Given the contingency table shown here find P(V or S)

Answer:

Step-by-step explanation:

(a) Land Purchase:

Land - $6,670,800

Cash - $6,670,800

(b) Machinery Cost and Installation:

Machinery - $1,648,080

Cash - $1,648,080

(c) First Five Months' Depletion assuming zero net salvage value:

Depletion per ton = ($6,670,800 - $0) / 7,848,000 tons = $0.85 per ton

Depletion expense = $0.85 per ton x 402,750 tons = $342,387

Ore Inventory - $342,387

Accumulated Depletion - $342,387

(d) First Five Months' Depreciation on Machinery:

Depreciation expense = (Machinery cost / Estimated recoverable ore) x Tons of ore removed

Depreciation expense = ($1,648,080 / 7,848,000 tons) x 402,750 tons = $84,513

Depreciation Expense - $84,513

Accumulated Depreciation - $84,513

The number which is neither prime οr cοmpοsite is 1.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here the number between 1 tο 16 is,

=> 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16.

Prime numbers are the number which is divided by 1 and itself. Then,

Prime numbers = 2,3,5,7,11,13

Cοmpοsite numbers are numbers which are have mοre than οne factοrs. Then,

Cοmpοsite numbers = 4,6,8,9,10,12,14,15,16.

Then number which is neither prime nοr cοmpοsite is 1.

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A parallelogram-shaped carpet has a surface area of 216 ft², according to the statement. The diameter of a mat is 12 feet, and it has an 18-foot base.

A rectangle possesses all the characteristics of a parallelogram since it contains two pairs of opposing sides that become consistent and two sets of equal spacing. As a square is always a parallelogram, this is the case. A parallelogram, however, is not invariably a rectangle.

Using the equation:

A = b*h

h = A/b

h = 216/18

h = 12 feet

The carpets is 12 feet high as a result.

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Dilations involve changing the size of a triangle, the correct options are (a), (c) and (f)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, the coordinates of a triangle are, A = (-2, 4), B = (-2, 8) and C = (6, 4).

The coordinates of the image of the triangle are given as:

A' = (-0.25, 0.5)

Scale factor = A' / A

K = 0.5/4 = 1/8

The coordinates of C' = (6, 4) x 1/8 = (0.75, 0.5)

The coordinates of B' = (-2, 8) x 1/8 = (-0.25, 1)

Hence, the true options are (a), (c) and (f)

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The equation of the parabola is y = (x + 2)² - 5. The correct option is E.

Since the directrix of the parabola is a horizontal line with equation y = -6 and the focus is the point (-2,-4), the parabola opens upward.

The vertex of the parabola is halfway between the focus and the directrix, which is the point (-2, -5). Therefore, the equation of the parabola in vertex form is:

y = a(x + 2²) - 5

Where a is a constant that determines the shape and size of the parabola.

To find the value of a, we use the fact that the distance between the focus and the vertex is equal to the absolute value of the constant a. The distance between (-2,-4) and (-2,-5) is 1, so we have:

|a| = 1

Since the parabola opens upward, a is positive, so we can write:

a = 1

Substituting this value of an into the vertex form equation, we get:

y = (x + 2)² - 5

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The correct options are given below.

A) y=1/8(x-2)²-5

B) y=-1/8(x+2²+5

C) y=1/4(x+2)²-5

D) y=-1/4(x - 2)²- 5

E) y = ( x + 2 )² - 5

An equation of the line that is parallel to the line y = 9 and passes through the point (3, -8) is y = -8.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 0 = 0

At point (3, -8), an equation of this line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

y - (-8) = 0(x - 3)

y + 8 = 0(x - 3)

y = -8.

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The expression in a fewer number of terms is y² + 4y +1

From the question, we have the following parameters that can be used in our computation:

y² + 3y +1+y​

Collect the like terms

So, we have the following representation

y² + 3y + y +1

Evaluate the like terms

y² + 4y +1

Hence, the expression is y² + 4y +1

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The chairs are congruent because they have the same shape and size.

What is Congruence?

In mathematics, congruence is a relationship between two shapes that have the same size and shape, and can be superimposed onto each other through rigid motions, such as translation or rotation, without changing their shape or size. Congruent shapes have corresponding angles and sides that are equal in length.

One example of a set of congruent figures in a house could be a set of identical dining chairs. The chairs are congruent because they have the same shape and size. Each chair has the same dimensions and angles, so they can be superimposed onto each other through rigid motions, such as translation or rotation, without changing their shape or size. Therefore, they are considered to be congruent.

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Step-by-step explanation:

very quick : as the new plant is shorter than all the others, it will decrease the mean value.

the only answer option with "decrease" is the 4th one and correct.

If another plant with a height of 11 inches is added to the data, the mean would increase in value to about 17.2 inches. The correct option is c.

Data analysis is the methodical application of logical and/or statistical approaches to describe and demonstrate, summarize and assess, and assess data.

here, we have,

from the given information, we get,

Every time we make a decision in daily life, as a simple example of data analysis, we consider what happened previously or what would happen if we make that particular choice.

The original mean of the 14 plants is 17.1

The new mean with the 23 in. plant is 17.2

Therefore, the correct option is c. The mean would increase in value to about 17.2 inches.

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To find (f - h)(x), we need to subtract h(x) from f(x), term by term.

f(x) = x^2 - x

h(x) = x^2 + 2x - 63

So, (f - h)(x) = f(x) - h(x) = (x^2 - x) - (x^2 + 2x - 63)

Simplifying this expression, we get:

(f - h)(x) = x^2 - x - x^2 - 2x + 63

= -3x + 63

Therefore, the function (f - h)(x) is equal to -3x + 63.

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Step-by-step explanation:

To solve the differential equation (2tx + 3t^2)x' = x^2, we can use separation of variables method:

First, we separate the variables:

x^-2 dx/dt = (2tx + 3t^2)^-1 dt

Next, we integrate both sides:

∫x^-2 dx = ∫(2tx + 3t^2)^-1 dt

Using u-substitution with u = 2tx + 3t^2, du/dt = 2x + 6t, and du = (2x + 6t)dt, we get:

-x^-1 = (1/6) ln|2tx + 3t^2| + C

where C is the constant of integration.

Now, we can use the initial conditions to solve for the constant C:

(a) x(1) = 5:

-5^-1 = (1/6) ln|2t(1) + 3(1)^2| + C

-6 = ln|2t + 3| + C

C = -6 - ln|2t + 3|

Therefore, the solution for x as a function of t with initial condition x(1) = 5 is:

x(t) = (-1/6) - (1/6) ln|2t + 3|

(b) x(1) = −3:

-3^-1 = (1/6) ln|2t(1) + 3(1)^2| + C

-2 = ln|2t + 3| + C

C = -2 - ln|2t + 3|

Therefore, the solution for x as a function of t with initial condition x(1) = −3 is:

x(t) = (-1/3) - (1/6) ln|2t + 3|

Answer:

Step-by-step explanation:

first start by reading the question then under line key deatails then gather the key deatails you read from the question then try to solve your problem

Answer:

Step-by-step explanation:

a)  (0, 12)

b)  12

P = 12 x 1.4⁰ = 12

c) P = 12 x 1.4³ ≈ 33 rabbits

The unknown digit in the number 3___5 is 1, and the number is 315.

We must examine the divisibility rule for 3 in order to determine what the unknown digit in the number 3 5 could be.

A number is three digits divisible if the sum of its digits is three digits divisible.

The equation is 3000 + 10x + 5, where x is the undetermined digit.

The number can be written as follows since the sum of its digits is divisible by three:

3 is divisible by the sum 3 + 0 + 0 + 0 + x + 5.

By condensing, we discover that x + 8 is divisible by 3.

Only one number, 1, makes the sum of x + 8 divisible by three.

The number 3 5 therefore has 1 for the unknown digit, making it 315.

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The amount that needs to be deposited in the account today is 4,097.72.

We are to determine the present value of $5000 given quarterly compounding with an interest rate of 4%.

Present value is the discounted value of a cash flow.

Present value = FV ÷ [1 + r]^nt

Where:

P = 5,000 ÷ [1 + 0.01]^(5 x 4)

P = 5000 ÷ [1.01^20]

P = 4,097.72

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Answer:

(5, -6)

Step-by-step explanation:

We have the two equations

[tex]\begin{aligned}2ax + 2y &= b \cdots\cdots [1]\\ 5 x + y &= -6 \cdots\cdots [2]\\\end{aligned}\\[/tex]

Multiply equation [2] by 2

[tex]10x + 2y = -6 \cdots\cdots[3][/tex]

There will be an infinite number of solutions when both equations [1] and [3] are exactly the same:
For this to happen the right sides must be the same
So b = -6

Also 2ax = 10x
so 2a = 10

a = 5

So the ordered pair(5, -6) results in an infinite number of solutions

Step-by-step explanation:

Here are the first four iterations of a Sierpinski triangle that is a scalene triangle:

/\

/__\

/\ /\

/__\/__\

/\ /\

/__\ /__\

/\ /\ /\ /\

/__\/__\/__\/__\

/\ /\

/__\ /__\

/\ /\ /\ /\

/__\/__\ /__\/__\

the values of given questions  are:

Σx = 115

Σf² = 877

Σxf = 1573

How to do and what is statistics?

Using the values given:

Σx = 25 + 24 + 20 + 25 + 21 = 115

To find Σf², we need to square each value of f and sum them:

Σf² = 19² + 27² + 12² + 15² + 13² = 877

To find Σxf, we need to multiply each value of x by its corresponding value of f and sum them:

Σxf = (25)(19) + (24)(27) + (20)(12) + (25)(15) + (21)(13) = 1573

Therefore, the values are:

Σx = 115

Σf² = 877

Σxf = 1573

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical methods to make sense of numerical data and to draw conclusions about populations or samples based on that data.

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Conclusion: There is sufficient evidence to say that, this represents a difference from the national average

Step 1)

Null hypothesis

H  o : μ = 8.5

Alternative hypothesis

[tex]H_{1}:\mu\neq 8.5[/tex]

Step 2)

i.e. Z critical values are for two-tailed alternative hypothesis at [tex]a-0.05 =\pm 1.96[/tex]

Step 3)

We have been given,

Using the Z test statistic formula

Z = 2.17

Step 4 ) Z test statistic value is 2.17 > Z critical value 1.96

Therefore, we reject H0 at a-0.05

Step 5) Conclusion: There is sufficient evidence to say that, this represents a difference from the national average

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A rectangular park with dimensions of 115 yards by 60 yards

To compute the area of a rectangle, multiply its base (width) by its height (length), A = b h. A rectangle's perimeter equals P = 2 b + 2 h, where is the base (or width) and is the height (or length).

If a rectangular park has a length of 105 yards and a width of 70 yards, its perimeter would be:

Perimeter = 2(Length + Width) = 2(105 + 70) = 350 yards

To find the length and width of another rectangular park with the same perimeter but a larger area, we need to keep the perimeter constant but increase the length or width, or both.

One way to do this is to keep the width the same and increase the length. Let's say we increase the length by 10 yards. The new length would be 105 + 10 = 115 yards. The perimeter of the new rectangular park would still be 350 yards, since we have not changed the width:

New Perimeter = 2(New Length + Width) = 2(115 + 70) = 370 yards

To calculate the width of the new rectangular park, we can use the formula for the area of a rectangle:

Area = Length x Width

The area of the original rectangular shape  park is:

Area = 105 x 70 = 7,350 square yards

To increase the area of the new park, we need to make the width larger. Let's call the new width "W". We can set up an equation based on the fact that the new rectangular park must have the same perimeter as the original:

2(New Length + W) = 350

Substituting in the value of the new length, we get:

2(115 + W) = 350

Simplifying and solving for W, we get:

230 + 2W = 350

2W = 120

W = 60

So the new rectangular park would have a length of 115 yards and a width of 60 yards. The perimeter of the new park is 350 yards, which is the same as the original park, but the area of the new park is larger:

Area = Length x Width = 115 x 60 = 6,900 square yards

Therefore, a rectangular park with dimensions of 115 yards by 60 yards would have the same perimeter but a larger area than a rectangular park with dimensions of 105 yards by 70 yards.

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Answer:

An error of p percent in the radius will cause an error of approximately 2p percent in the volume of the can.

To see why, we use differentials. We have:

v = pi r^2 h

Taking the differential with respect to r, we get:

dv = 2pi rh dr + pi r^2 dh

Dividing both sides by v, we get:

dv/v = 2(r/h)dr + (r^2/h)dh

If we assume that the percentage error in the radius is p, then dr = (p/100)r. Substituting this into the previous equation, we get:

dv/v = 2(p/100)(r/h) + (r^2/h)dh

The first term represents the error due to the radius, and the second term represents the error due to the height.

If we assume that the percentage error in the height is p, then dh = (p/100)h. Substituting this into the previous equation, we get:

dv/v = 2(r/h)dr + (p/100)(r^2/h)

= (2r/h)(p/100)r + (r^2/h)(p/100)

= (p/100)(2r^2/h + r^2/h)

= (p/100)(3r^2/h)

Therefore, an error of p percent in the height will cause an error of approximately (3p/100) percent in the volume of the can

Answer:

  100°

Step-by-step explanation:

You want the measure of angle θ = ∠BDC in the figure of isosceles triangle ABC with vertex angle A=40° and interior point D such that AD≅BC and ∠BAD = 10°.

We can define the midpoint of BC as the origin of a coordinate plane, and points B(-1, 0) and C(1, 0). Then point A will be located at A(0, tan(70°)).

Point D will be located at 2∠-100° from A, since AD=BC=2 units, and D is located 10° west of south relative to A.

This locates point D on the coordinate grid.

To find the angle between DC and DB, we can divide vector DC by vector DB. The angle of the quotient is the angle between those vectors. The calculator result in the second attachment shows the angle is 100°, in agreement with the geometry program's result in the first attachment.

  θ = 100°

Given our assignment of a length of 2 to AD and BC, we know the lengths of AC and AB are sec(70°) ≈ 2.9238. This lets us use the law of cosines to find lengths DC and DB:

  CD = √(2.9238² +2² -2·2.9238·2·cos(30°)) ≈ 1.5557

  DB = √(2.9238² +2² -2·2.9238·2·cos(10°)) ≈ 1.0154

Then the law of cosines can be used again to find θ.

  θ = arccos((1.5557² +1.0154² -2²)/(2·1.5557·1.1054))

  θ = 100°

The third attachment shows a geometrical solution to finding the angle. We define O as the center of the circle. Angle BAC is an inscribed angle of 40°, so angle BOC will be double that value, 80°.

Locating point G so that AOG is 80° makes segment AG the same length as segments AB and AD. AO bisects angle A, so angle GAD is 10° less than angle GAO, making ∆GAD~∆ACG and locating point D on segment AG. While point D can be shown to lie on segment AG using angle sums, it takes Law of Sines and Law of Cosines relations to demonstrate that point D lies on segment BO, which it does.

The angle of interest, BDC, is an external angle to triangle COD. As such, its measure is the sum of the remote interior angles of that triangle:

  ∠BDC = 80° +20°

  ∠BDC = 100°

Answer:

y = -x + 4

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (4,0) and (3, 1)

We see the y increase by 1 and the x decrease by 1, so the slope is

m = -1

Y-intercept is located at (0,4)

So, our equation is y = -x + 4

The radius of the sphere to the nearest tenth of a meter 5.8 meters.

A sphere is simply a three dimensional solid, that has all its surface points at equal distances from the center.

The volume of a sphere is expressed as;

V  = (4/3) × π × r³

Where V is the volume of the sphere and r is the radius.

Given the data in the question;

To find the radius of a sphere with a given volume, we can use the formula for the volume of a sphere:

V = (4/3) × π × r³

We can rearrange the formula to solve for r:

r = (3V / 4π)^(1/3)

Plugging in the given volume V = 802 m³ we get:

r = (3(802) / 4(3.14)^(1/3)

r = ( 191.56 )^(1/3)

r = 5.8m

Therefore, the radius of the sphere is 5.8 meters.

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The answer is 9,000

You first multiply 36 by 50 to get 1,800. You then multiply 1,800 by 5 to get the answer of 9,000.

Answer:

45

Step-by-step explanation:

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

[tex](0.31)^4=0.00923521[/tex]

please give the height of the pool

Formula Is :

SA=2lw+2lh+2hw

The proportional relationship between the distance (d) traveled by a car and time (t) is shown in the graph attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 10/1 = 10.

In this exercise, we would use an online graphing calculator to plot the proportional relationship between the distance (d) traveled by a car and time (t) as shown in the graph attached below.

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