Use technology to compute each probability and to carefully sketch a graph corresponding to each expression. a. X N(3.7, 4.55), P(3.0 sX3 4.0) b. X~N(62, 100), P50-45) f. X~N(7.6, 12), P(8 XS 9) P(X 2 45)

Answer:

Step-by-step explanation:

you can complete the square or use a calculator online that does it for you.

the equation is in the for y = a(x-h)^2 + k

it should be y = (x + 3)^2 + 3

Answer:

The correct answer is \(y = - (x - 3)^{2} +21\).

Step-by-step explanation:

To solve this equation (y = \(-x^{2} +6x + 12\)), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve \(y = -x^{2} +6x - 9 + 12\).

Then, you want to add the -9 to the other side of the equation to get \(y - 9 = -x^{2} + 6x - 9 + 12\).

Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with \(y - 9 = -(x^{2} -6x+9) + 12\).

Now, we use an identity in algebra that is difference of two squares identity. This says that \(a^{2} -2ab +b^{2} =(a-b)^{2}\).

So, we will then factor the trinomial -\(x^{2} -6x+9\) to get \(-(x-3)^{2}\). Our new and updated equation is \(y-9 = -(x-3)^{2} +12\).

Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us \(y = -(x-3)^{2} +21\).

This is our final equation.

The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

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Answer:

x= 7

Step-by-step explanation:

5/8 - 1/3 = x/24

Get a common denominator or 24

5/8 *3/3 = 15/24

1/3 *8/8 = 8/24

15/24 - 8/24 = x/24

7/24 = x/24

Multiply by 24

7 =x

The system of linear equations above, k is a constant. if the system has no solution is  \(\frac{7}{6}\)

\(\begin{aligned}& (k-1) x+\frac{1}{3} y=4 \\& k(x+2 y)=7\end{aligned}\)

What is equations?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7

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Answer:

1.25 meters

HOPE THIS HELPS

-Todo ❤️

Step-by-step explanation:

.5*2.5=1.25

Answer:

That's incredible.  I have that exact problem on my website.

Here is my explanation.

My website says probability = 0.131944444444445

https://www.1728.org/occupncy8.htm

Step-by-step explanation:

Answer:

8.388511

Step-by-step explanation:

Divide by 1.609

We have:

Total number of cards in a pack = 52

Total number of aces in a pack = 4

The probability of drawing an ace is:

The probability that both are aces is:

Answer: the probability is 1/221

Answer:

-64

Step-by-step explanation:

we should put -2 for j and -1 for k,

Answer:

the answer is 64

The main difference between the denominator of the F-ratio (the error term) for a repeated-measures ANOVA and an independent-measures ANOVA lies in the way variability is accounted for within the groups.

In a repeated-measures ANOVA, the same participants are exposed to multiple conditions or measured at different time points. Therefore, this design accounts for individual differences, leading to a smaller error term in the denominator of the F-ratio.

The error term in repeated-measures ANOVA represents the variability due to individual differences and the residual error, but not the variability between participants. In contrast, an independent-measures ANOVA involves separate groups of participants for each condition, meaning that variability between participants is included in the error term.

As a result, the error term for the independent-measures ANOVA is larger than that of the repeated-measures ANOVA. This difference in the denominator of the F-ratio affects the sensitivity of the statistical test, with the repeated-measures ANOVA being more sensitive due to its smaller error term.

In summary, the denominator of the F-ratio (the error term) differs for a repeated-measures ANOVA compared to an independent-measures ANOVA in terms of the variability accounted for within groups. The repeated-measures ANOVA error term is smaller, as it controls for individual differences, while the independent-measures ANOVA error term is larger because it includes variability between participants.

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Answer:

a trail rating is (green circle)

Using the perimeter of the rectangle, it is found that she should buy at most 16 plants.

---------------------------

The perimeter of a rectangle of length l and width w is given by:

\(P = 2(l + w)\)

In this question, the perimeter is of 1 ft by 4.5, thus, \(l = 1, w = 4.5\), and the perimeter is:

\(P = 2(1 + 4.5) = 2(5.5) = 11\)

1 plant - 2/3 ft

x plants - 11 ft

Applying cross multiplication:

\(\frac{2x}{3} = 11\)

\(2x = 33\)

\(x = \frac{33}{2}\)

\(x = 16.5\)

At least 8 inches apart(can be more), thus she should buy at most 16 plants.

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Answer:

We can start by isolating the variable "h".

5 8 h + 1 1 2 = 5

Subtracting 11/2 from both sides:

5 8 h = 5 - 1 1 2

Simplifying:

5 8 h = 8 1 2

Dividing both sides by 5/8:

h = 8 1 2 ÷ 5 8

Converting the mixed number to an improper fraction:

h = (8 x 8 + 1) ÷ 5 8

h = 65/8

Now, we can convert this fraction to a mixed number:

h = 8 1/8

Brigid has already picked for 8 1/8 hours, so the amount of time needed to pick the remaining strawberries is:

5 - (1 1/2 + 5/8 x 8) = 5 - (3 5/8) = 1 3/8

Therefore, Brigid still needs to pick for 1 3/8 hours to fill 5 bushels of strawberries. The answer is 1 and 3/8 hours or 2 and 3/16 hours (if simplified).

Step-by-step explanation:

A clockwise rotation of 144° about the origin will map the pentagon onto itself. Option(c) is the correct answer.

The number of sides (n) of the pentagon is:

n =5

The pentagon will not be plotted onto itself when reflected across the x-axis because the pentagon has 5 sides (an odd number of sides).

To draw the pentagon onto itself, the pentagon has to be rotated.

The angle of rotation is:

θ \(= \frac{360}{n}\)

θ  \(=\frac{360}{5} = 72\)

Other possible angles of rotation must be multiple of 72. i.e.

θ= 72, 144, 216, 288...

Hence, a clockwise rotation of 144° about the origin will map the pentagon onto itself.

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The complete question is:

A regular pentagon is centered about the origin and has a vertex at (0, 4). Which transformation maps the pentagon to itself?

a. A reflection across line m

b. A reflection across the x-axis

c) A clockwise rotation of 144 degrees about the origin

Answer:

-75

Step-by-step explanation:

\(f(x)=5-x^2\\g(x)=2x\\\\f(-10)=5-(-10)^2\\f(-10)=-95\\\\g(10)=2(10)\\g(10)=20\\\\f(-10)+g(10)=-95+20\\f(-10)+g(10)=-75\)

Answer:

1.654

Step-by-step explanation:

Plugged in the calculator

The maximum possible loss associated with a single hurricane for Acme Company would depend on various factors such as the severity of the hurricane, the location of each plant, the strength and durability of the manufacturing facilities, and the insurance coverage.

Assuming that the three identical plants are located far apart from each other, the risk of all three being destroyed by a single hurricane is considered extremely low.

Therefore, the maximum possible loss would be the value of one plant, which is $200 million.

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The total number of fish caught during the festival can be calculated by adding the number of fish caught for each value of n.

For example, if 10 contestants caught 4 fish, 5 caught 8 fish, 7 caught 10 fish, and 8 caught 7 fish, the total number of fish caught would be 104 + 58 + 710 + 87 = 330.

The argument states that the total number of fish caught during the Frostbite Falls Fishing Festival can be determined by adding the number of fish caught by each contestant.

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A ray from Trevor to the fish is the hypotenuse side of a right triangle  with

vertices at Trevor's position, the hook and the fish.

Reasons:

The distance of the hook below Trevor, y = 8 meters

The horizontal distance of the fish from the hook, x = 5 meters

Required:

The distance of the fish from Trevor

Solution:

A line drawn from Trevor's position to the fish, h, then to the hook, x, and

then to Trevor, y, forms a right triangle with the distance from Trevor to the

fish being the hypotenuse side, h.

Therefore, by Pythagorean theorem, we have;

Which gives;

h² = 8² + 5²

h = √(8² + 5²) = √(89 ≈ 9.4

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The following equation could be used to represent a function w:

= w(x)=v(x-7)+7

According to the information provided,

The point of discontinuity of rational functions is at x=7.

When a rational function has a point of discontinuity, it generally occurs when,

q(x) = r(x-a), where x = a

In this case, we must pay attention to the following relationship, which is a combination of a parent rational function and a vertical translation:, (2)

If we know that a=7 and k=7.

The equation which can represent w is as follows,

w(x) = v ( x-7 ) + 7

A rational function can be represented as a polynomial split by another polynomial. Because polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros in the denominator.

Example: x = f(x) (x - 3). The denominator, x = 3, has only one zero. Rational functions are no longer defined when the denominator is zero.

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Answer:

I don't know what your numbers are, but if it is on a number line, just add the absolute values (always positive) of the endpoints together, and divide by 2 (find the average).

On a graph, find the average of the x coordinates, (that is midpoint x value) and the average of the y coordinates (that is midpoint y value)

Step-by-step explanation:

If you have a negative number, the absolute value is the same number, just positive. E.X. -4 the absolute value is 4.

TThe answer to the question "find the MAD. 3 9 4 3 6 2" is 1.5. If the answer were a decimal, we would round it to the nearest tenth, which is not necessary in this case.

To find the MAD (Mean Absolute Deviation) of a set of numbers, we first need to find the mean or average of those numbers. In this case, the mean is the sum of all the numbers divided by the total number of numbers.

Adding all the given numbers,

3+9+4+3+6+2 = 27

we get 27.

=  27÷ 6

=4.5

(the total number of numbers), we get the mean as 4.5. Next, we find the absolute deviation of each number from the mean, which is simply the absolute value of the difference between the number and the mean.

For example, the absolute deviation of 3 from 4.5 is 1.5. Adding all the absolute deviations and dividing it by the total number of numbers gives us the MAD. In this case, the MAD is 1.5.

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The number of minutes it takes for the earth to travel one full rotation around the sun is 529, 960

A proportion can simply be described as an equation in which varying elements, or given numbers are set equal to each other.

It is seen as  a mathematical method of comparing two elements or numbers.

It is also defined as a relation that entails comparison on the basis of size or magnitude of numbers, quantities or elements.

From the information given, we have that;

The earth travels for 365. 25 days round the sun.

If 24 × 60 minutes = 1 day

Then x minutes = 365. 25 days

cross multiply, we have;

x = 24 × 60 × 365. 25

Multiply the values

x = 529, 960 minutes

Hence, the value is 529, 960 minutes

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Answer:

The answer is -2

Step-by-step explanation:

Start at -7 on the number line. Work your way to the right towards the positive numbers by five and there is your answer!

Then the position of the expression 5 + (-7) on the number line will be at negative 2.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5 + (-7)

Calculated the expression, then we have

⇒ 5 + (-7)

⇒ 5 - 7

⇒ - 2

Then the position of the expression 5 + (-7) on the number line will be at negative 2.

The diagram is given below.

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Answer:

A=35 B=100 C=45

Step-by-step explanation:

All triangles equal 180 degrees, add 45 and 35 and you get 80. 180-80 is 100 this gets you angle b. The rest is obvious

Step-by-step explanation:

Your work is correct, but you need to round.  x and y have 2 significant figures, so round your final answer to 2 significant figures:

2.4×10⁶

The expression f(x) / (g(x) + h(x)) = f(x) / g(x) + f(x) / h(x) using the Sum law and Quotient law is proved.

Let us first substitute the limits of f(x), g(x) and h(x) in the function as given;

f(x) = 7

g(x) = 7

h(x) = 6f(x) / (g(x) + h(x))

= 7 / (7 + 6)

= 7/13

This is the computed limit.

Now let's see how the limit laws used to justify the computation.

Limit laws used to justify the computation are:

Sum law

Product law

Quotient law

Let's have a brief description of these laws:

Sum Law:If lim f(x) = L and lim g(x) = M, then

lim[f(x) + g(x)] = L + M.

Product Law:If lim f(x) = L and lim g(x) = M, then

lim[f(x)g(x)] = LM.Quotient Law:If lim f(x) = L and lim g(x) = M ≠ 0, then

lim[f(x) / g(x)] = L / M.

Thus, f(x) / (g(x) + h(x)) = f(x) / g(x) + f(x) / h(x) using the Sum law and Quotient law.

Now, substitute the limits, we get

7/13 = 7/7 + 7/6 using the above limit laws.

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Answer:

89 seats are not being used

Step-by-step explanation:

You subtract the seats being used by teachers

342 - 75 =267

Change 2/3 into a percentage = 66.6%

Find 66.6% of 267= 177.8 (I rounded up to 178)

Then subtract 177.8/178 from 267 to find the amount of seats not being used.

The amount of seats not being used would come down to 89 seats.

I hope this helps!