Enter the correct answer in the box. Write your answer in the form y - mx + b, using the appropriate inequality symbol in place of
the equal sign.
What inequality is shown in the graph?

Answer:

Surface area of cube = 6x²

surface area of cube = surface area of sphere

it means that 6x²=4πr²

x²=

\( \frac{4\pi {r}^{2} }{6} = \frac{4 \pi9}{6} = \frac{4\pi3}{2} = 6\pi\)

\(x = \sqrt{6\pi} \)

\( \sqrt{6\pi} = \sqrt{k\pi} \)

\(6\pi = \pi \: k\)

\(k = 6\)

Answer:

x² + y² - 12x - 6y + 29 = 0

Step-by-step explanation:

Simplifying the equation using (a + b)² = a² + 2ab + b²:

(x - 6)² + (y - 3)² = 16

⇒ [x² - 2(x)(6) + 6²] + [y² - 2(y)(3) + 3²] = 16

⇒ [x² - 12x + 36] + [y² - 6y + 9] = 16

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

General form of a circle = x² + y² + Cx + Dy + E = 0

Before we reorganize the equation in general form, we need to have the R.H.S as 0. For that, we need to subtract 16 both sides.

Subtract 16 both sides:

⇒ x² - 12x + 36 + y² - 6y + 9 = 16

⇒ x² - 12x + 36 + y² - 6y + 9 - 16 = 16 - 16

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

Reorganizing the equation in general form:

x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² - 12x + 20 + y² - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x + 20 - 6y + 9 = 0

⇒ x² + y² - 12x - 6y + 20 + 9 = 0

⇒ x² + y² - 12x - 6y + 29 = 0

Thus, the equation in general form is x² + y² - 12x - 6y + 29 = 0.

The journal entry on April 13, to record the payment of the amount owed would be: Debit Credit Account Receivable$2,637 (2% discount on $2,700) Cash$2,584 [(Cost of Merchandise - return) - discount] Cost of Merchandise$2,700 Inventory $2,700 (original price of merchandise purchased)

On April 5, Fair Coffee, Incorporated purchased merchandise with a list price of $2,700 and credit terms 2/10, n/30. On April 6, Fair Coffee returns $100 of the merchandise.On April 5, Fair Coffee, Incorporated purchased merchandise with a list price of $2,700 and credit terms 2/10, n/30. The company receives a discount of 2% if they pay within 10 days.On April 6, Fair Coffee returns $100 of the merchandise. The company will deduct the return amount from the cost of merchandise they will pay for.On April 13, the company is making payment of the amount owed. Since the company is eligible for a discount of 2% as they are paying within 10 days. The journal entry would be to debit the Account Receivable for the amount after deducting the discount and credit the cash account for the amount they are paying. The cost of merchandise purchased account would be credited with the original amount and inventory would be debited for the same amount.

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Answer:

{} , {red}, {blue}, {pink}, {green} , {red, blue}, {red, pink}, {red, green}, {blue, pink} , {blue, green} , {pink, green}, {red, blue, pink}, {red, pink, green}, {blue, pink, green}, {red, blue, green}, {red, blue, pink, green}

Step-by-step explanation:

Given set is:

{red, blue, pink, green}

First of all, we have to calculate the number of subsets

In the given set,

n =  4

So the number of subsets will be: 2^4 = 16

The subsets are:

{} , {red}, {blue}, {pink}, {green} , {red, blue}, {red, pink}, {red, green}, {blue, pink} , {blue, green} , {pink, green}, {red, blue, pink}, {red, pink, green}, {blue, pink, green}, {red, blue, green}, {red, blue, pink, green}

Step-by-step explanation:

a 68% mixture means it has a 68/100 fraction of alcohol :

68 ml of alcohol as part of a 100 ml mixture.

I am not sure how to understand the problem description, so I solve for 2 different problems.

1. create a new 600 ml mixture with 68% alcohol.

since we want to have a 600 ml mixture, we need to multiply the denominator of the fraction by 6.

to keep the value of the fraction unchanged, we need then also to multiply the numerator by 6 :

68/100 × 6/6 = 408/600

that means they need to include 408 ml of 100% alcohol with 192 ml of the rest of the ingredients to create 600 ml of a 68% mixture.

2. we have 600 ml of 50% mixture and are adding 100% alcohol to get a 68% mixture.

the current mixture has a 50/100 fraction of alcohol.

so, 300 ml of the 600 ml mixture are 100% alcohol.

we need to add x ml of 100% alcohol to make it a 68% mixture of 600 + x ml.

that means the sum of the existing 600 ml plus the added 100% alcohol must reach the same (68/100) fraction of alcohol.

(300 + x) / (600 + x) = 68/100

100(300 + x) = 68(600 + x)

30000 + 100x = 40800 + 68x

30000 + 32x = 40800

32x = 10800

2x = 675

x = 337.5 ml

we need to add 337.5 ml of 100% alcohol to the existing 600 ml mixture to get a a mixture of 68% alcohol in the in total 937.5 ml.

Answer:

Arithmetic

Step-by-step explanation:

Given sequence

We can observe it is increasing sequence

The rate of increase is linear and equal to 17

Therefore it is an arithmetic progression

-64,-47,-30,-13 is arithmetic .

\( \huge \red {explanation}\)

this is arithmetic progression because ;

The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

To determine the surface area from the net of the box, we simply calculate the area of each shape.

From the given figure, we have the following shapes and dimensions:

The area is then calculated using:

Area = Areas of the rectangle + Area of the triangle

So, we have:

Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7

Evaluate the sum of products

Area = 430.35

Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet

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Answer:577.35 square feet

Step-by-step explanation:

‍♀️

Statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

It is defined as the depiction of numerical data in a graph using a bar with no space. The histogram depicts the approximate distribution of the data.

We know on the left side skewed histogram has more data on the right and on the left side, there are fewer data. It is also called a negatively skewed histogram.

On the right side skewed histogram, there is fewer data on the right side and more data on the left side. It is also called a positive histogram.

Thus, statement (B) The mean lies to the left of the median for a positively skewed distribution because there will be fewer data on the right side is correct.

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Answer:

$22560

step 1

$270 × 4month

=$1880 for a month

step 2

$1880×12months

= $22560

The expected value of the number of rejected items per day is 2.7.

The variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.

a) The completed probability mass function (PMF) and cumulative distribution function (CDF) tables are as follows:

X f(x) F(x)

0 0 0

1 1/20 1/20

2 0.05 3/40

3 7/20 1/2

4 0.1 9/20

5 4/20 1

b) P(X=5) = 4/20 = 0.2

c) P(X ≤ 2) = F(2) = 1/20 + 0.05 = 0.1 + 0.05 = 0.15

d) The expected value (or mean) of X is:

E(X) = ∑[x * f(x)] = (0 * 0) + (1 * 1/20) + (2 * 0.05) + (3 * 7/20) + (4 * 0.1) + (5 * 4/20) = 2.7

Therefore, the expected value of the number of rejected items per day is 2.7.

e) The variance of X is:

Var(X) = ∑[(x - E(X))^2 * f(x)] = (0 - 2.7)^2 * 0 + (1 - 2.7)^2 * 1/20 + (2 - 2.7)^2 * 0.05 + (3 - 2.7)^2 * 7/20 + (4 - 2.7)^2 * 0.1 + (5 - 2.7)^2 * 4/20

= 0.81 * 0 + 0.49 * 0.05 + 0.0225 * 0.05 + 0.09 * 0.35 + 0.0225 * 0.1 + 0.49 * 0.2

= 0.107

The standard deviation of X is:

SD(X) = sqrt(Var(X)) = sqrt(0.107) = 0.327

Therefore, the variance and standard deviation of rejected items per day are 0.107 and 0.327, respectively.

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The undefined geometric term described is a point.The undefined geometric term described as a location on a coordinate plane that is designated is called a point. A point is a fundamental concept in geometry and represents a specific location in space.

In geometry, a point is a fundamental concept that represents a specific location in space. It is considered an undefined term because it is not defined in terms of other geometric objects. A point has no size or dimensions and is typically represented by a dot. On a coordinate plane, a point is designated by its coordinates, which consist of an ordered pair (x, y). The x-coordinate represents the position along the horizontal axis (x-axis), and the y-coordinate represents the position along the vertical axis (y-axis). So, a point is a designated location on a coordinate plane.It is typically represented by a dot and has no size or dimensions. In a coordinate plane, a point is defined by its coordinates, which consist of an ordered pair (x, y) that indicates its position along the x-axis and y-axis.

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Answer:

No, the poster would not fit in the frame

Step-by-step explanation:

A rectangle is a quadrilateral (has 4 sides and 4 angles) with two pair of opposite and equal sides.

A square is a quadrilateral in which all sides are equal.

Given that the rectangular frame has a width of 40 inches and a length of 30 inches. The area of the rectangular frame is:

Area of rectangular frame = length * breadth = 40 inches * 30 inches = 1200 in²

Since the square frame has the same area as the rectangular frame, hence:

Area of square frame = length * length

length² = 1200

length = √1200 = 34.64

Therefore the dimensions of the square frame is 34.64 inches by 34.64 inches.

Hence a poster with dimensions of 36 inches X 36 inches cannot fit in the square frame.

We can write the potential function for G as,Φ = ∫yzi dx + C1 = ½ x²yz + C1 Differentiating Φ with respect to x gives us G. Hence,∂Φ/∂x = yz + 0 + 0 = GxHence, the potential function for G is Φ = ½ x²yz + C1.

Given,F(x,y)

=(ycos(xy)+1)i+xcos(xy)jG(x,y,z)

=yzi+xzj+xyk To find the potential function for F, we need to take the partial derivative of F with respect to x, keeping y as a constant. Hence,∂F/∂x

= cos(xy) - ysin(xy)Similarly, to find the potential function for G, we need to take the partial derivative of G with respect to x, y and z, respectively, keeping the other two variables as a constant. Hence,∂G/∂x

= z∂G/∂y

= z∂G/∂z

= y + x The three partial derivatives are taken to ensure that the curl of G is zero (since curl is the vector differential operator that indicates the tendency of a vector field to swirl around a point), thus making G a conservative field. We can write the potential function for G as,Φ

= ∫yzi dx + C1

= ½ x²yz + C1 Differentiating Φ with respect to x gives us G. Hence,∂Φ/∂x

= yz + 0 + 0

= GxHence, the potential function for G is Φ

= ½ x²yz + C1.

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The lateral surface area of cone A unwrapped is a sector with central angle 6 radians and radius pi. The length of the radius of cone A is pi/6.

Since the lateral surface area of cone A is a sector with central angle 6 radians and radius pi when unwrapped, we can use the formula for sector area to find the lateral surface area of the cone. Area of sector=θ/2π×π² where θ is the central angle and π is the radius.

Area of cone’s lateral surface area=L=θ/2π×2πr=rθ. So, r=L/θ=π/6 (when L=π and θ=6 radians). The length of the radius of cone A is π/6 which is approximately 0.524. Thus, the length of the radius of cone A is pi/6 when unwrapped, given that the lateral surface area of cone A is a sector with central angle 6 radians and radius pi.

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To express the population after hours as a function of time, we need to use the information that the bacteria culture grows at a rate proportional to its size. Let's denote the population of bacteria after hours as P(t), where t represents the number of hours.

According to the problem, the growth rate is proportional to the current size of the bacteria culture. This can be represented mathematically as:
dP/dt = kP

Where dP/dt represents the rate of change of the population with respect to time, k is the proportionality constant, and P represents the population at any given time.

To solve this differential equation, we can separate variables and integrate both sides:
∫(1/P) dP = ∫k dt

This simplifies to:
ln|P| = kt + C

Where C is the constant of integration.

To determine the constant of integration, we can use the initial condition that after 0 hours, the population is bacteria. Substituting t = 0 and P = , we get:
ln| | = C

Now we can rewrite the equation as:
ln|P| = kt + ln|

By exponentiating both sides, we get:
|P| = e^(kt) * |

Since population cannot be negative, we can remove the absolute value:
P = e^(kt) *

This equation represents the population after hours as a function of time.

In conclusion, the population after hours can be expressed as the function P(t) = e^(kt) *, where k is the proportionality constant and represents the initial population.

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Answer:

mean = 52

Step-by-step explanation:

In mathematics, the mean is a measure of central tendency that represents the average of a set of numbers. It is also commonly known as the arithmetic mean.

To calculate the mean, you add up all the numbers in a set and then divide by the total number of values in the set.

So in tho case we would add all the values then divide by the amount of values there are.

1) rewrite values:

42  45  58  63

2) add:

42 + 45 + 58 + 63
= 208

3) divide:

Since there arev4 values we will divide by 4.

208 / 4 = 52

Therefore, the mean is 52

Answer:

\(\huge\boxed{\sf Mean = 52}\)

Step-by-step explanation:

42, 45, 58, 63

\(\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{42+45+58+63}{4} \\\\Mean = \frac{208}{4} \\\\Mean = 52\\\\\rule[225]{225}{2}\)

Answer:

60km/h

Step-by-step explanation:

Answer:80100

Step-by-step explanation:

Since "per cent" means parts per hundred, if we can convert the fraction to have 100 as the denominator, we then know that the top number, the numerator, is the percentage. Our percent fraction is 80/100, which means that 80100 as a percentage is 80%.

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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a) If M is a 2 × 2 matrix with det M = −2, we have:

det((3M)-1) = (det(3M))⁻¹ = (3² * det(M))⁻¹ = (9 * (-2))⁻¹ = (-18)⁻¹ = -1/18.

det(3M-1) = 3² * det(M-1) = 9 * det(M⁻¹). Since M is a 2 × 2 matrix, we can calculate M⁻¹ as follows:

M⁻¹ = (1/det(M)) * adj(M),

where adj(M) represents the adjugate of M.

Since M is a 2 × 2 matrix, we have:

M⁻¹ = (1/(-2)) * adj(M).

To find the determinant of M⁻¹, we use the fact that det(AB) = det(A) * det(B):

det(M⁻¹) = (1/(-2))² * det(adj(M)) = (1/4) * det(adj(M)).

We don't have enough information to determine the value of det(adj(M)) without further details about matrix M.

b) If A is a 5 × 5 matrix and det((2A)-1) = 1/8, we have:

det(A⁻¹) = (det(2A))⁻¹ = (2⁵ * det(A))⁻¹ = 32⁻¹ * det(A)⁻¹ = 1/8.

From this, we can conclude that det(A)⁻¹ = 1/8.

To find det(A), we take the reciprocal of both sides:

1/(det(A)⁻¹) = 1/(1/8),

which simplifies to:

det(A) = 8.

Therefore, the determinant of matrix A is 8.

c) Since we don't have specific information about the matrices A and B, we cannot determine det A and det B based solely on the given equations.

d) To find det(ATB²A⁻¹C³A²BT), we can use the properties of determinants:

det(ATB²A⁻¹C³A²BT) = det(A) * det(T) * det(B²) * det(A⁻¹) * det(C³) * det(A²) * det(B) * det(T).

Using the given determinants:

det(A) = -3,

det(B) = 2,

det(C) = -1.

We substitute these values into the expression:

det(ATB²A⁻¹C³A²BT) = (-3) * det(T) * (2²) * (1/(-3)) * (-1)³ * (-3)² * 2 * det(T).

Simplifying the expression:

det(ATB²A⁻¹C³A²BT) = -3 * det(T) * 4 * (-1/3) * (-1)³ * 9 * 2 * det(T) = 216 * det(T)².

Therefore, the determinant of the given expression is 216 times the square of the determinant of matrix T.

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Answer:

90°

Step-by-step explanation:

X = 90°

A right angle is 90° and they are all 90° (right-angles).

As well as that is, that there are 360° on a point

9x4=36 so it must be the same 90° (1 right angle) times 4

90x4 = 360

Answer:

C.

Step-by-step explanation:

For any of the given functions, all of the first input values (x-values) in the relation are considered the domain values. On the other hand, the output values (y-values) are called the range values of the given equation.

The mapped relation is the domain (1, 2, 3). Since this is domain values (x-values), the correct answer will be the mapped with 1, 2, and 3 on the left side.

The correct answer is C.

Hope this helps!

Answer:

1/125 cm^3

Step-by-step explanation:

Given data

Length of one side = 1/5cm

Required

The volume of the cube

We know that

V= l^3

substitute

V= (1/5)^3

V= 1/125cm^3

Hence the volume is 1/125 cm^3

Answer:

x ≈ 370

Step-by-step explanation:

1. The variable used to predict another variable is called the dependent variable.

2. The predicted attendance if the temperature is 90 degrees would be 9,750.

3. The computed test statistic, rounded to three decimal places, would be approximately 2.071.

1. The variable used to predict another variable is called the dependent variable. It is the variable that is being predicted or explained by the independent variable.

The variable used to predict another variable is called the dependent variable.

2. The given equation is Attendance = 16,500 - 75 * Temperature.

If Temperature is 90 degrees, we can substitute this value into the equation to find the predicted attendance.

Attendance = 16,500 - 75 * 90

Attendance = 16,500 - 6,750

Attendance = 9,750

Therefore, the predicted attendance if the temperature is 90 degrees would be 9,750.

The predicted attendance if the temperature is 90 degrees would be 9,750.

3. To calculate the test statistic, we need to use the formula:

test statistic = (sample correlation coefficient * sqrt(sample size - 2)) / sqrt(1 - sample correlation coefficient^2)

Given:

Sample size (n) = 25

Sample correlation coefficient (r) = 0.60

Substituting these values into the formula:

test statistic = (0.60 * sqrt(25 - 2)) / sqrt(1 - 0.60^2)

test statistic ≈ (0.60 * sqrt(23)) / sqrt(1 - 0.36)

test statistic ≈ (0.60 * sqrt(23)) / sqrt(0.64)

test statistic ≈ (0.60 * sqrt(23)) / 0.8

test statistic ≈ 1.380 / 0.8

test statistic ≈ 1.725

Rounding to three decimal places, the computed test statistic would be approximately 2.071.

The computed test statistic, rounded to three decimal places, would be approximately 2.071.

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By trigonometric functions the length of the cable rounded to the nearest foot is 4810 ft.

What is trigonometric functions?

Trigonometric functions which are also known as Circular Functions in mathematics can be  defined as the functions of an angle of a mainly right angled  triangle. It means that the relationship between the angles and sides of a right angled triangle are given by the trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, cosecant, secant.

A zipline cable is attached to two platforms 1000 ft apart at an angle of depression from the taller platform of 12º.

If the angle of depression from the taller platform of 12° then the angle of elevation should be (90-12)° = 78° as they are in complementary angle.

The problem can be solved by trigonometric functions.

Here we use the cosine.

We have to determine the hypotenuse of the triangle formed by the given data.

Let the hypotenuse be h ft.

So,

cos 78° = base/ hypotenuse.

Here base or the adjacent side is 1000 ft.

cos 78° = 1000/h

⇒ h= 1000/ cos 78°

In trigonometry the value of cos 78°= 0.2079

Hence, h= 4810.00

rounding to the nearest foot we get, h= 4810 ft.

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