We are given a Student's t distribution with d.f. = 11 and t = 1.910. We wish to find an interval containing the corresponding P-value for a two-tailed test. To do this, we will use the Critical values for Student's t Distribution. Below is an excerpt from this table.
one-tail area 0.250 0.125 0.100 0.075 0.050 0.025 0.010 0.005 0.0005
two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010
d.f. \ c 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999
⋮
9 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781
10 0.700 1.221 1.372 1.559 1.812 2.228 2.764 3.169 4.587
11 0.697 1.214 1.363 1.548 1.796 2.201 2.718 3.106 4.437
To determine where the given t-value would fall, we look for the row with heading d.f. =
. In this row, the sample statistic t = 1.910 falls between t = 1.796 and t =

Answer:

10

Step-by-step explanation:

[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]

Given equation:

[tex]2y=x^3+2x^2[/tex]

Isolate y by dividing both sides by 2:

[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]

Differentiate with respect to x:

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]

[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]

Finally, substitute x = 2 into the differentiated equation:

[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]

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The values of a and b of the exponential function are 10000 and 0.6 respectively

We are given that the exponential function is expressed in general form as; f(x) = abˣ

where;

a is a non-zero real number called the initial value

b is any positive real number such that

b ≠ 1.

The domain of f is all real numbers.

The range of f is all positive real numbers if a > 0.

The range of f is all negative real numbers if a < 0.

The y-intercept is (0, a)

The horizontal asymptote is; y = 0.

We are told that this exponential function passes through the coordinate points (0, 10000) and (3, 2160).

At coordinate point (0, 10000), we have;

10000 = ab⁰

a = 10000

Now, at the coordinate point (3, 2160), we have;

2160 = 10000(b)³

2160/10000 = b³

0.216 = b³

b = ∛0.216

b = 0.6

Thus, we can conclude that the values of a and b of the given exponential function are respectively 10000 and 0.6.

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the probability of getting heads on a two-face coin is simply 1/2.

now, what is the probability of getting 1/2 AND 1/2 AND 1/2 AND 1/2 AND 1/2?   well, AND means "times", namely

[tex]\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\stackrel{and}{\cdot }\cfrac{1}{2}\implies \cfrac{1}{32}[/tex]

well, and since it's a two-face coin, the probability for each face is equal, 1/2, so Heads has a chance of 1/2 each time, or we can also say that Tails has a chance of 1/2 each time, so if Tails has the same probability over 5 times as Head does.

The complete proof for part D is given in the attached text. Hence, by the nature of the converse corresponding angle,

OP is parallel to MN. (OP ║ MN).

A mathematical proof is an argument that is inferential with respect to a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.

The complete proof for part D is given as follow:

If a transversal line "t" divides through OP and MN as given in the attached image, and SE and "T.F" are the divider of ∠QSD and ∠STM, then:

∠QSE = 1/2 ∠QSO; and

∠"STF" = 1/2 ∠STM

If the corresponding angle is ∠QST = "STF", then

QSD = "STF"

Hence, by the nature of the converse corresponding angle,

OP is parallel to MN

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Answer:

8by + 2ax - 4bx - 4ay

Step-by-step explanation:

I assume you mean expand so:

(a - 2b)(3x - 5y) + (2b - a)(x - y)

3ax - 5ay - 6bx + 10by + 2bx - 2by - ax + ay

Now collect like terms:

2ax - 4ay - 4bx + 8by

This is your answer but in a better order:

8by + 2ax - 4bx - 4ay

The percentage of students that have scored more than you is 1.39%

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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Subtracting 4 from both sides of the equation ¹/₂x = -¹/₂ gives us; ¹/₂x - 4 = -¹/₂ - 4

We want to simply the expression which is;

¹/₂x = -¹/₂

Now, when we subtract 4 from both sides, it means we are using subtraction property of equality which states that subtracting the same value from both sides of an equation makes the equation still to be equal. Thus, we have;

¹/₂x - 4 = -¹/₂ - 4

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I assume you're asked to compute

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx[/tex]

using both of the substitutions provided.

With [tex]u=x-4[/tex], we have [tex]x=u+4[/tex] and [tex]dx=du[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{30(u+4)^2}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \frac{u^2 + 8u + 16}{\sqrt u} \, du \\\\ ~~~~~~~~ = 30 \int \left(u^{3/2} + 8u^{1/2} + 16u^{-1/2}\right) \, du \\\\ ~~~~~~~~ = 30 \left(\frac25 u^{5/2} + \frac{16}3 u^{3/2} + 32 u^{1/2}\right) + C \\\\ ~~~~~~~~ = 12 u^{5/2} + 160 u^{3/2} + 960 u^{1/2} + C \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4 \sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

With [tex]u=\sqrt{x-4}[/tex], we have

[tex]u^2 = x-4 \implies x^2 = (u^2+4)^2[/tex]

and [tex]2u\,du=dx[/tex]. Then

[tex]\displaystyle \int \frac{30x^2}{\sqrt{x-4}} \, dx = \int \frac{60u \left(u^2+4\right)^2}u \, du \\\\ ~~~~~~~~ = 60 \int \left(u^4 + 8u^2 + 16\right) \, du  \\\\ ~~~~~~~~ = 60 \left(\frac15 u^5 + \frac83 u^3 + 16u\right) + C  \\\\ ~~~~~~~~ = 12 (x-4)^{5/2} + 160 (x-4)^{3/2} + 960 (x-4)^{1/2} + C \\\\ ~~~~~~~~ = 4 \sqrt{x-4} \left(3 (x-4)^2 + 40 (x-4) + 240\right) + C \\\\ ~~~~~~~~ = \boxed{4\sqrt{x-4} \left(3x^2 + 16x + 128\right) + C}[/tex]

The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

Other functions are nonlinear

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Answer:

You will need 187 80 pounds bags of concrete.

Step-by-step explanation:

12x14x(2/3) x 0.6 = 186.666 or 187

Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7

The resulting equation will represent a line whose slope is 1/2 times the slope of the line

The equation of the line is given as:

y = 3x/a + 5

The constant a is a positive constant.

So, when the value of a in the equation is doubled, we have:

y = 3x/2a + 5

A linear equation is represented as

y = mx + b

Where m represents the slope.

So, we have:

m1 = 3/a

m2 = 3/2a

Substitute m1 = 3/a in m2 = 3/2a

m2 = 1/2 * m1

Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line

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Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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The probability is P = 0.135

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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The estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

Fractions describe the regions of a complete or group of objects. A fraction contains two regions. The number on the top of the line exists named the numerator. It describes how many equivalent regions of the real or group stand accepted. The number below the line exists named the denominator. It exhibits the total number of equivalent regions the whole exists divided into or the total number of the exact objects in a group.

The value of 5,016 can be simplified by using a fraction

Consider a denominator 19, then

19 divided by 5,016, then we get

19 and 5016 have a common divisor of 19.

then, we get

19 / 5016 = 1 / 264

Now, you need to divide.

1 / 264 ≈ 0.00379

Therefore, the estimated value of 5,016 exists 1 / 264 ≈ 0.00379.

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The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

The function is given as:

y = 2∕3 cos(4∕7x) + 2.

The above function is a cosine function

A cosine function is represented as:

y = A cos(B(x + C)) + D

Where the period is

Period = 2π/B

By comparing the equations, we have

B = 4/7

Substitute B = 4/7 in Period = 2π/B

Period = 2π/(4/7)

Express as product

Period = 2π * 7/4

Divide 4 by 2

Period = π * 7/2

Evaluate the product

Period = 7/2π

Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

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According to the data, the cost of this house would increase by 0.08 thousand dollars ($80) for each additional square foot of living space.

By critically observing the scatter plot, we can logically deduce that it shows a linear trend. Thus, the slope of the line of best fit is given by a ratio of change in cost to the change in living space.

Next, we would approximate two points on the line of best fit and then find the slope as follows:

Slope, m = ΔC/Δx

Slope, m = (C₂ - C₁)/(x₂ - x₁)

Slope, m = (400 - 200)/(4000 - 1500)

Slope, m = 0.08.

Therefore, the cost of this house would increase by approximately 0.08 thousand dollars ($80) for each additional square foot of living space.

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Using simple interest, it is found that the APR is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Answer:

M = $2.5; V = $5

Step-by-step explanation:

We need to set up a system of equations to find the price for both movies (M) and video games (V).

We can use 2M + 5V = 30 and 8M + 3V = 35

We can use elimination:

[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]

Answer:

3x(10x10x10): 3x(1000): 3000-7000: -4000. (8x(-5)): -40. (4x4) +(2x2): (16 +4): 20

a. The reason why this question is a binomial experiment is based on the fact that it is made up of an independent sample, it has a number that is fixed and a probability.

Each event is made up of two outcomes and they are random with the same success rate.

we have the following data n = 12, p = 0.27 and k = 5

We have to use the function to solve electronically

binompdf(n,p,k)

input the values

= binompdf(12,0.27,5)

This gives us

= 0.1255

We use the formula below

= binompdf(12,0.27,5-1)

This is = 0.7984

D. Probability of at least 5

1 - probability of fewer than 5

= 1 - 0.7984

= 0.2016

How to solve for the Mean = n*p

n = 12 , p = 0.27

Mean = 12*0.27 = 3.24

and

standard deviation = √npq

n = 12, p = 0.27 , q = 1- 0.27

= 0.73

sd = √12*.27*.73

= 1.54

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The difference of two squares is (5x+3y) (5x-3y)

The difference of two squares of variables a and b is represented as:

(a + b)(a - b) = a^2 - b^2

By comparing the list of options, we have:

(5x+3y) (5x-3y)

This means that

a = 5x and b = 3y

Hence, the difference of two squares is (5x+3y) (5x-3y)

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The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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The amount of paint that would be contained in each of the can would be 8.

Using the information in the question we have the following

We have to solve the equation as

(2  1/2)   + 2(4)  + 1(5  1/2)  =

2.5 + 8 + 5.5

= 16

Each of these would have to hold 16/2 = 8 pints.

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Answer:

4 pints

Step-by-step explanation:

the expert is wrong

Rational expressions are often used in combining rates of work. Therefore, it's true.

It should be noted that a rational expression is simply defined by a rational fraction.

They're are used in combining rates of work. Fir example, if Mr John performs 1/2 of his work and does 1/3 on another day. This can be expressed as:

= 1/2 + 1/3

= 5/6

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Answer:

5040 is the right answer

Step-by-step explanation:

5040/1=5040

5040/2=2520

5040/3=1680

5040/4=1260

5040/5=1008

5040/6=840

5040/7=720

5040/8=630

5040/9=560

5040/10=504

From the Δ YWZ we get c = 5 then the value of  [tex]$a= 5 \frac{1}{3}[/tex].

In the given Δ YWZ

WZ² = YW² + YZ²

c² = 4² + 3² = 16 + 9 = 25

c = 5

In the Δ XYW

b² = 4² + a²-----(1)

In the right-angle Δ WXZ

(a + 3)² = b² + c²

a² + 9 + 6a = b²+ c²

By putting the value of b² from (1)

a² + 9 + 6a = 16 + a² + 25

Simplifying the above equation, we get

6a + 9 = 41

6a = 41 - 9

6a = 32

[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]

[tex]$a= 5 \frac{1}{3}[/tex]

Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].

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Answer:

THE ANSWER for this IS d) 53

The value of x from the figure is 70°

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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The complex conjugate roots exists A = -1 - 4i or A = -1 + 12i.

If one of the roots exists w = B + 2i, then the other root exists its conjugate w = B - 2i. So we can factorize the quadratic to

[tex]z^2+4z+20+iz(A+1) = (z-(B+2i))(z-(B-2i))[/tex]

Expand the right side and collect all the coefficients.

[tex]z^2+(4+(A+1)i)z+20 = z^2-2Bz+B^2+4[/tex]

From the z and constant terms, we have

[tex]$\left \{ {{4+(A+1)i = -2B} \atop {20 = B^2+4}} \right.[/tex]

From the second equation, we get

[tex]B^2 = 16[/tex]

B = ± 4

Then 4+(A+1)i = ± 8

(A + 1)i = 4 or (A + 1)i = -12

Since [tex]$\frac{1}{i} = -i[/tex], we have

[tex]$\frac{-A+1}{i} =4[/tex] or [tex]$\frac{-A+1}{i} =-12[/tex]

A+1 = -4i or A+1 = 12i

A = -1-4i or A = -1+12i

Therefore, the complex conjugate roots exists A = -1-4i or A = -1+12i.

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