere, ocean, and land surface to ...

Answer: It would be C and D

Step-by-step explanation:

By the phythagorean theorem, the 2 legs would equal to the hypothesize.

Choice A would not form a triangle.

Choice B does not follow the pythagorean theorem. 84 plus 16 does not equal 100.

Choice C does. 8 + 121 = 129.

Choice D does. 1 + 3 = 4.

Answer:  

_______________________________________

→   x  = - 1 ±  i√7     ;

                  4    

_______________________________________

Or:  Write as:

_______________________________________

 →   x  = -1  +  i√7     ;   -1  −   i√7     ;

                   4                       4  

_______________________________________

Step-by-step explanation:

_______________________________________

Given:

 -2x² − x − 1 = 0 ;

Solve for " x " .

________________

First, let us multiply BOTH sides of the equation by "-1" ;

     to get rid of that "negative sign" in the coefficient:  " -2" ;

    →  as follows:

________________

  -1 * {-2x² − x − 1 } = 0 *{-1} ;

_________________

Rewrite the value: "x" on the "left-hand side" of the question; as:  "1x" ;

since "any value" ; multipled by "1" ; results in that same individual value:

_________________

    -1 * {-2x² − 1x − 1 } = 0 *{-1} ;  

________________

Note the "distributive property" of multiplication:

________________

 a(b + c) = ab + ac ;

________________

Likewise, from the "left-hand side" of the equation:

   -1 * {-2x² − 1x − 1 } =  {-1 * -2x²}  +  {-1 * -1x}  +  {-1* -1 } ;    

                                =      2x²       +  1x           + 1 ;

_______________________________________

Rewrite the "left-hand side" of the equation:

   2x² + 1x + 1 ;

Now, the "right-hand side of the equation:

            " { 0 * -1 } = 0 " .

Now, rewrite the entire equation:

    2x² + 1x + 1 = 0 ;

________________

Note:  This equation is written in "quadratic format" ;

that is:   " ax² + bx + c " ;   [a ≠ 0] ;

         →  in which:

                   a = 2 ;  b = 1 ; c = 1 ;

________________

 →  which means we can solve for the value(s) for "x" ; by using the

"quadratic equation formula" ;

   →  that is:

________________

   →    x  = -b ± √(b² − 4ac)       ;

                           2a                      

________________

 So;  to solve for the values for "x" ;  we substitute our known values for:

    "a" ; "b" ; and "c" ; and solve:

________________

   →   x  =   -1  ±  √(1² − 4*2 *1)       ;

                              4                    

_________________________

   →   x   =    -1  ±  √(1 − 8)       ;

                            4                              

_________________________

   →   x  =   -1  ±  √(-7)     ;

                         4        

_________________________

Note: "√(-7)"  ;  is the square root of a negative number.

Note that we use the lower case  letter, " i "  ;  

        as a symbol to represent the imaginary number:  " √(-1) " .

This is an "imaginary number" ;  since one cannot take the "square root" of a "number lower than zero."  

So, we write:  √-7 ;   as:   " i * 7 " ;  or, just:  " i √7 " ;  since:

  "i  = √-1" ;  and since:  " √-7"  would "factor out" to:  "√7  * √-1 " .

_________________________

Note:  In the mainstream U.S.A. , the concept of " i " as the  "imaginary number" — " √-1 "  ;  is usually introduced in the second year college-prep algebra class (after "first year high school algebra" in 9th grade; and after "geometry" in 10th grade).

_________________________

So;  we have:

→   x  = -1  ± √(-7)     ;

                   4        

___________

We can rewrite this as:

____________

→   x  = -1  ±  i√7    ;

                   4    

_____________

  We can leave our answer written like that.

We have two (2) solutions—so we can also write out both solutions for the value of x:

_____________

 →   x  = -1  +  i√7    ;   -1  +  i√7     ;

                   4                        4

_____________________________________________

Hope this explanation is helpful to you!

  Best of luck— and best wishes!

_____________________________________________

A pencil consists of a cylindrical body (10 cm long, radius 0.3 cm) with a cone-shaped eraser (1 cm slant height) and a hemisphere-shaped eraser.

A pencil consists of three main parts: a cylindrical body, a cone-shaped eraser, and a hemisphere-shaped eraser. Let's break down the dimensions of each part:

Cylindrical Body:

Length: 10 cm

Radius: 0.3 cm

Cone-shaped Eraser:

Slant height: 1 cm (assumed height of the cone)

Hemisphere-shaped Eraser:

Since the dimensions of the hemisphere-shaped eraser are not specified in detail, we'll assume a few things:

Let's assume that the hemisphere is attached to the cone in such a way that the flat surface of the hemisphere is aligned with the circular base of the cone.

We'll assume that the radius of the hemisphere is the same as the radius of the cylindrical body, which is 0.3 cm.

Please note that the actual dimensions of a pencil can vary, and these assumptions are made for the purpose of explanation.

It's worth mentioning that the cylindrical body of the pencil is the main part used for writing, while the cone-shaped and hemisphere-shaped erasers are located at the opposite end of the pencil, typically used for erasing mistakes.

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The approximate value for e, rounded to five decimal places, is 2.71828.

The approximate value for e, rounded to five decimal places, is 2.71828.

The natural exponential function, denoted as f(x) = e^x, represents exponential growth or decay with the base e.

In this function, e is the base and x is the exponent.

The value of e is an irrational number,

which means it cannot be expressed as a fraction and its decimal representation goes on infinitely without repeating.

The value of e is approximately equal to 2.71828,

and it is often used in various fields of mathematics, such as calculus and finance, due to its unique properties.

It is an important constant in mathematics, similar to the role of π.

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Answer:

They can finish the race in 15 x 14 x 13 x 12 x 11 = 360360 order.

Step-by-step explanation:

There are 15 bicyclists in the race. The first position would come from the first bicyclist to the 15th. Meaning the first position can be occupied by 15 individuals. The second position can only be occupied by 14 individuals since one person is already first. Same way the third, fourth and fifth positions can be occupied by 13, 12 and 11 individuals respectively.

Therefore, they can finish the race in

15 x 14 x 13 x 12 x 11 = 360360 order.

If one of you has a comparative advantage at baking cookies, it means that one of you c) gives up fewer cupcakes for each cookie baked.

When manufacturing a specific good, agents in an economic model have a comparative advantage over rivals if they can do so at a lower relative opportunity cost or autarky price, that is, at a lower relative marginal cost before trade.

Comparative advantage is the term used to express the economic reality of trade-related employment advantages for individuals, businesses, or nations that result from variations in their factor endowments or technology advancement.

(The absolute advantage, comparing production per unit of time (labor efficiency) or per unit of money (monetary efficiency), is generally thought to be more intuitive but less accurate – as long as the opportunity costs of manufacturing commodities across countries differ, productive trade is conceivable.)

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By probability , S = {D, I, V, S, O, N}  is the sample space for choosing one card .

Describe probability using an example ?

A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.

                             The probability formula states that the ratio between the number of favorable outcomes and the total number of outcomes determines the likelihood that an event will occur. The number of favorable outcomes divided by the total number of outcomes is the probability of an event occurring, or P(E).

S = {V, S, I, D, I, I, N, O}

S = {D, I, S, O, N}

S = {V, I, O}

S = {D, I}

S = {D, I, V, S, O, N}  is the sample space for choosing one card .

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Answer:

T(x) or total account balance = C(x) + S(x)

Step-by-step explanation:

where = C(x) = -2401 - 140 + 1,400  

and

S(x) = 4503 + 100

This implies that:

C(x) = 3,661

S(x) = 4,603

Therefore, T(x) 3,661 + 4,603 = 8,264

T(x) is the total account balance or the addition of the balances of checking and saving accounts.

C(x) is the checking account balance.

S(x) is the saving account balance.

Answer

(On attachment)

Step-by-step explanation:

The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).

A function is a mathematical rule that gives each input value a distinct output value. A function, then, is a relationship between two sets of numbers in which each element of the first set (referred to as the domain) corresponds to exactly one element of the second set (called the range). An equation or formula that describes how input values are changed into output values defines a function, which is typically represented by a letter, such as f. For instance, the rule represented by the function f(x) = x2 produces the value x squared from any input value x.

given

We must finish the square and rewrite the function in vertex form in order to determine the vertex's coordinates for the provided function, y = x2 + 2x + 3.

y = x² + 2x + 3

y = (x + 1)² - 1 + 3 (completing the square)

y = (x + 1)² + 2 (simplifying) (simplifying)

A quadratic function's vertex form is denoted by y = a(x - h)2 + k, where (h,k) denotes the vertex's coordinates.

The vertex form of the given function reveals that a = 1, h = -1, and k = 2 are true. Hence, the vertex's coordinates are (-1, 2).

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The complete question :- Read the question and write your answer in the box provided. Your answer will be saved

Consider the function:

y = x² + 2X +3

What are the coordinates of the vertex of the given function?

Answer:

a(n)=60-30n

Step-by-step explanation:

Equation to use:

a(n) = a(1) + d(n-1)

where a(1) is the first term, d is the common difference between terms, and n is the nth term you are trying to find.

In this case, a(1) is 30, d is -30, and n is just n.

If you plug that into the equation and use the distributive property, you would get: a(n) = 30 -30n + 30.

Adding the two 30's gets you: a(n) = 60 - 30n, which is the solution.

Answer:

y=5x-1

Step-by-step explanation:

Slope-intercept form: y=mx+b

m=Slope

b=y-intercept

y=5x-1

Hope this helps!

Answer:

y=5x-1

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Diagonals of an isosceles trapezoid are congruent, so:

\(3x+18=11x-6 \\ \\ 18=8x-6 \\ \\ 8x=24 \\ \\ x=3\)

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Answer:The concentration of the salt solution is 9 g/L, which means that for every liter of water, there are 9 grams of salt dissolved in it. To determine how much salt should be added to 350 mL of water, we need to calculate how much salt is needed to make a solution with the same concentration.

We can start by calculating how many grams of salt are in one milliliter of the salt solution:

9 g/L = 9/1000 g/mL

This means that for every milliliter of the salt solution, there are 0.009 grams of salt dissolved in it.

To determine how much salt should be added to 350 mL of water, we can use the following formula:

Amount of salt = Concentration x Volume

where the concentration is in grams per milliliter, and the volume is in milliliters.

Substituting the values we have:

Amount of salt = 0.009 g/mL x 350 mL

Amount of salt = 3.15 g

Therefore, 3.15 g of salt should be added to 350 mL of water to create a salt solution with the same concentration as the original solution.

Step-by-step explanation:

Answer:

600

Step-by-step explanation:

We have to find the number of calories that 6 pounds is.

1 pound = 3500 calories

6 pounds = 6 * 3500 = 21000 calories

In 5 weeks we have 35 days. Let us divide 21000 by 35 to find how many calories that is per day:

21000 / 35 = 600

The number of calories must therefore be decreased by 600 every day.