Sample _________ play a very critical role to determine whether or not to ""reject the null hypothesis"" or ""do not reject the null hypothesis"".

Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2  such that f'(c) = 0.

Given:

Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.

f(x)=x^2−4x+8, [0,4]

when, x = 0

f(x) = x^2 -4x +8

f(0) = y = 0 - 0 + 8 = 8

when, x=4

f(5) = y = 16 - 16+8 =

thus, we have 2 points (0, 8) ; (4, 8)

slope,m = {8-(8)} / {4-0} = 0

hence, we have to calculate all the points,x where 0<x<8 and slope=0

f '(x) = 2x - 4 = 0

or, f '(c) = 2c - 4 = 0

c = 4/2 =2 ( 0<x<4)

hence, the there is only one solution c=2 which satisfies Rolle's theorem.

Learn more about the rolle's theorem here:

https://brainly.com/question/13972986

#SPJ4

Answer:

23.9 mm

Step-by-step explanation:

A cube can be unfolded into the net shown below. Find the total

surface area of the cube.

23.9 mm

Answer:

The equation would be wrote (5/25 ÷ 10/25)

The answer is FALSE. The alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.

The alternative hypothesis is a statement that contradicts the null hypothesis and is generally the hypothesis that the researcher wants to support. It is a statement that there is a difference or an effect in the population being studied.

In hypothesis testing, the null hypothesis is a statement that there is no difference or no effect in the population being studied. The null hypothesis is typically the default hypothesis, which is assumed to be true unless evidence suggests otherwise. The alternative hypothesis, on the other hand, is a statement that there is a difference or an effect in the population being studied, and it is typically the hypothesis that the researcher wants to support.

For example, if a researcher wants to test the effectiveness of a new drug, the null hypothesis might be that the drug has no effect on the condition being treated, while the alternative hypothesis might be that the drug has a positive effect on the condition being treated.

In summary, the alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.

To know more about hypothesis:

https://brainly.com/question/14957391

#SPJ11

Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Factors of 51: 1, 3, 17, 51

Factors of 68: 1, 2, 4, 17, 34, 68

As you can see the greatest common factor of both numbers is 17.

Therefore, the answer is C.

Best of Luck!

we know that

The formula for combinations is

\(C=n!/[(n-r)!*r!]\)

where

\(n\) is the total number of objects you choose from

\(r\) is the number that you choose to arrange

in this problem

\(n=15\) students

\(r=4\) students

\(C=15!/[(15-4)!*4!]\) → \(C=15!/[11!*4!]\) → \((15*14*13*12*11!)/(11!*4*3*2*1)\)

\(C=(15*14*13*12)/(24)\) → \(C=1365\)

the answer is

1,365

Answer:

Step-by-step explanation:

distributive

In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expansion is given by the following formula: \(\left(a + b\right)^{n} = \sum_{k=0}^{n} {\binom{n}{k}} a^{n - k} b^{k}\), where \({\binom{n}{k}} = \frac{n!}{\left(n - k\right)! k!}\)

As given to us, a = 2a, b = 4 b, and n = 8.

Therefore, \(\left(2 a + 4 b\right)^{8} = \sum_{k=0}^{8} {\binom{8}{k}} \left(2 a\right)^{8 - k} \left(4 b\right)^{k}(2a+4b)\).

Thus, \(\left(2 a + 4 b\right)^{8} = 256 a^{8} + 4096 a^{7} b + 28672 a^{6} b^{2} + 114688 a^{5} b^{3} + 286720 a^{4} b^{4} + 458752 a^{3} b^{5} + 458752 a^{2} b^{6} + 262144 a b^{7} + 65536 b^{8}.\)

Hence, In the expansion of (2a+4b)⁸ the possible variable terms are a⁸, a⁵b³, a³b⁵, a⁷b, and b⁸.

Learn more about Expression:

https://brainly.com/question/13947055

#SPJ1

Answer:

The circumference of any circle is 2πr, where r is the radius.

Step-by-step explanation:

Answer:

If $x=3$, then $y=2*3^{3}$. Using order of operations, we evaluate the exponent first, then perform the multiplication:

\begin{align*}

y &= 2 * 3^{3} \\

&= 2 * 27 \\

&= 54

\end{align*}

Therefore, $y=54$.

Answer:

yes, because 6 is less than 11

Step-by-step explanation:

Hope this helps!!
Mark me brianliest and good luck!!

The solution of the division of the fraction is expressed as; -⁴/₁₅

When dividing fractions, what will carry out first is to turn it into multiplication. Thereafter, we will make use of the multiplicative inverse (reciprocal) to multiply.

We have the expression as;

-¹/₃ ÷ ⁵/₄

By the method described above, we can say that the solution is;

-¹/₃ × ⁴/₅

= -⁴/₁₅

Read more about Fraction division at; https://brainly.com/question/4917910

#SPJ1

Answer:

1 or x (the equation is y=x+1)

Step-by-step explanation:

Answer:

5.5

Step-by-step explanation:

Add each side of the triangle.

3z+z+1+4z-3 = 8z - 2

8z - 2 is equivalent to the  perimeter.

Since you know the perimeter is 38 units, you can set 8z-2 to 38.

8z-2 = 38

Solve for z. Subtract 2 from each side.

8z = 36

Divide each side by 8.

z = 4.5

Now solve for side WX.

WX = z + 1

WX = 4.5 + 1

WX = 5.5

\(\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=65\pi \end{cases}\implies 65\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3}{4\pi}\cdot 65\pi =r^3 \\\\\\ \cfrac{195}{4}=r^3\implies \sqrt[3]{\cfrac{195}{4}}=r\implies 3.65\approx r\)

Answer:

given in picture

Step-by-step explanation:

(-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,-5)

Answer:

Las tres líneas coinciden cada 90 minutos, es decir, al mismo tiempo que pasa el Rápido, con lo cual en ningún momento coinciden todas las líneas menos el Rápido.

Step-by-step explanation:

Dado que la Línea 6 pasa cada 45 minutos, la Línea 15 pasa cada 15 minutos, la Línea 10 pasa cada 30 minutos, y los Rápidos por autopista pasan cada 90 minutos, para determinar si coinciden en algún momento todas las líneas, menos el rápido, se deben realizar los siguientes cálculos:

Línea 6 = 00:45, 01:30, 02:15, 03:00

Línea 15 = 00:15, 00:30, 00:45, 01:00, 01:15, 01:30, 01:45, 02:00, 02:15, 02.30, 02:45, 03:00

Línea 10 = 00:30, 01:00, 01:30, 02:00, 02:30, 03:00

Rápido = 01:30, 03:00

Así, como puede verse, las tres líneas coinciden cada 90 minutos, es decir, al mismo tiempo que pasa el Rápido, con lo cual en ningún momento coinciden todas las líneas menos el Rápido.

Answer:

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

r=√15.60509554,√15.60509554

r=15.60509554,15.60509554

Decimal Form:

r=3.95032853…,3.95032853…

Answer:

I believe it's either between a or d

Step-by-step explanation:

I am not really sure but hope it helps

Hope you also have a great day!

Here is step-by-step answer.

Step 1b: Fill in your times tables answers in sequence and check if you got them all right. Step 2: Drag the correct answers to the questions. Step 3: Fill in your answers for the mixed questions and check if you got them all right. Step 4: Multiple choice questions will help you to improve by looking at the questions in a different way.

a) The composition Rα ◦ Rβ rotates the space R2 by an angle of (α + β) counter-clockwise around the origin.

b) The standard matrix of Rα ◦ Rβ is \begin{bmatrix} cos(α + β) & -sin(α + β) \ sin(α + β) & cos(α + β) \end{bmatrix}.

c) The standard matrix of Rα ◦ Rβ is calculated by multiplying the standard matrices of Rα and Rβ.

d) The formulas for sin(α + β) and cos(α + β) in terms of sin(α), sin(β), cos(α), and cos(β) are: sin(α + β) = sin(α)cos(β) + cos(α)sin(β) and cos(α + β) = cos(α)cos(β) - sin(α)sin(β).

a) Geometrically, the composition Rα ◦ Rβ is the rotation of R2 counter-clockwise around the origin by an angle of (α + β). This is because Rα rotates R2 counter-clockwise around the origin by an angle of α, and Rβ rotates R2 counter-clockwise around the origin by an angle of β. This composition is therefore rotating the space R2 by an angle of (α + β).

b) The standard matrix of the composition Rα ◦ Rβ is:

\begin{bmatrix}
   cos(α + β)       & -sin(α + β) \\
   sin(α + β)       & cos(α + β)
\end{bmatrix}


c) We can also use the properties of matrix multiplication to find the standard matrix of the composition Rα ◦ Rβ. We know that the standard matrices for Rα and Rβ are:

Rα = \begin{bmatrix}
   cos(α)       & -sin(α) \\
   sin(α)       & cos(α)
\end{bmatrix}

Rβ = \begin{bmatrix}
   cos(β)       & -sin(β) \\
   sin(β)       & cos(β)
\end{bmatrix}


Therefore, the standard matrix of the composition Rα ◦ Rβ is:

Rα ◦ Rβ = \begin{bmatrix}
   cos(α)cos(β) - sin(α)sin(β)       & -sin(α)cos(β) - cos(α)sin(β) \\
   cos(α)sin(β) + sin(α)cos(β)       & sin(α)sin(β) + cos(α)cos(β)
\end{bmatrix}


d) By comparing our two standard matrices for Rα ◦ Rβ, we can see that:

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

Therefore, the composition of Rα and Rβ rotates the space R2 by an angle of (α + β) counter-clockwise around the origin, and its standard matrix is calculated by multiplying the standard matrices of Rα and Rβ.

To know more about standard matrix click here:

https://brainly.com/question/31040879

#SPJ11

Answer:

10(6 + 4  + 5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can calculate probability by looking at the outcomes of an experiment or by reasoning about the possible outcomes.

Compare 1/7 to consecutive multiples of 1/9. This is easily done by converting the fractions to a common denominator of LCM(7, 9) = 63:

1/9 = 7/63

2/9 = 14/63

while

1/7 = 9/63

Then 1/7 falls between 1/9 and 2/9, so 1/7 = 1/9 plus some remainder. In particular,

1/7 = 1/9¹ + 2/63.

We do the same sort of comparison with the remainder 2/63 and multiples of 1/9² = 1/81. We have LCM(63, 9²) = 567, and

1/9² = 7/567

2/9² = 14/567

3/9² = 21/567

while

2/63 = 18/567

Then

2/63 = 2/9² + 4/567

so

1/7 = 1/9¹ + 2/9² + 4/567

Compare 4/567 with multiples of 1/9³ = 1/729. LCM(567, 9³) = 5103, and

1/9³ = 7/5103

2/9³ = 14/5103

3/9³ = 21/5103

4/9³ = 28/5103

5/9³ = 35/5103

6/9³ = 42/5103

while

4/567 = 36/5103

so that

4/567 = 5/9³ + 1/5103

and so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/5103

Next, LCM(5103, 9⁴) = 45927, and

1/9⁴ = 7/45927

2/9⁴ = 14/45927

while

1/5103 = 9/45927

Then

1/5103 = 1/9⁴ + 2/45927

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/45927

One last time: LCM(45927, 9⁵) = 413343, and

1/9⁵ = 7/413343

2/9⁵ = 14/413343

3/9⁵ = 21/413343

while

2/45927 = 18/413343

Then

2/45927 = 2/9⁵ + remainder

so

1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/9⁵ + remainder

Then the base 9 expansion of 1/7 is

0.12512..._9

Answer:

Given:

To Find:

Solution:

★ Firstly, we have to find the amount:

According, to the question by using the formula, we get:

\( \longmapsto \: { \bold{ \boxed{\pink{ \rm{A \: = P \left( 1 + \frac{ \frac{r}{2} }{100} \right)^{2n} }}}}}\)

Here,

So by putting their values, we get:

\( { \large{\longrightarrow{ \rm{A = 5000 \left( 1 + \frac{ \frac{10}{2} }{100} \right)^{2 \times 2} }}}}\)

\( { \large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10}{2} \times \frac{1}{100} \right)^{4} }}}}\)

\( {\large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10 \times 1}{2 \times 100} \right)^{4} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left(1 + \frac{10}{200} \right)^{4} }}}}\)

\({ \large \longrightarrow {\rm{A =5000 \left( \frac{200 \times 1 + 10}{200} \right)^{4} }}}\)

\({ \large \longrightarrow{ \rm{A = 5000 \left( \frac{200 + 10}{200} \right)^{4} }}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \right)^{4} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210 \times 210 \times 210 \times 210}{200 \times 200 \times 200 \times 200} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{1944810000}{1600000000} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{1944810000}{1600000000} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{194481}{160000} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5 \times \frac{194481}{160} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = \frac{972405}{160} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 6077.53 \: (approx.)}}}}\)

Hence, the amount is Rs 6078.

★ Now, we have to find the compound Interest:

According, to the question by using the formula, we get:

\({ \large{ \dashrightarrow{ \boxed{\green{ \rm{Compound \: Interest = A \: - \: P}}}}}}\)

Here,

So, by putting their values we get:-

\( { \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 6078 \: - \: Rs \: 5000}}}}\)

\({ \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 1078}}}}\)

Hence, Compound Interest is Rs 1078.

Answer:

$768

Step-by-step explanation:

8 x 12 = 96 m²

1 m² = $8.00

96m² x $8.00 = $768

To find the slope of the tangent line at t = -1, we need to take the derivative of the function with respect to t and evaluate it at t = -1. We have the derivative, we substitute t = -1 to find the slope of the tangent line at that point.

The points where the tangent line is vertical or horizontal occur when the derivative is either undefined or equal to zero.

To find the slope of the tangent line at t = -1, we differentiate the given function with respect to t. Let's assume the function is denoted by y(t). We calculate dy/dt, which represents the derivative of y with respect to t. Once we have the derivative, we substitute t = -1 to find the slope of the tangent line at that point.

To find the points where the tangent line is vertical or horizontal, we set the derivative equal to zero and solve for t. This will give us the values of t where the tangent line is horizontal. To find the points where the tangent line is vertical, we look for values of t where the derivative is undefined. These points correspond to vertical tangents on the graph of the function.

Learn more about function here: brainly.com/question/30721594

#SPJ11

The sum of integers is: S = n(a + l)/2

Integer numbers are those without fractional or decimal parts. When there are fewer numbers to add, it is possible to determine the sum of integers using basic mathematics. However, we employ the sum of integers formula if we need to add multiple consecutive integers at once. Our computations are made easier, and the amount of time we spend adding is reduced.

The sum of an arithmetic sequence's n terms is what is meant by the sum of integers formula. The formula for the sum of integers is:

S = n(a + l)/2

where,

S = sum of the consecutive integers

n= number of integers

a= first term

l = last term

Know more about Integer at:

https://brainly.com/question/26009132

#SPJ4