A group of students were asked to choose their favorite course. The results are shown in the two-way frequency table. Which of the following can be concluded from the joint and marginal frequencies of the table? Math is the most popular subject in the 10th grade. History is the least popular subject in the 9th grade. Science is more popular than math among 12th grade students. Students in the 11th grade like English more than students in the 12th grade. The overall favorite course is history.

A.) III and IV only
B.) II and V only
C.) I, III, and V
D.) II and IV only

Answer:

x = -1.964636

Step-by-step explanation:

Given equation;

eˣ = 4 - x²

This can be re-written as;

eˣ - 4 + x² = 0

Let

f(x) = eˣ - 4 + x²    -----------(i)

To use Newton's method, we need to get the first derivative of the above equation as follows;

f¹(x) = eˣ - 0 + 2x

f¹(x) = eˣ + 2x         -----------(ii)

The graph of f(x) has been attached to this response.

As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.

Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0

From Newton's method,

[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]

=> When n=0, the equation becomes;

[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]

[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]

Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;

f(-2) = e⁻² - 4 + (-2)²

f(-2) = e⁻² = 0.13533528323

And;

f¹(2) = e⁻² + 2(-2)

f¹(2) = e⁻² - 4 = -3.8646647167

Therefore

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]

[tex]x_{1} = -2 - -0.03501863503[/tex]

[tex]x_{1} = -2 + 0.03501863503[/tex]

[tex]x_{1} = -1.9649813649[/tex]

[tex]x_{1} = -1.96498136[/tex]         [to 8 decimal places]

=> When n=1, the equation becomes;

[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]

[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]

Following the same procedure as above we have

[tex]x_{2} = -1.96463563[/tex]

=> When n=2, the equation becomes;

[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]

[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]

Following the same procedure as above we have

[tex]x_{3} = -1.96463560[/tex]

From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately  -1.964636 to 6 decimal places.

Newton's method of approximation is one of the several ways of estimating values.

The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

The equation is given as:

[tex]\mathbf{e^x = 4 - x^2}[/tex]

Equate to 0

[tex]\mathbf{4 - x^2 = 0}[/tex]

So, we have:

[tex]\mathbf{x^2 = 4}[/tex]

Take square roots of both sides

[tex]\mathbf{ x= \pm 2}[/tex]

So, the negative root is:

[tex]\mathbf{x = -2}[/tex]

[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]

Differentiate

[tex]\mathbf{f'(x) = e^x +2x }[/tex]

Using Newton's method of approximation, we have:

[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]

When x = -2, we have:

[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]

[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]

So, we have:

[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]

[tex]\mathbf{x_{1} = -1.96498136}[/tex]

Repeat the above process for repeated x values.

We have:

[tex]\mathbf{x_{2} = -1.96463563}[/tex]

[tex]\mathbf{x_{3} = -1.96463560}[/tex]

Up till the 6th decimal places,

[tex]\mathbf{x_2 = x_3}[/tex]

Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]

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Answer:

b, c, e

Step-by-step explanation:

the reasons have to include an angle from both of the parallel lines. by using process of elimination it is b, c, e. I also got it right

Answer:

B. a=d

C. c=d

E. b + d=180°

Step-by-step explanation:

Got Correct On MyPath.

Answer:

The answer is #3 which is 24%.

Step-by-step explanation:

6 × 100

25

25 into 100 is 4, then 6×4 = 24%

I really hope this helps :)

Answer:

5u+8

Step-by-step explanation:

Both of the 4's will cancel out with each other.

5u+8. it works actuallly by taking common nunbers and cancelling them. in this case. 4. leaving it with just 5u+8 :)

Answer:

The expression that fits into the box is x¹⁵⁸

Step-by-step explanation:

Let the empty box be y

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Here, we will apply the laws of indices.

The laws of indices gives the answer for the expressions

1) xᵏ × xˢ = xᵏ⁺ˢ

2) xᵏ ÷ xˢ = xᵏ⁻ˢ

3) (xᵏ)ˢ = xᵏ•ˢ

So,

(x¹²)⁵ = x⁶⁰

(x⁻²)⁹ = x⁻¹⁸

(x⁴⁰)⁵ = x²⁰⁰

(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵

Becomes

x⁶⁰ × x⁻¹⁸ × y = x²⁰⁰

x⁶⁰⁻¹⁸ × y = x²⁰⁰

x⁴² × y = x²⁰⁰

y = x²⁰⁰ ÷ x⁴²

y = x²⁰⁰⁻⁴² = x¹⁵⁸

Hope this Helps!!!

Answer:

The possible arrangement= 18 ways

Step-by-step explanation:

Six identical coin are tossed.

Coin has only a tail and a head.

In how many possible ways can the arrangement be 3 head and 3 tail.

The possible arrangement= (3! * 3!)/2

The reason for dividing by two because coin has two face.

The possible arrangement= (3! * 3!)/2

The possible arrangement=( 6*6)/2

The possible arrangement= 36/2

The possible arrangement= 18 ways

Answer:

184, 185, 186

Step-by-step explanation:

If the first number is x, the other numbers are x + 1 and x + 2, therefore we can write:

x + x + 1 + x + 2 = 555

3x + 3 = 555

3x = 552

x = 184 so the other numbers are 185 and 186.

Answer:

504 ways.

Step-by-step explanation:

In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.

The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).

9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.

Hope this helps!

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{3375} - \sqrt[4]{38416}[/tex]

Factorizing 3375 gives 15 * 15 * 15 which equals 15^3 and factorizing 38416 gives 14 * 14 * 14 * 14 which equals 14^4

=> [tex]\sqrt[3]{15^3} - \sqrt[4]{14^4}[/tex]

=> 15 - 14

=> 1

Answer:

Step-by-step explanation:

[tex] \sqrt[3]{3375} - \sqrt[4]{38416} [/tex]

Calculate the cube root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{38416} [/tex]

Calculate the root

[tex] \sqrt[3]{ {15}^{3} } - \sqrt[4]{ {14}^{4} } [/tex]

[tex] {15}^{ \frac{3}{3} } - {14}^{ \frac{4}{4} } [/tex]

[tex]15 - 14[/tex]

Subtract the numbers

[tex]1[/tex]

Hope this helps...

Answer:

0.8390

Step-by-step explanation:

From the question,

Z score = (Value-mean)/standard deviation

Z score = (150.2-160.5)/10.4

Z score = -0.9904.

P(x>Z) = 1- P(x<Z)

From the Z table,

P(x<Z) = 0.16099

Therefore,

P(x>Z) = 1-0.16099

P(x>Z) = 0.8390

Hence the probability that a person weighs more than 150.2 pounds = 0.8390

Answer:

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Step-by-step explanation:

GIven that :

sample size n = 17

sample mean [tex]\overline x[/tex] = 97.5

standard deviation [tex]\sigma[/tex] = 21.9

At 95% Confidence interval

the level of significance ∝ = 1 - 0.95

the level of significance ∝ =  0.05

[tex]t_{\alpha/2} = 0.025[/tex]

Degree of freedom df = n - 1

Degree of freedom df = 17 - 1

Degree of freedom df = 16

At ∝ =  0.05 and df = 16 , the two tailed critical value from the t-table [tex]t_{\alpha/2 , 16}[/tex] is :2.1199

Therefore; at 95% confidence interval; the mean wake time is:

= [tex]\overline x \pm t_{\alpha/2,df} \dfrac{s}{\sqrt{n}}[/tex]

= [tex]97.5 \pm 2.1199 \times \dfrac{21.9}{\sqrt{17}}[/tex]

= 97.5 ± 11.2599

= (86.2401 , 108.7599)

Therefore; the mean wake time before the treatment was 104.0 min

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Answer:

m<1 = 50

Step-by-step explanation:

We can first find the angle next to 140, by doing 180 - 40 = 40.

Now that we know that one of the triangles angle is 40, we also know that there's a 90 degree angle, so we can do:

180 - 90 - 40 = 50

So m<1 = 50

The question in part c is not clear, nevertheless, part a and part b would be solved.

Answer:

a. The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

b. The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Step-by-step explanation:

a. Given

an + 2 = an + an + 1

where a1 = 1 and a2 = 1.

a3 = a1 + a2

= 2

a4 = a2 + a3

= 3

a5 = a3 + a4

= 5

a6 = a5 + a4

= 8

a7 = a6 + a5

= 13

a8 = a7 + a6

= 21

a9 = a8 + a7

= 34

a10 = a9 + a8

= 55

a11 = a10 + a9

= 89

a12 = a11 + a10

= 144

The first twelve terms are:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.

(b)

Given

bn = an+1/an

b1 = a2/a1

= 1/1 = 1.000

b2 = a3/a2

= 2/1 = 1.000

b3 = a4/a3

= 3/2 = 1.500

b4 = a5/a4

= 5/3 = 1.667

b5 = a6/a5

= 8/5 = 1.600

b6 = a7/a6

= 13/8 = 1.625

b7 = a8/a7

= 21/13 = 1.615

b8 = a9/a8

= 34/21 = 1.619

b9 = a10/a9

= 55/34 = 1.618

b10 = a11/a10

= 89/55 = 1.618

The first ten terms are:

1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.

Answer:

36 cups of Chex total.

Step-by-step explanation:

Well, he will obviously be using 12 cups of pretzels, so let's set that aside. For every cup of pretzels, there are 3 cups of chex. So, multiply 3x12. That will give you how much chex you will need.

Answer:

253°

Step-by-step explanation:

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: 253°

The solution is, the measure of Arc A D B is 253°.

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

Here, we have,

given that AC and BD are diameters of circle O.

AC and BD intersect at point C the centre of the circle.

The central angle of a circle is the angle based at the circle's center. In other words, the vertex of the angle must be at the center of the circle. A central angle is formed by two radii that start at the center and intersect the circle itself.

The central angle whose rays intercept a diameter of the circle has measure 180 deg.

m<AOD = 73 deg

m<DOB = 180 deg

m<ADB = m<AOD +m<DOB = 73 deg + 180 deg = 253 deg

The measure of an arc of a circle is equal to the measure of the central angle that subtends it.

m(arc)AOD = m<AOD = 253 deg

Answer: the measure of Arc A D B is 253°.

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Answer:

$1387.4

Step-by-step explanation:

Total cost for the computer will be sum of down payments and monthly installments.

____________________________________

Given

down payment = $200

monthly installment value = $98.85

no. of installments = 12

total value of monthly installments = 12*98.95 = $1187.4

Total cost of computer system = $200+  $1187.4 = $1387.4

Answer:

14v - 5

Step-by-step explanation:

The product of 14 and v is 14v. 5 less than that is 14v - 5.

Answer:

7v = 119

Step-by-step explanation:

Answer:

I'm not entirely sure what you are asking, could you comment on this answer the full question so I can edit this question to provide you an answer?

Answer: biosphere

Step-by-step explanation:

I am not sure what picture you are looking at but if it is 3 barbeque chicken legs in one image than this is your answer. The reason being that chickens can only be found on land and the land is considered part of the biosphere because bio = life

Answer:

The correct answer is option a.

a. 5( √3+ 1 )

Step-by-step explanation:

Given that the angle changes from 45° to 60° in 10 minutes.

This situation can be represented as right angled triangles [tex]\triangle[/tex]ABC (in the starting when angle is 45°)and [tex]\triangle[/tex]ABD (after 10 minutes when the angle is 60°).

AB is the tower (A be its top and B be its base).

Now, we need to find the time to be taken to cover the distance D to B.

First of all, let us consider [tex]\triangle[/tex]ABC.

Using tangent property:

[tex]tan\theta =\dfrac{Perpendicular}{Base}\\\Rightarrow tan 45=\dfrac{AB}{BC}\\\Rightarrow 1=\dfrac{h}{BC}\\\Rightarrow h = BC[/tex]

Using tangent property in [tex]\triangle[/tex]ABD:

[tex]\Rightarrow tan 60=\dfrac{AB}{BD}\\\Rightarrow \sqrt3=\dfrac{h}{BD}\\\Rightarrow BD = \dfrac{h}{ \sqrt3}\ units[/tex]

Now distance traveled in 10 minutes, CD  = BC - BD

[tex]\Rightarrow h - \dfrac{h}{\sqrt3}\\\Rightarrow \dfrac{(\sqrt3-1)h}{\sqrt3}[/tex]

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

[tex]\Rightarrow \dfrac{(\sqrt3-1)h}{10\sqrt3}[/tex]

Now, we can say that more distance to be traveled to reach the base of tower is BD i.e. '[tex]\bold{\dfrac{h}{\sqrt3}}[/tex]'

So, more time required = Distance left divided by Speed

[tex]\Rightarrow \dfrac{\dfrac{h}{\sqrt3}}{\dfrac{(\sqrt3-1)h}{10\sqrt3}}\\\Rightarrow \dfrac{h\times 10\sqrt3}{\sqrt3(\sqrt3-1)h}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{(\sqrt3-1)(\sqrt3+1)} (\text{Rationalizing the denominator})\\\Rightarrow \dfrac{10 (\sqrt3+1)}{3-1}\\\Rightarrow \dfrac{10 (\sqrt3+1)}{2}\\\Rightarrow 5(\sqrt3+1)}[/tex]

So, The correct answer is option a.

a. 5( √3+ 1 )

Answer:

A. 1 4/6 cups of blueberries

Step-by-step explanation:

1 -- 2/3                      

Proportion, Batches to Blueberries

1*(2 1/2) -- (2/3)( 2 1/2)              

Because we are now multiplying the 1 batch to 2 1/2 batches. So to keep the proportion balanced/equal we are using the same operation on the right side of the proportion

2 1/2 -- (2/3)( 5/2 )      

2 1/2 -- 5/3

2 1/2 -- 1 2/3

Simplify

On the right side shows the blueberries for 2 1/2 batches. 1 2/3 = 1 4/6    

Hope that helps! Tell me if you need more info

Answer: $34.18

Step-by-step explanation:

Let the cost of the Jacket = $x and

The cost of the sweater. = $y

Now total price. = $71.55.

So, $x + $y. = $71.55 -- 1

From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation

y = ( x - $3.19 )

Now substitute for y in the equation (1) above.

x + ( x - 3.19 ) = 71.55

Now solve the equation

x + x - 3.19 = 71.55

2x - 3.19. = 71.55

2x = 71.55 + 3.19

2x. = 74.74

x = 74.74/2

= $37.37. cost of the jacket

Now to determine the cost of the sweater,

$71.55 - $37.37 = $34.18

The cost of the sweater = $34.18.

Answer:

13°

Step-by-step explanation:

The trigonometric ratio formula can be used in calculating the angle of elevation (x°) of the sun, as the person makes a right angle with the ground.

The height of the person would be the opposite length = 6 ft, the shadow of the person would be the adjacent length = 26 ft

Therefore, according to the trigonometric ratio formula, we would calculate angle of elevation (x°) as follows:

[tex] tan x = \frac{opposite}{adjacent} [/tex]

[tex] tan x = \frac{6}{26} [/tex]

[tex] tan x = 0.2308 [/tex]

x = tan-¹(0.2308)

x = 12.996

x ≈ 13° (to the nearest whole degree)

The angle of elevation of the sun = 13°

Answer:

111.33667

Step-by-step explanation:

You add percentages just like you would any other number.

122.9%   +   108.46%  +   102.65% = 334.01%

334.01%/3 = 111.33667

Answer:

40

Step-by-step explanation:

The measure of m∠B in the triangle is 40°.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Since the triangles are congruent, we know that their corresponding angles are congruent as well.

Therefore, we have:

m∠B = m∠F = 40°.

Note that we also have:

m∠C = m∠A = 80° (by corresponding angles)

m∠H = m∠G = 60° (by corresponding angles)

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find the measure of angle D:

m∠D = 180° - m∠B - m∠C = 180° - 40° - 80° = 60°.

Therefore,

m∠B = 40°.

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Answer:

y = -(1/2)x+1

Step-by-step explanation:

-2Y - X = -2

Add x to both sides:

-2Y = X - 2

Divide both sides by -2:

Y = -(1/2)x+1

You could also use the shortcuts:

For Ay+Bx=C, the slope is -B/A and the y-intercept is C/A.

Slope = -B/A = -(-1)/(-2) = 1/-2 = -(1/2)

Y-intercept = C/A = (-2)/(-2) = 1

y = mx + b ---> y = -(1/2)x + 1

Answer:

y = -1/2x +1

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

-2y -x = -2

Solve for y

Add x to each side

-2y = x-2

Divide by -2

-2y/2- = x/-2 -2/-2

y = -1/2x +1

Answer:  B) 10 three-point questions and 14 five-point questions

Step-by-step explanation:

x represents three-point questions

y represents five-point questions

3x + 5y = 100  →  1(3x + 5y = 100)  =  3x + 5y = 100

 x  +  y  = 24   → -3(x  +  y  = 24)   = -3x  -3y  = -72

                                                                  2y = 28

                                                                    y = 14  (five-point questions)

x +  y = 24

x + 14 = 24

     x = 10  (three-point questions)

Answer:

a =7.5

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 10 ^2 = 12.5^2

a^2 + 100  =156.25

Subtract 100 from each side

a^2 = 56.25

Take the square root of each side

sqrt(a^2) = sqrt( 56.25)

a =7.5

Answer:

  216

Step-by-step explanation:

  y = ±√36 = ±6

  y³ = (±6)³ = ±216

The largest of these values is 216, the greatest possible value of y.

Answer:

area = 1800 m²

Step-by-step explanation:

area of one triangle = 900 m²

if a parallelogram has the same height and base as the triangle, then that means the area or the two triangle and shaped as a parallelogram

is twice the area given.

area = 900 * 2

area = 1800 m²

Answer:

7 cm

Step-by-step explanation:

14 / 2 = 7 cm

7cm is the distance Harry needs to walk on the map?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.

Given that,

Harry is trying to complete his hill walking scouts badge.

He is using a map with a scale of 1 cm : 2 km.

To earn the badge he needs to walk 14 km.

Let the distance he needs to walk on the map is x.

By given data we write an equation

1/2=x/14

Apply Cross Multiplication

14/2=x

7=x

Hence, 7cm is the distance he needs to walk on the map.

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