Two dice are rolled. What is the probability that the sum of the numbers rolled is either 6 or 9? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population  'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]

Let X₂ = 25

[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

                     = P( Z≤0) - P(Z≤-2)

                     = 0.5 + A(0) - (0.5- A(-2))

                     = A(0) + A(2)        ( ∵A(-2) =A(2)

                     = 0.000+ 0.4772

                     = 0.4772

Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Answer:

the slope equation is y2 - y1 divided by x2 - x1

Step-by-step explanation:

so the answer would be 3 over 2 because of this method

Answer:

3/2

Step-by-step explanation:

Use the easy rise over run method.

start at the point (50,20) then go up 3 units and 2 units to the right to get the next point.

3/2 should be the slope.

Hope I helped you!

Answer:

don't know

Step-by-step explanation:

sorry buddy

Answer:

x = 74.3

Step-by-step explanation:

Using the trigonometric ratio formula, the missing side, x, of the right angled triangle, can be found as follows:

Ѳ = 22°,

adjacent side length = x

Opposite side length = 30

Thus, we would apply the formula:

tan Ѳ = opposite length/adjacent length

[tex] tan 22 = \frac{30}{x} [/tex]

Multiply both sides by x

[tex] tan 22*x = \frac{30}{x}*x [/tex]

[tex] tan 22*x = 30 [/tex]

[tex] 0.4040*x = 30 [/tex]

Divide both sides by 0.4040 to make x the subject of the formula

[tex] \frac{0.4040*x}{0.4040} = \frac{30}{0.4040} [/tex]

[tex] x = \frac{30}{0.4040} [/tex]

[tex] x = 74.26 [/tex]

x ≈ 74.3 (to the nearest tenth)

Answer:

2.598 and -2.598.

Step-by-step explanation:

f(x) = 2 cos x + sin 2x

f'(x) = -2 sin x + 2 cos 2x = 0   for turning points.

cos 2x =  1 - 2 sin^2 x so we have

-2 sin x + 2 - 4 sin^2 x = 0

4sin^2 x + 2 sin x - 2 = 0

2(2 sin^2 x + sin x - 1) = 0

2(2sinx - 1)(sinx + 1) = 0

sin x  = 0.5, -1   when  f(x) is at a turning point.

x = π/6,  -π/2, 5pi/6

The second derivative is  2 cos x + 2 * -2 sin 2x

= 2 cos x - 4 sin 2x

When x = π/6, this is negative , when x = -π/2 it is positive

so x = π/6 gives a maximum f(x) and x = -π/2 gives 0 so this is a point of inflection

When x = π/6 , f(x) = 2.598

When x = 5pi/6,  f(x) = -2.598.

Answer:

{$3.60; $3.68}

Step-by-step explanation:

The confidence interval for a sample of size 'n', with mean price 'X' and standard deviation 's' is determined by:

[tex]X\pm z*\frac{s}{\sqrt n}[/tex]

The z-score for a 95% confidence interval is 1.96.

Applying the given data, the lower and upper bounds of the confidence interval are:

[tex]3.64\pm 1.96*\frac{0.0835}{\sqrt 20} \\L=\$3.60\\U=\$3.68[/tex]

The confidence interval for the mean price received by farmers for corn sold in January is:

CI : {$3.60; $3.68}

Answer:

8, 8, 13

Step-by-step explanation:

The three numbers 8, 8, 13 have a range of 5.

13 - 8 = 5

The mode is 8, the repeated number.

Answer:

need pls

Step-by-step explanation:

Answer:

With 99% confidence the proportion of all smart phones that break before the warranty expires is between 0.041 and 0.069.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.055.

[tex]p=X/n=97/1750=0.055[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.055*0.945}{1750}}\\\\\\ \sigma_p=\sqrt{0.00003}=0.005[/tex]

The critical z-value for a 99% confidence interval is z=2.576.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.005=0.014[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.055-0.014=0.041\\\\UL=p+z \cdot \sigma_p = 0.055+0.014=0.069[/tex]

The 99% confidence interval for the population proportion is (0.041, 0.069).

Answer:

m = 0.5

Step-by-step explanation:

m = (y2 - y1) / (x2 - x1)

= (0.25 - 0) / (0.5 - 0)

= 0.25/0.5

= 0.5

Answer:

(D)Jaleel's method is correct because 2(x-2)=2x-4.

Step-by-step explanation:

Jaleel and Lisa are simplifying the expression 2(x-2)+2 as shown.

[tex]J$aleel's Method: \left\{\begin{array}{ccc}2 (x -2) + 2 \\= 2 x - 4 + 2 \\= 2 x - 2\end{array}\right[/tex]

[tex]L$isa's Method: \left\{\begin{array}{ccc}2 (x-2) + 2 \\= 2 x -2 + 2 \\= 2 x\end{array}\right[/tex]

We can see that Jaleel's method is correct because:

2(x-2)=2x-4.

When you expand, you must multiply the term outside by all the terms inside the bracket.

The correct option is D.

Answer:

Jaleel is correct because 2 (x minus 2) equals 2 x minus 4.

D is correct

Step-by-step explanation:

i just took the quiz.

Answer: m=0.5 or m=1/2

Step-by-step explanation:

To find the slope, you use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. Since we are given the coordinate points, we can directly plug them in.

[tex]m=\frac{0.25-0}{0.5-0} =\frac{0.25}{0.5} =0.5[/tex]

Answer:

  (x, y) = (-3, -2)

Step-by-step explanation:

Perhaps this is a system of equations you want the solution for.

Since you have an expression for y, substitution is a viable approach.

  5x +7(x+1) = -29 . . . . . . substitute for y

  12x = -36 . . . . . . subtract 7 and simplify

  x = -3 . . . . . . . . . divide by 12

  y = (-3) +1 = -2 . . . use the expression for y

The solution is (x, y) = (-3, -2).

Answer:

y = -2x +4

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -2x +4

Answer: 2 1/2 or 2.5 hours

Step-by-step explanation:

Add 360 and 330

360 + 330 = 690

Divide 1,725 by 690

1,725 / 690 = 2.5

The two planes will meet in 2.5 hours

The speed is the distance covered by an object at a particular time. The time it will take for the two planes to meet is 2.5 hours.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given that the speed of the two planes is 360 km/hr and 330 km/hr. Therefore, the relative speed of the two planes with respect to each other is,

Relative speed = 360 km/hr + 330 km/hr

                         = 690 km/hr

Now, since the total distance between the two cities is 1725 km. Therefore, the time it will take for two planes to meet is,

Time = Distance /Speed

         = 1725 km / 690 km/hr

         = 2.5 hour

Hence, the time it will take for the two planes to meet is 2.5 hours.

Learn more about Speed:

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Answer:

(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]

Step-by-step explanation:

Volume of fluid in the tank =1000 gallons

Initial Amount of Salt in the tank, A(0)= 30 pounds

Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]

The resulting mixture is pumped out at the same rate, therefore:

Rate Out =(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]

Therefore:

The rate of change of amount of salt in the tank,

[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]

Answer:

Step-by-step explanation:

The angle next to 90 degrees is also 90 degrees and it's supplementary

the angle next to 133 degrees is 47 degrees and it's also supplementary

p + 90 + 47 = 180

p + 137 = 180

p = 43 degrees

the solution is d

Answer:

d

Step-by-step explanation:

Answer:

42 m

Step-by-step explanation:

First, find <S

<S = 180 - (41+113) [ sum of angles in a triangle)

<S = 180 - 154 = 26°

Next is to find length of ST, using the law of sines: a/sin A = b/sinc B = c/sin C

Let a = RT = 28m

A = <S = 26°

b = ST

B = <R = 41°

Thus, we have:

28/sin(26°) = b/sin(41°)

Cross multiply

28*sin(41°) = b*sin(26°)

28*0.6561 = b*0.4384

18.3708 = b*0.4384

Divide both sides by 0.4384 to make b the subject of formula

18.3708/0.4384 = b

41.9041971 = b

b ≈ 42m (rounded to nearest meter)

Length of ST to nearest meter = 42 meters

Answer:

  x = 17.349

Step-by-step explanation:

The right-most x-intercept is 17.349, where the curve continues upward to the right.

Answer:

7/ (3a-1)

Step-by-step explanation:

3a^2 -13a +4        28+7a

------------------ * --------------------

9a^2 -6a+1         a^2 -16

Factor

(3a-1)(a-4)           7(4+a)

------------------ * --------------------

(3a-1) (3a-1)        (a-4)(a+4)

Cancel like terms

1                    7

------------------ * --------------------

(3a-1)                  1

Leaving

7/ (3a-1)

Answer:

It cannot be extended.

Step-by-step explanation:

Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.

In this case, consider the case in which y =0. When y=0 then

[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]

But, when x=0, we get

[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].

So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.

Answer:

a. The 95% confidence interval for the mean is (33.52, 35.48).

b. The 95% confidence interval for the mean is (34.02, 34.98).  

c. n=49 ⇒ Width = 1.95

n=196 ⇒ Width = 0.96

Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.

d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

Step-by-step explanation:

a. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=34.5.

The sample size is N=49.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]

The 95% confidence interval for the mean is (33.52, 35.48).

b. We have to calculate a 95% confidence interval for the mean.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=196-1=195[/tex]

The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]

The 95% confidence interval for the mean is (34.02, 34.98).

c. The width of the intervals is:

[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]

d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.

i think it is ur required ans..

Answer:

-2/5

Step-by-step explanation:

The slope of two parallel lines will be the same.

Here, our equation is 5y + 2x = 12. Let's find the slope by isolating y:

5y + 2x = 12

5y = -2x + 12

y = (-2/5)x + 12/5

So, the slope is -2/5.

Thus, the slope of the line parallel to the given one will be -2/5.

~ an aesthetics lover

Answer:

-2/5

Step-by-step explanation:

5y+2x=12

Solve for y

Subtract 2x

5y = -2x+12

Divide by 5

5y/5 = -2/5 x +12/5

y = -2/5x +12/5

The slope is -2/5

Parallel lines have the same slope

Answer:

0.6

Step-by-step explanation:

3+2=5

P (white) = 3/5 = 0.6

(Hopefully this works, if not, on hearty maths you can go back to your assigned tasks page and go back onto the task to get a new question if that makes sense)

Answer:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Step-by-step explanation:

In parallelogram ABCD, BC=AD

Given:

BC=(6-x) units

AD =(x+2) units

Therefore:

6-x=x+2

x+x=6-2

2x=4

x=2

BC=(6-x) units

=(6-2) units

BC=4 units

The opposite angles of a parallelogram are equal. Therefore:

[tex]m\angle BCD=m\angle BAD\\12^\circ+y^\circ=100^\circ-y^\circ\\y^\circ+y^\circ=100^\circ-12^\circ\\2y^\circ=88^\circ\\y=44^\circ[/tex]

[tex]m\angle DAB=100^\circ-y^\circ\\=100^\circ-44^\circ\\m\angle DAB=56^\circ[/tex]

Therefore, the match is:

[tex]L$ength of \overline{BC} \rightarrow 4$ units\\Value of y\rightarrow44^\circ\\m\angle DAB\rightarrow56^\circ\\$Value of x \rightarrow 2$ units[/tex]

Answer:

Step-by-step explanation:

plato i guess

Answer:

[tex]slope = \dfrac{-680}{9}[/tex]

Step-by-step explanation:

We are given coordinates of two points:

Let the points be A and  B respectively:

[tex]A(\dfrac{7}{20}, \dfrac{8}{3})\\B(\dfrac{3}{8}, \dfrac{7}{9})[/tex]

To find the slope of line AB.

Formula for slope of a line passing through two points with coordinates [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]m = \dfrac{y_2- y_1}{x_2- x_1}[/tex]

Here, we have:

[tex]x_2 = \dfrac{3}{8}\\x_1 = \dfrac{7}{20}\\y_2 = \dfrac{7}{9}\\y_1 = \dfrac{8}{3}\\[/tex]

Putting the values in formula:

[tex]m = \dfrac{\dfrac{7}{9}- \dfrac{8}{3}}{\dfrac{3}{8}- \dfrac{7}{20}}\\\Rightarrow m = \dfrac{\dfrac{7-24}{9}}{\dfrac{15-14}{40}}\\\Rightarrow m = \dfrac{\dfrac{-17}{9}}{\dfrac{1}{40}}\\\Rightarrow m = \dfrac{-17\times 40}{9}\\\Rightarrow m = \dfrac{-680}{9}[/tex]

So, the slope of line AB passing through the given coordinates is:

[tex]m = \dfrac{-680}{9}[/tex]

Answer:

The correct answer would be C

Step-by-step explanation:

please mark brainliest

The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.

From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.

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I'm pretty sure that ' HL ' stands for "hypotenuse and leg". That's the one.

-- We see the little boxes in the lower left corners, so we know that these are right triangles, and we can use the rules we know about for right triangles.

-- The hypotenuses of both triangles are marked with the same length.

-- The base legs of both triangles are marked with the same length.

-- So we have (the hypotenuse and one leg of one right triangle) equal to (the hypotenuse and corresponding leg of another right triangle). That's exactly the description of the HL conguence theorem, so we know that these two triangles are congruent.