A Box contains 2,00,000 medicine tablets each weighing 20 mg. What is total weight of all the tablets in the box in grams and kilo grams? Please answer only with full SOLUTION

Answer:

225 trains

Step-by-step explanation:

since they are using the same process and materials, we expect them to have the same ratio between trains made and defective trains :

600 / 30 = 20/1

one out of 20 is defect.

so, when they make 4500 trains, we need to divide this by 20 to get the number of expected defective trains :

4500 / 20 = 225

I find the answer option of 6000 defective trains really funny : if that were true, more than the produced trains (4500) would be defective. how ... ?

As three dice are thrown together and the probability of any two of them being the same will be 5/12.

When a dice is thrown there are 6 possible outcomes. So, when three dice are thrown, the number of outcomes will be 6× 6× 6 = 216.

The probability of a number repeating = ₆C₂ = (6×5)/2 = 15

So each number will have possible 15 outcomes.

6 numbers will have 6 × 15 outcomes = 90 outcomes

So probability = Number of desired outcomes/ total number of outcomes  = 90 / 216 = 5/12

So the probability of any two number matches when three dices are thrown together will be 5/12.

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Answer:

(0, 0)

(4, 16)

Step-by-step explanation:

[tex]y = 4x[/tex]

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

Using substitution, we can replace y in the second equation with 4x from the first equation.

[tex]4x = x^2[/tex]

Now, we can move all the x's to one side and complete the square to solve for x.

[tex]0 = x^2 - 4x[/tex]

↓ adding 4 to both sides

[tex]4 = x^2 - 4x + 4[/tex]

↓ factoring the right side

[tex]4 = (x-2)^2[/tex]

↓ taking the square root of both sides

[tex]\sqrt4 = \sqrt{(x-2)^2[/tex]

[tex]\pm2 = x - 2[/tex]

↓ adding 2 to both sides

[tex]2 \pm 2 = x[/tex]

[tex]\boxed{x = 0 \ \ \ \text{or} \ \ \ x = 4}[/tex]

Then, we can solve for y by plugging both x-values into the first equation.

[tex]y = 4(0)[/tex]     or     [tex]y = 4(4)[/tex]

[tex]\boxed{y = 0 \ \ \ \text{or} \ \ \ y=16}[/tex]

Finally, we can form two ordered pairs that are the solutions to the system of equations.

[tex]\boxed{(0,0)}[/tex]

[tex]\boxed{(4,16)}[/tex]

If your index is used to access the indexed variables of the array has the value of a non-existent index, this is called Index out-of-bounds.

What is Index out-of-bounds?

An index out-of-bounds error happens when an index used to access the indexed variables of an array or a list has a value that is outside the valid index range. This signifies that the index is either less than zero or larger than or equal to the array or list's size.

Assume we have a 5-element array and want to retrieve the entry at index 7. Because the array only has 5 entries, index 7 is out of limits, and attempting to access it will result in an index out-of-bounds error.

An index out-of-bounds error can create unpredictability in a program, such as reading or writing to memory regions not intended for usage by the program, causing the program to crash. To prevent index out-of-bounds issues, make sure the index used to access the array or list is inside the valid index range.

Therefore, if your index is used to access the indexed variables of the array has the value of a non-existent index, this is called Index out-of-bounds.

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If your index is used to access the indexed variables of the array has the value of a non-existent index, this is called an "out-of-bounds" error. This means that the index being used to access the array is either too high or too low, and there is no corresponding variable at that index.

This can cause unexpected behavior in a program and can even cause it to crash. It is important to always ensure that your indexes are within the bounds of the array and that the values being used are valid.
When an index is used to access the indexed variables of an array, but the value of the index is not within the valid range of indices for that array (i.e., the index is for a non-existent element), this situation is called an "out-of-bounds" access.

When you attempt to access an element using an out-of-bounds index, you might encounter unexpected behavior or errors, as the program tries to access a memory location that is not part of the array. To avoid this, always ensure that the index value is within the valid range of indices for the given array.

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2x² - 6у² is a difference of two squares since we can rewrite it as (x√2)² - (y√6)². Therefore, the answer is D.

A binomial expression is a polynomial with two terms. The terms can be added or subtracted from each other and may contain variables, coefficients, and exponents.

A common example of a binomial expression is (x+y). This binomial expression has two terms, x and y, which are added together. Another example is (2a - b), which has two terms, 2a and -b, which are subtracted from each other.

Binomial expressions are commonly used in algebra to express equations, formulas, and identities. They can be combined with other binomial expressions, constants, and variables to create more complex expressions. For example, (x+y)(x-y) is a binomial expression that represents the difference of two squares and can be simplified to x² - y².

Binomial expressions can also be raised to powers using the binomial theorem. This theorem provides a formula for expanding the power of a binomial expression, such as (x+y)^n or (a-b)^n, where n is a positive integer. The resulting expression will contain multiple terms, which can be simplified and rearranged using algebraic techniques.

The difference of two squares is a binomial expression in the form of a² - b², where a and b are terms. Using this definition, we can identify which of the given expressions is the difference of two squares:

A. 9g - 36h is not a difference of two squares since there are no squares involved.

B. 9a² - 4b⁶ is not a difference of two squares since both terms are squares, but they are not subtracted from each other.

C. 49m² + 81n² is not a difference of two squares since both terms are squares, but they are not subtracted from each other.

D. 2x² - 6у² is a difference of two squares since we can rewrite it as (x√2)² - (y√6)². Therefore, the answer is D.

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The x - intercepts, when entered as ordered pairs, would be (2, 0) and (-4, 0).

The y - intercepts would be (0, -8).

The equation for the line of symmetry for the graph of f(x) would be x = -1.

The vertex of the graph of f(x) would be (-1, -9).

To find the x-intercepts, we need to set f(x) = 0 and solve for x:

x = (-2 ± √(2² - 4 x 1 x (-8))) / (2 x 1)

x = (-2 ± √(4 + 32)) / 2

x = (-2 ± √36) / 2

x = (-2 ± 6) / 2

There are two solutions:

x1 = (-2 + 6) / 2 = 4 / 2 = 2

x2 = (-2 - 6) / 2 = -8 / 2 = -4

So the x-intercepts are (2, 0) and (-4, 0).

To find the y-intercept, we need to set x = 0 and solve for f(0):

f(0) = 0² + 2 x 0 - 8 = -8

So the y-intercept is (0, -8).

To find the line of symmetry, we can use the formula:

x = -b / 2a

x = -2 / (2 x 1) = -1

So the equation of the line of symmetry is x = -1.

To find the vertex, we need to substitute the x-coordinate of the line of symmetry into the function:

f(-1) = (-1)² + 2 * (-1) - 8 = 1 - 2 - 8 = -9

So the vertex is at the point (-1, -9).

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the equivalent form of the trinomial x² - 11x + 18 is (x - 2)(x - 9). We can verify this by multiplying the two binomials using the distributive property:

How to solve the question?

The given trinomial is x² - 11x + 18. To find an equivalent form, we can factorize the trinomial by finding two binomials whose product is equal to the trinomial.

We can start by finding two factors of 18 that add up to -11, the coefficient of x. The factors of 18 are 1, 2, 3, 6, 9, and 18. We can see that 9 and 2 are the two factors that add up to -11. So, we can write:

x² - 11x + 18 = (x - 2)(x - 9)

Therefore, the equivalent form of the trinomial x² - 11x + 18 is (x - 2)(x - 9). We can verify this by multiplying the two binomials using the distributive property:

(x - 2)(x - 9) = x(x - 9) - 2(x - 9) = x² - 9x - 2x + 18 = x² - 11x + 18

So, we have successfully found the equivalent form of the given trinomial.

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On simplifying the expression (−1 3/4)²- √ [127−2(3)]  we get -127/16

Simplifying an expression:

To simplify the expression, we need to follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we simplify the exponent by squaring -1 3/4 to get 49/16. Then, we simplify the expression under the square root by subtracting 2 times 3 from 127 to get 121, and we take the square root of 121 to get 11.

Here we have

(−1 3/4)²- √ [127−2(3)]  

The above expression can be simplified as follows

=>  (−1 3/4)²- √ [127−2(3)]    

Convert the mixed fraction into an improper fraction  

=> 1 3/4 = 7/4    [ ∵ 4 × 1 + 3 = 7 ]  

So given expression can be

=>  (−7/4)²- √ [127−2(3)]      

=>  (49/16) - √ [121]      

=>  (49/16) - 11

=>  (49 - 176 /16)

=>  -127/16  

Therefore,

On simplifying the expression (−1 3/4)²- √ [127−2(3)]  we get -127/16

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To find the mean height of a football player on this Florida team, we need to know the mean of the normal distribution (Morlam) and the standard deviation of the Florida distribution. Since the Florida distribution is also approximately normal (Morlam) with a standard deviation of 2.9 inches, we can use the Empirical Rule to estimate the mean height.

According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% within two standard deviations, and approximately 99.7% within three standard deviations. Since we know that the standard deviation of the Florida distribution is 2.9 inches, we can assume that the mean height falls within three standard deviations of the mean.

So, if we assume that the mean height is at the centre of the distribution, we can estimate it by adding and subtracting three standard deviations from it. Therefore, the mean height of a football player on this Florida team can be estimated to be:

Mean height = Mean of the Morlam distribution ± 3 x Standard deviation of the Florida distribution
Mean height = Mean of the Morlam distribution ± 3 x 2.9 inches

Without knowing the mean of the Morlam distribution, we cannot calculate the exact mean height. However, if we assume that the Morlam distribution has a mean height of 70 inches (a typical average height for a football player), then the mean height of a football player on this Florida team can be estimated to be:

Mean height = 70 ± 3 x 2.9
Mean height = 70 ± 8.7
Mean height = 61.3 to 78.7 inches

Therefore, we can estimate that the mean height of a football player on this Florida team is between 61.3 and 78.7 inches.

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We can estimate that the mean height of a football player on the Florida team is approximately 70 inches.

To find the mean height of a football player on the Florida team, we need to know the exact distribution of heights. However, since we only have information about the standard deviation and the fact that it is approximately normal, we can make an educated guess that the distribution is still normal with a mean somewhere close to the national average of 70 inches.
Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean. In this case, one standard deviation is 2.9 inches.

So, we can assume that about 68% of the heights on the Florida team fall between (70-2.9) = 67.1 inches and (70+2.9) = 72.9 inches.
If we assume that the distribution is symmetric, we can estimate the mean height of the Florida team by taking the average of the lower and upper bounds of the interval: (67.1 + 72.9)/2 = 70 inches.

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Kaylee will have to pay $28 in interest.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

The interest Kaylee will have to pay is calculated as follows:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the time period in years. Since Kaylee has to pay back the loan in 24 months, or 2 years, we can plug in the given values to get:

Interest = 700 x 0.02 x 2 = $28

Therefore, Kaylee will have to pay $28 in interest.

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Answer:

15π

Step-by-step explanation:

If it is in terms of pi, then it would be 15π.

If you want the full circumference, it would be 47.1.

Explanation:

15/2 = 7.5.

7.5*2 = 15.

15π = 47.1.

Hope this helped!

Answer:

1767.1

Step-by-step explanation:

circle = 4/3 x pie x r^3

Divid 15 by 2 to get radius

15/2=7.5

7.5^3 = 421.875

421.875 x pie = 1325.359401

1325.359401 x 4/3 = 1767.145868

1767.145868 Estimated = 1767.1

The compound inequality ​20 < 90 + x < 30 when solved has a solution of -70 < x < -60.

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

20 < 90 + x < 30

Subtracting 90 from all parts of the inequality, we get:

-70 < x < -60

Therefore, the solution to the compound inequality is: -70 < x < -60.

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Therefore, y is equal to 12 2/5 and n is equal to 2 2/5 in the equation.

An equation is a mathematical statement that shows that two expressions are equal. An equation is typically written with an equal sign (=) between two expressions. Equations can involve various mathematical operations, such as addition, subtraction, multiplication, division, exponents, and logarithms. Solving an equation typically involves performing mathematical operations on both sides of the equation to isolate the variable (the unknown value) and find its value.

Here,

To solve for y in the equation 2y + 8 1/5 = 33, we can follow these steps:

Subtract 8 1/5 from both sides of the equation:

2y = 33 - 8 1/5

2y = 24 4/5

Divide both sides of the equation by 2:

y = (24 4/5) / 2

y = 12 2/5

Therefore, y is equal to 12 2/5.

To solve for n in the equation 2n + 4 1/5 = 9, we can follow these steps:

Subtract 4 1/5 from both sides of the equation:

2n = 9 - 4 1/5

2n = 4 4/5

Divide both sides of the equation by 2:

n = (4 4/5) / 2

n = 2 2/5

Therefore, n is equal to 2 2/5.

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If Sam is making chili for a get-together, his recipe calls for 1 1/2 cups of kidney beans for every 4 cups of chili, Sam should put 4 1/2 cups of kidney beans in his 12 cups of chili.

To determine how many cups of kidney beans Sam should put in his 12 cups of chili, we need to use the ratio of 1 1/2 cups of kidney beans for every 4 cups of chili.

First, we need to calculate the number of times the recipe ratio fits into the desired quantity of chili.

12 cups of chili ÷ 4 cups of chili per ratio = 3 ratios of chili

Therefore, Sam needs to use 3 ratios of chili to make 12 cups of chili.

Next, we need to multiply the number of ratios of chili by the number of cups of kidney beans in each ratio:

3 ratios of chili × 1 1/2 cups of kidney beans per ratio = 4 1/2 cups of kidney beans

Note that we can also write 4 1/2 as a mixed number, which is 4 cups and 1/2 cup. Therefore, Sam can use 4 cups of kidney beans and half a cup of kidney beans to make his chili.

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The position of the image is approximately 1.71 cm from the ornament's surface.

To determine the position of the image, we need to use the mirror formula for a concave mirror, which is \frac{1}{f} = [tex]\frac{1}{do} + \frac{1}{di},[/tex] where f is the focal length, do is the object distance, and di is the image distance.

First, we need to find the focal length (f) of the spherical ornament. The radius of curvature (R) is half the diameter, so R = 6.00 cm / 2 = 3.00 cm. For a spherical mirror, the focal length is half the radius of curvature: f = R/2 = 3.00 cm / 2 = 1.50 cm.

Next, we need to find the object distance (do). The object is 19.0 cm from the center of the ornament, but we need the distance from the ornament's surface. Since the radius is 3.00 cm, we subtract that from the total distance: do = 19.0 cm - 3.00 cm = 16.0 cm.

Now, we can use the mirror formula:
\frac{1}{f} = [tex]\frac{1}{do} + \frac{1}{di},[/tex]
1/1.50 cm = 1/16.0 cm + 1/di

To solve for di, subtract 1/16.0 cm from both sides and then take the reciprocal:

1/di = 1/1.50 cm - 1/16.0 cm

di ≈ 1.71 cm

The position of the image is approximately 1.71 cm from the ornament's surface.

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The position of the image is 20.8 cm from the center of the spherical ornament, counting from the ornament surface.

To find the position of the image, we can use the mirror equation:

1/o + 1/i = 1/f

where o is the object distance from the center of the spherical ornament, i is the image distance from the center of the spherical ornament, and f is the focal length of the ornament.

Since the ornament is a spherical mirror, the focal length is half the

radius of curvature, which is half the diameter of the ornament:

f = R/2 = 6.00 cm/2 = 3.00 cm

Substituting the given values, we get:

1/19.0 cm + 1/i = 1/3.00 cm

Solving for i, we get:

1/i = 1/3.00 cm - 1/19.0 cm = (19.0 cm - 3.00 cm)/(3.00 cm x 19.0 cm) = 0.0481 cm^-1

i = 1/0.0481 cm = 20.8 cm

Therefore, the position of the image is 20.8 cm from the center of the

spherical ornament, counting from the ornament surface.

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The value of x at which f(x) is a minimum is 3/2.

To find the minimum value of f(x), we need to calculate its derivative and set it equal to zero.

So,

[tex]f(x) = ∫(x^2 - 3x - 2) e^(t^2) dt[/tex]

Taking the derivative of f(x) with respect to x, we get:

[tex]f'(x) = 2x e^(x^2 - 3x - 2) - 3 e^(x^2 - 3x - 2)[/tex]

Setting f'(x) equal to zero:

[tex]2x e^(x^2 - 3x - 2) - 3 e^(x^2 - 3x - 2) = 0[/tex]

Factorizing, we get:

[tex]e^(x^2 - 3x - 2) (2x - 3) = 0[/tex]

So, either e[tex]^(x^2 - 3x - 2)[/tex]= 0 (which is not possible), or

2x - 3 = 0

Solving for x, we get:

x = 3/2

Therefore, the value of x at which f(x) is a minimum is 3/2.

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f'(x) changes from negative to positive at x = 2.105, we know that f(x) has a local minimum at x = 2.105.
Therefore, the answer is c. 2.

To find the value of x at which f(x) is a minimum, we need to find the critical points of f(x) and then determine whether each critical point is a minimum or maximum using the first derivative test.

To find the critical points of f(x), we need to find where f'(x) = 0. Using the Fundamental Theorem of Calculus and the Chain Rule, we can find that:

[tex]f'(x) = 2x - 3 - 2xe^{(x^2-3x-2t^2)}[/tex]

To find where f'(x) = 0, we need to solve the equation[tex]2x - 3 - 2xe^{x^2-3x-2t^2} = 0[/tex] for x. Unfortunately, this equation cannot be solved algebraically, so we need to use numerical methods. One way to do this is to use a graphing calculator or computer program to graph y = 2x - 3 and[tex]y = 2xe^{x^2-3x-2t^2)[/tex]and find their intersection(s).

Using this method, we can find that there is only one critical point, which is approximately x = 2.105. To determine whether this critical point is a minimum or maximum, we need to use the first derivative test. Since f'(x) changes from negative to positive at x = 2.105, we know that f(x) has a local minimum at x = 2.105.

Therefore, the answer is c. 2.

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The calculated equation for the function g(x) is g(x) = (1/2) x²

Since g(x) is a scaled version of f(x) = x², we can write:

g(x) = a f(x)

where a is a scaling factor.

Since g(x) passes through (4, 8), we can substitute x = 4 and g(x) = 8 into this equation:

8 = a f(4) = a (4²) = 16a

Solving for a, we get:

a = 8/16 = 1/2

Therefore, the equation for g(x) is: g(x) = (1/2) f(x) = (1/2) x²

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The circumference of the circle is approximately 54.1 yards.

Circumference is a term used to describe the distance around the edge of a circular object. It is a measurement of the total length of the circle's perimeter. The circumference of a circle is calculated by multiplying its diameter by the mathematical constant pi (π), which is approximately equal to 3.14.

The formula for calculating circumference is C=πd or C=2πr, where C represents the circumference, d represents the diameter, and r represents the radius of the circle. The diameter is the distance across the circle, passing through its center, while the radius is the distance from the center to the edge.

Circumference is a fundamental concept in geometry and is used to solve various real-world problems, such as calculating the distance traveled by a rotating wheel or finding the length of a wire needed to make a circular ring. Additionally, many physical phenomena, such as the movement of planets and the orbits of electrons, can be described using the concept of circumference.

The circumference of a circle with a radius of 8.6 yards can be found using the formula:

C = 2πr

where r is the radius and π is the mathematical constant approximately equal to 3.14.

Substituting the given value of the radius, we get:

C = 2 × 3.14 × 8.6

C = 54.088

Rounding this to the nearest tenth, we get:

C ≈ 54.1 yards

Therefore, the circumference of the circle is approximately 54.1 yards.

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The answer is: There were about 169 principals in attendance.

what is proportion?

In mathematics, a proportion is an equation that states that two ratios or fractions are equal. A proportion can be written in the form of a/b = c/d, where a, b, c, and d are numbers or variables.

Proportions are used to compare two or more quantities or to find an unknown value. For example, if we know that the ratio of the length of a rectangle to its width is 2:1, and we also know that the length is 6 feet, we can use a proportion to find the width. We set up the proportion as 2/1 = 6/w, where w is the width of the rectangle, and then solve for w by cross-multiplying and simplifying the equation.

Proportions are also used in many real-world applications, such as cooking, finance, and science.

To make a prediction about the number of principals in attendance at the conference, we need to use the given information and make some assumptions.

We know that in one exhibit room of 80 people, there were 15 principals. Let's assume that this exhibit room is representative of the entire conference, and that the proportion of principals to attendees in this room is the same as the proportion of principals to attendees in the entire conference.

Using this assumption, we can set up a proportion:

15 principals / 80 attendees = x principals / 900 attendees

To solve for x, we can cross-multiply and simplify:

15 * 900 = 80 * x

x = (15 * 900) / 80 = 168.75

So our prediction is that there were about 169 principals in attendance at the conference.

Therefore, the answer is: There were about 169 principals in attendance.

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The impact propensity can be interpreted as the slope coefficient for the tax personal exemption (pe) or its first lag in

the regression equation.

To determine the impact propensity in the regression of the general fertility rate (GFR) on the tax personal exemption

(PE) and its first lag, you should follow these steps:

Estimate the regression model using the available data. The model should look like this:

GFR = β0 + β1 × PE + β2 × PE_lag + ε

Where GFR is the general fertility rate, PE is the tax personal exemption, PE_lag is the tax personal exemption's first

lag, and ε is the error term.

Obtain the estimated coefficients (β0, β1, and β2) from the fitted regression model.

These coefficients will help you determine the impact propensity.

Calculate the impact propensity. The impact propensity in this context refers to the change in the general fertility rate

resulting from a one-unit increase in the tax personal exemption, taking into account both its current and lagged

effects.

To find the impact propensity, sum the coefficients for the tax personal exemption and its first lag:

Impact propensity = β1 + β2

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The length of the diagonals in ascending order is: 140/3 inches

Algebra is a branch of mathematics that deals with mathematical operations and symbols to represent numbers and their relationships. It involves the use of variables, which are letters or symbols that represent unknown or unspecified quantities, and manipulating equations and expressions to solve problems.

To compare the lengths of the diagonals of the three TV screens, we can simplify each expression and put them in order:

5 square roots of 84 inches

= 5 * √(4 * 21) inches

= 10 * √(21) inches

46 2/3 inches

= 140/3 inches

46.625 inches

Therefore, the length of the diagonals in ascending order is:

46.625 inches < 140/3 inches < 10 * √(21) inches

Note that we can also write the second diagonal as a mixed number, which is the form of a whole number and a fraction:

140/3 inches

= 46 2/3 inches

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The unction: f(x) = -√(x + 5 - 4)

Transformations: Horizontal shift of 4 units to the left, vertical flip about the x-axis.

Domain: x ≥ -1

Range: (-∞, 0]

Intercepts: x-intercept: None; y-intercept: (0, -1).

The function: f(x) = -√(x + 5 - 4)

Transformations: Horizontal shift: The function is shifted 4 units to the left, which means the vertex of the function is at x = -5 + 4 = -1.

Vertical shift: The function is reflected about the x-axis due to the negative sign in front of the square root, resulting in a vertical flip.

Stretch: There is no stretching or compressing factor since the square root is not multiplied by any constant.

Domain: The square root function is defined for non-negative real numbers. Since the square root is taken of (x + 5 - 4), the function will be defined as long as x + 5 - 4 ≥ 0, which simplifies to x ≥ -1.

Range: The function f(x) is always negative or zero, due to the negative sign in front of the square root. So the range of the function is (-∞, 0].

Intercepts: x-intercept: To find the x-intercept, we set f(x) = 0 and solve for x: -√(x + 5 - 4) = 0. Since the square root of a real number is never negative, there are no x-intercepts for this function.

y-intercept: To find the y-intercept, we set x = 0 and calculate f(0): f(0) = -√(0 + 5 - 4) = -√1 = -1. So the y-intercept is (0, -1).

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The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:

P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)

where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.

Substituting the given probabilities into the formula, we get:

P(puncture or smashed corner) = 0.03 + 0.06 - 0.014

P(puncture or smashed corner) = 0.076

Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

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Answer:

8 is the answer

Step-by-step explanation:

4 daughters and each of the daughters has one brother. So 4 daughters have 4 brothers, all in total that will lead to 8 children

The total surface area of the given figure is 619.2 in², which is not listed in the provided options.

The surface area is known to be measure of the total area occupied by the surface of the object. Defining the surface area mathematically in the presence of a curved surface is better than defining the arc length of a one-dimensional curve, or the surface area of ​​a polyhedron (i.e. an object with flat polygonal faces). Much more complicated. For a smooth surface sphere such as the following, surface area is assigned using representation as a parametric surface. This surface definition is based on calculus and includes partial derivatives and double integrals.

The triangular face of the given figure represent an equilateral triangle of sides 12 in.

Area of the triangle = (√3/4) × a²

Area of the triangular face:

= (√3/4) × 12²

= (√3/4) × 144

= 57.6 in²

Area of the rectangle = Length × width

Area of the rectangular face:

= 12 × 14

= 168 in²

Area of the given figure:

= (2 × 57.6) + (3 × 168)

= 115.2 + 504

= 619.2 in²

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The expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

The value of an electronic book device before a holiday is represented by the variable t. After the holiday, the value of the device decreased by 15%. To find the value of the device after the holiday, we need to multiply the original value by the percentage decrease, which is 0.85 (or 1-0.15). Therefore, the expressions that correctly show the value of the electronic book device after the holiday are B and D.

Option A (1.15) represents the percentage increase and not the decrease, so it is incorrect. Option C (-0.15) represents the percentage decrease, but it cannot be used alone to find the new value. Option E (-0.85) is the negative of the percentage decrease, so it is also incorrect. Finally, option F is equivalent to option D, so it is also correct.

In summary, the expressions that correctly show the value of the electronic book device after the holiday are B and D, which represent the percentage decrease of 15% as 0.85 (or 1-0.15).

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In the given triangle, α is equal to 67.36°.

What is a triangle's definition?

A triangle is a two-dimensional closed geometric form that has three sides, three angles, and three vertices (corners). It is the most basic polygon, produced by joining any three non-collinear points in a plane. The sum all angles of a triangle is always 180°. Triangles are classed according to their side length (equilateral, isosceles, or scalene) and angle measurement (acute, right, or obtuse).

Now,

Using Trigonometric functions

We can use the sine function

So,

Sin α=Perpendicular/Hypotenuse

Sin α = 12/13

α=67.36°

Hence,

           The value of α will be 67.36°.

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The amount of people infected after t weeks is modeled by the function presented as follows:

[tex]f(t) = \frac{675000}{1 + 4000e^{-t}}[/tex]

When the epidemic began, we have that t = 0, hence the number of people is given as follows:

f(0) = 675,000/(1 + 4000)

f(0) = 169 people.

Six weeks after the epidemic began, we have that t = 6, hence the number of people is given as follows:

f(6) = 675,000/(1 + 4000 x e^(-6))

f(6) = 61,841 people.

The limiting size of the infected population is the numerator of the fraction, which is 675,000, as the denominator goes to zero when t goes to infinity.

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the value of The Donut Hole in two years with a 12% growth rate would be $152,666.20

How to solve the question?

To determine the value of The Donut Hole in two years with a 12% growth rate, we can use the formula for compound interest:

A = P*(1+r/n)^(n*t)

where A is the future value, P is the present value, r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, P = $115,000, r = 0.12, n = 1 (compounded annually), and t = 2.

Plugging in these values, we get:

A = $115,000*(1+0.12/1)₁₂

A = $115,000(1.12)²

A = $152,666.20

Therefore, the value of The Donut Hole in two years with a 12% growth rate would be $152,666.20.

It's important to note that this is a rough estimate and assumes that the business will continue to grow at a steady rate without any significant changes in the market or the business itself. It's also possible that the actual value could be higher or lower depending on various factors.

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