What is the solution to this inequality? x/10+6 ≥ 8
A. x ≥ 74
B. x ≤ 20
C. x ≥ 20
D. x ≤ 74

The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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The domain of the function h(x)=9x/x(x²-49) is (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

In math the term called the domain of a function is the set of its possible inputs which is the set of input values where for which the function is defined.

Here we have know the function is h(x)=9x/x(x²-49)

And we need to find the domain of the function.

Here we know that this function is defined for values where the denominator is not equal to zero.

Which is written as,

=> x(x²-49) ≠ 0

When we elaborate the equation based on the difference between the two squares property, it can be written as,

=> x(x + 7)(x - 7)  ≠ 0

Based on this we have identified that the value of x must not be

=> x  ≠ -7, 7, 0

Then the domain of the function is written as,

=> (-∞, -7) ∪ (-7, 0) ∪ (0, 7) ∪ (7, ∞).

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Answer:

19/25

Step-by-step explanation:

7/10 + 6/100

= 70/100 + 6/100

= 76/100

= 19/25

So, the answer is 19/25

The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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The number of Walmart stores per 100,000 people in the United States is obtained as follows:

1.4 stores.

The number of Walmart stores per 100,000 people in the United States is obtained applying the proportions in the context of this problem.

The proportion is applied via a rule of three, as follows:

4,740 stores - 332,400,000 people

n stores - 100,000 people

Applying cross multiplication, the value of n is obtained as follows:

332,400,000n = 100,000 x 4,740

n = 100,000 x 4,740/332,400,000

n = 1.4 stores.

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Answer:

y = 3/4x - 8/3

Step-by-step explanation:

Slope m = 3/4 passes through (4,1/3)

y = mx + b

1/3 = 3/4(4) + b

b = 1/3 - 3 = 1/3 - 9/3 = -8/3

so y = 3/4x - 8/3

Answer:

D) y = x - 1

Step-by-step explanation:

First we need the general equation of point slope form:

(y - y0) = m(x - x0)

Where y0 is the y coordinate and x0 is the x coordinate and m is the slope.

For the line to be perpendicular, we need the slope to be the negated opposite of the other equation.  So the negated opposite of -1 is 1.

So our m = 1, y0 = -2, and x0 = -1.  Now let's plug this into the equation and reform the equation into slope-intercept form

(y - (-2)) = 1 (x - (-1))

y + 2 = 1 (x + 1)

y + 2 = x + 1

y = x - 1

So the equation of the line that goes through the point (-1,-2) and is perpendicular to the line y = -x -1, is y = x - 1.

Cheers.

Answer:

B) y = -x - 3

Step-by-step explanation:

slope = -1

y = mx + b

-2 = -1(-1) + b

-3 = b

y = -x - 3

Answer:

I believe it has to be placed about 8 feet from the base

Step-by-step explanation:

sorry if wrong

Answer:

They will be driving for a total of 10 hours or 8 more hours than they've already traveled.

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\\)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4,-1) and (-39,-121)

The distance between them is

\(d = \sqrt{ ({ - 4 + 39})^{2} + ({ - 1 + 121})^{2} } \\ = \sqrt{ {35}^{2} + {120}^{2} } \: \: \: \: \\ = \sqrt{1225 + 14400} \\ = \sqrt{15625} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 125 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

Hope this helps you

Each of the shapes below, The polygons are identified as:

A- Irregular polygon

B- Neither

C- Regular polygon

D- Regular polygon

E- Regular polygon

A polygon is a two-dimensional geometric shape that is defined as a closed figure with three or more straight sides and angles. Polygons can be convex or concave, depending on whether all of their interior angles are less than or greater than 180 degrees, respectively. Some common examples of polygons include triangles (3 sides), squares (4 sides), pentagons (5 sides), hexagons (6 sides), and octagons (8 sides). Polygons are frequently used in geometry, as they can be used to calculate areas, perimeters, and other properties of shapes.

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Common stock $12240 and paid-in capital in excess of par value $5100.

What is the common stock?

Common stock is a sort of instrument that represents company equity ownership. Outside of the United States, the words voting share and ordinary share are also commonly used. In the United Kingdom and other Commonwealth countries, they are referred to as equity shares or ordinary shares.

Here, we have

Given:  Nexis Corp. issues 1020 shares of $12 par value common stock at $16 per share.

So $5 per share is the premium on the issued share.

The premium is commonly recorded in a paid-in capital account.

1020×12 =  $1,2240 and a premium would be recorded in common stock.

1020×5 = 5100, would be recorded in the paid-in capital account.

Hence, Common stock is $12240, and paid-in capital in excess of par value is $5100.

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Answer:

X= -6

Step-by-step explanation:

subtract 25 from both sides then you simplify the expression  when you do that you divide both sides from the same factor which is 3 then you get you're solution x=-6

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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Answer:

9/8

Step-by-step explanation:

3/16 x 6

= 3/16 x 6/1

= 18/16

= 9/8

Answer:

9. yes

10. no

11. yes

Step-by-step explanation:

A Pythagorean triple are 3 numbers that work out to be sides of a right triangle, for which we use the Pythagorean theorem, a^2 + b^2 = c^2.

"a" and "b" are the legs of the triangle, and "c" is the hypotenuse, which is the longest side.

For problem 9, we can plug in 5^2 + 12^2 = 13^2 and see if it's true. If it is true, those numbers are a Pythagorean triple. If it is false, than they are not.

9. 5^2 + 12^2     13^2 = 169

    25 + 144 = 169

Squaring the legs and adding them come up with 169, which is "c" squared, the hypotenuse, or longest leg, 13. So, take the square root of 169, the answer of the left side of the equation, and we see that it works out.

10. 10^2 + 17^2 = 24^2    24^2 = 576

     100 + 289 = 289

After doing the left side of the equation by squaring the shorter numbers, those add up to 289. The hypotenuse squared (24^2) = 576, which is not 289, so this set of numbers are not a Pythagorean triple

11. Here, you need to figure out what number 7\(\sqrt{5}\) is to see if it's a leg or hypotenuse. I like to make it all into a square root of a number (desymplifying it) first. the 7 comes from a perfect square root, \(\sqrt{49}\), so we can multiply these numbers under the radical sign to equal \(\sqrt{245}\) which equals about 15.65, so it is the hypotenuse ("c") because it is the largest number.

7^2 + 14^2    (7\(\sqrt{5}\))^2 = \(\sqrt{245}\)^2 = 245

49 + 196 = 245

245 = 245

a^2 + b^2 = c^2 works out for this equation so it is a Pythagorean triple.

Answer:

the total money they get by the morning show is 2790$

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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We need to make the graph for the pair (x, y_1) and for the pair (x,y_2).

The graph for the two colums is:

We can see that the given points describe a line for each pair of points. These lines are parallel. Since parallel lines never cross, then there can be no intersection;then, for a system of equations that graphs as parallel lines, there can be no solution.

Therefore, the answer is NO SOLUTION. This kind of system is called INCONSISTENT.

The cube root of -1 is -1, and the cube root ∛(-125) is -5.

To find the real nth roots of a number a, we can use the formula:

\(√(a) = a^(1/n)\)

For the case where n=3 and a=-125, we have:

\(√(-125) = (-125)^(1/3)\)

We can simplify this using the fact that

\((-a)^(1/n) = -(a^(1/n)):\)

√(-125) = - (√125)

Now we need to find the cube root of 125. We can factor 125 as 555, so:

√(-125) = - (√125) = - (√(555)) = - (5√5)

Therefore, the real cube root of -125 is -5√5.

The cube root of -125 is the real number x that satisfies the equation

\( {x}^{3} \)

= -125.

We can rewrite -125 as -1*5^3, which means we can write the cube root of -125 as ∛(-1)*∛(5^3).

The cube root of -1 is -1, and the cube root of 5^3 is 5, so ∛(-125) = -1*5 = -5.

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Answer:

a fair cube is expected to come up an equal number of times on each side

6 sides, 60 rolls

... each side is expected 10 times

a) 10 ... expected outcome

b) 30 ... expected outcome

c) 30 ... expected outcome

d) 0 ... only 6 sides

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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(a) There exists a student in your school who has visited North Dakota.

(b) Every student in your school has visited North Dakota.

(c) There exists a student in your school who has not visited North Dakota.

(d) No student in your school has visited North Dakota.

In (a), the existential quantifier (∃) indicates that there is at least one student in your school who has visited North Dakota. The statement N(x) is true for at least one student.

In (b), the universal quantifier (∀) indicates that the statement N(x) is true for every student in your school. In other words, every student in your school has visited North Dakota.

In (c), the existential quantifier (∃) indicates that there is at least one student in your school who has not visited North Dakota. The negation of N(x), denoted by ¬N(x), is true for at least one student.

In (d), the universal quantifier (∀) indicates that the negation of N(x) is true for every student in your school. In other words, no student in your school has visited North Dakota.

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The equation y = x² represents a curve in the set of real numbers2 called a parabola. Hence, the correct option is: Parabola.

What is a parabola?

A parabola is a curve that is shaped like an arch and has one axis of symmetry. The graph of a parabola is U-shaped, and it can open up or down. It is a conic section in geometry, a section of a cone that intersects at a particular angle.

How can you sketch a parabola?

To sketch a parabola, one can use the following steps:

Draw the axis of symmetry and plot the vertex on the line.

Use the axis of symmetry to plot at least two points on one side of the vertex. Then, plot the same points on the other side of the vertex.

Draw a curve through the plotted points that passes through the vertex.

Finally, sketch the graph in both directions until the graph becomes infinitely small or too large.

A circle is represented by \(x^{2} +y^{2} =r^{2}\)

A line is represented by y= mx+ c

Hence, the correct option is: Parabola.

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Answer:

Yes, he got the correct quotient

Step-by-step explanation:

1.5 divided by 1/3 is 4.5, and 4.5 is equal to 4 1/2

Answer:

Sage did it right.

your work:

1 1/2 ÷ 1/3

3/2 ÷ 1/3

3/2 × 3/1

9/2

4 1/2

Step-by-step explanation:

first convert 1 1/2 into an improper fraction:

multiply the 2 and 1, you get 2, than add that to the current numerator to get a new one. You get 3/2 as your improper fraction

you now have: 3/2 ÷ 1/3

then turn the division sign into a multiplication sign by flipping the divisor:

you get 3/2 × 3/1

solve this:

multiply the numerators together, you get 9 as a new numerator

multiply your denominators, you get 2 as your new denominator

so now you have 9/2

next turn this into a mixed fraction, you get 4 1/2

so Sage did it right.

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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Answer:

The answer is "\(m=4(25)+2(5)\\\\\)".

Step-by-step explanation:

Please find the complete question in the attached file.

A party of 20 adults and 5 children needs 90 meatballs. A party with 25 adults and 5 children needs 110 meatballs.\(\to m=4(20)+2(5)\\\\\to m=80+10\\\\\to m=90\\\\\text{The final answer is : }\bold{ m=4(20)+2(5)}\)

Answer:

It will continue to be a negative