Determine if the following scenarios are mutually exclusive or overlapping. Explain your reasoning.
1. You are taking a multiple choice test. Event A is you choose the correct answer. Event B is you choose D as the answer.
2.You survey students in your school about what grade they are. Event A is the person is a senior. Event B is the person is a junior.

Answer:

[tex]\fbox {Work is attached below.} \downarrow[/tex]

Step-by-step explanation:

Based on the given probability events, we can calculate that Events A and B are independent, because P(B) = P(B|A) = 1/2.

Events are independent if P(B) = P(B|A)

The probability of event B is:

= 3 odd numbers / 6 numbers

= 1 / 2

The probability of A is:

= 3 prime numers / 6

= 1/2

P(B|A) = ((1 / 2) x (1 / 2)) / (1 / 2)

= 1/2

So P(B) = P(B|A) = 1/2.

The events are independent.

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ST and RU are equal,

24x =  23x + 1

Subtract 23x from both sides:

x = 1

Now replace x to solve for ST

24x = 24(1) = 24

ST = 24

Answer:

x=8

Step-by-step explanation:

You cross multiply, 6 times 4 is 24, so what times 3 is 24. 8 times 3 is 24.

Answer:

  x = 8

Step-by-step explanation:

There are several ways you can solve a proportion like this. Most of the algebraic solutions involve what amounts to multiplying both sides by (4x/3). There are also graphical solutions and solutions that rely on relations that make fractions be equal.

__

The method of solution usually recommended is to "clear fractions" and then solve the resulting one-step linear equation. To "clear fractions," multiply both sides of the equation by the least common denominator: 4x.

  [tex](4x)\dfrac{3}{4}=(4x)\dfrac{6}{x}\\\\3\cdot x=4\cdot6\qquad\text{looks like "cross multiplication"}[/tex]

We describe this as "cross-multiplication" because it looks like each numerator has been multiplied by the opposite denominator.

This "one-step" linear equation is solved by dividing by the coefficient of x, which is 3:

  [tex]\dfrac{3x}{3}=\dfrac{4\cdot6}{3}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]

Note that we could have done these operations in one step. The two steps, multiply by 4x and divide by 3, are identical to the one step, multiply by (4x/3).

  [tex]\left(\dfrac{4x}{3}\right)\cdot\dfrac{3}{4}=\left(\dfrac{4x}{3}\right)\cdot\dfrac{6}{x}\\\\\boxed{x=8}\qquad\text{simplify}[/tex]

__

We can see the solution almost immediately if we rewrite the fractions so they have the same numerator.

  [tex]\dfrac{3}{4}=\dfrac{6}{x}\\\\\dfrac{3\cdot2}{4\cdot2}=\dfrac{6}{x}\\\\\dfrac{6}{8}=\dfrac{6}{x}\ \Longrightarrow\ \boxed{x=8}[/tex]

The same thing happens if we multiply the equation by the inverse of either side.

  [tex]\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{4}{3}\right)\dfrac{3}{4}=\left(\dfrac{4}{3}\right)\dfrac{6}{x}\ \Longrightarrow\ 1=\dfrac{8}{x}\ \Longrightarrow\ \boxed{x=8}\\\\\textsf{ or ...}\\\\\dfrac{3}{4}=\dfrac{6}{x}\ \Longrightarrow\ \left(\dfrac{x}{6}\right)\dfrac{3}{4}=\left(\dfrac{x}{6}\right)\dfrac{6}{x}\ \Longrightarrow\ \dfrac{x}{8}=1\ \Longrightarrow\ \boxed{x=8}[/tex]

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If the equation is rewritten to a form that has a value of 0 at the solution, then the x-intercept of the graph will be the solution to the equation.

  3/4 = 6/x . . . . . . . . original equation

  6/x -3/4 = 0   ⇒   f(x) = 0

  f(x) = 6/x -3/4

The graph shows the solution to f(x) = 0 is x=8.

Inequalities help us to compare two unequal expressions. The correct option is A.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

The complete question is:

The sum of 16 and a number is less than 24. Which of the following inequalities expresses the solution?

x<8

x>8

x=8

x<-8

Given the sum of 16 and a number is less than 24. Let the number be represented by x, therefore,

16 + x < 24

x < 24 - 16

x < 8

Hence, the correct option is A.

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Answer:

Reason -

In the question it is given that triangle ABC is congruent to triangle DEF

if a triangle is congruent to other triangle than the corresponding parts of it (.ie sides and angles) are equal to that of other

Answer:

range of f is [0,3]

Step-by-step explanation:

The "square root" symbol, [tex]\sqrt{\text{ \quad }}[/tex], is a function.  As a result, it only has a single output because functions must only have a single output for each input.

Thinking about it graphically, if the square root function did give both a positive and a negative result, the function "f" would not pass the vertical line test and it would not be a function.

When solving an equation like [tex]x^2=25[/tex], to solve, we must apply the square root property.  The square root property says that to find both solutions, one must look at both the positive and the negative of the square root.  So, to solve:

[tex]x^2=25[/tex]

Apply square root property...

[tex]\sqrt{x^2} = \pm \sqrt{25}[/tex]

[tex]x=\sqrt{25}[/tex]  or  [tex]x=-\sqrt{25}[/tex]

[tex]x=5[/tex]  or  [tex]x=-5[/tex]

In this case, because the square root function itself only outputs non-negative results (so, including zero, as you already identified), the range will only be [0,3].

Answer:

20

Step-by-step explanation:

each year each child will get additional age

example 5 children average of the age 20 years old.

after 20 years all of them.will be 20+20=40 years old.

the group of the children not changing but average of the groups will be increase in 20 years.

Answer:

60 ft

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{CD}{AD}[/tex] = [tex]\frac{30}{AD}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

AD = 60 ft

Rationalizing the numerator, it is found the result of the limit is given as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{1}{2\sqrt{x}}[/tex]

A limit is given by the value of function f(x) as x tends to a value.

The first step to find the limit is replace the variable by the value, hence:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} = \frac{0}{0}[/tex]

Undefined limit, hence we have to find another way. The numerator includes square roots, hence it should be rationalized using the subtraction of perfect squares, as follows:

[tex]\lim_{h \rightarrow 0} \frac{(\sqrt{x + h} - \sqrt{x})}{h} \times \frac{(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{(\sqrt{x + h})^2 - (\sqrt{x})^2}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{x + h - x}{h(\sqrt{x + h} + \sqrt{x})} = \lim_{h \rightarrow 0} \frac{h}{h(\sqrt{x + h} + \sqrt{x})}[/tex]

Then we simplify the h, so:

[tex]\lim_{h \rightarrow 0} \frac{1}{\sqrt{x + h} + \sqrt{x}} = \frac{1}{2\sqrt{x}}[/tex]

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The height at 150°, 240°, and 315° will be 208.66 feet, 169.5 feet, and 40.34 feet, respectively.

The quantity which has magnitude, direction and follows the law of vector addition is called a vector.

A Ferris wheel with a diameter of 214 feet was built in a city.

The top of the wheel stands 223 feet above the ground.

Then the radius will be

r = 214 / 2

r = 107 feet

The distance between the ground and bottom of the Ferris wheel will be

d = 223 – 214

d = 9 feet

Then the height will be given as

h = r(1 – cos θ) + h

h = 107(1 – cos θ) + 9

At θ = 150°, then the height will be

h = 107(1 – cos 150°) + 9

h = 208.66 feet

At θ = 240°, then the height will be

h = 107(1 – cos 240°) + 9

h = 169.5 feet

At θ = 315°, then the height will be

h = 107(1 – cos 315°) + 9

h = 40.34 feet

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The coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have:

Image of R(-4, 3) after a reflection in the line y = x

The rule for the reflection over y = x is:

(x, y) = (y, x)

(-4, 3) = (3, -4)

Thus, the coordinate for the R' is (3, -4) if the R(-4, 3) is reflected in the line y = x option (D) is correct.

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The area of the shaded sector must be 144π units².

The area of the circle is defined as the product of the pie and the square of the radius.

The area of the circle = [tex]\pi r^{2}[/tex]

We know that the angle measurement of central angle QRS is less than π radians.

for r = 18 units

The area of the circle = π18² = 324π  units²

The area of ​​the half of a circle = 324π /2 = 162π units²

The area of ​​a quarter of a circle = 324π /4 = 81π  units²

so

The area of the shaded sector < 162π  units²

and

The area of the shaded sector > 81π  units²

Hence the answer must be 144π units²

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Answer:

A.) 588329.896

B.) 274300

C.) 1657.18474

D.) 1.002

(All answers unrounded.)

Explanation:

I converted each unit to the unit used in the other number (E.g., for question A I converted tons to kilograms, and then finished solving.)

Answer:

I'm not sure how to interpret "y = 3√x+1-2."

I'll assume y = 3[tex]\sqrt{x+1}[/tex] - 2

Step-by-step explanation:

Use the free online app DESMOS.  Either enter the equation, or make a table of individual points and plot them as ordered pairs.

GRAPH:   See attached image

PLOT:  Calculate a few points, mark them on the graph and then connect the dots.  I selected a few values of x and calculated y from the equation.  Each calculation provides a (x,y) ordered pair which can be marked on the graph and the dots are then connected.  Note that x values less than -1 result in a value of y that includes i, an imaginary number.  So the graph ends abruptly at that point.

Answer:

Step-by-step explanation:

Ratio and proportion:

   [tex]\sf \dfrac{x}{3}=\dfrac{6}{9}\\\\ x = \dfrac{6*3}{9}\\\\x = 2[/tex]

[tex]\sf \dfrac{8}{y}=\dfrac{6}{9}\\\\Cross \ multiply,\\\\y*6=9*8\\\\y=\dfrac{9*8}{6}\\\\y=3*4\\\\\bf y = 12[/tex]

[tex]\sf \dfrac{a}{15}=\dfrac{6}{9}\\\\a =\dfrac{6}{9}*15\\\\a=2*5\\\\\bf a = 10[/tex]

This is a polynomial of degree 4, for each value of x, we get only one value of y, so we conclude that this is a function.

A function is a relation that maps inputs (usually written as x) into outputs (usually written as y). Such that each input is mapped into only one output.

For example, if we had:

y = ±√x

Notice that for the same input x = 1, we would have two outputs:

y = 1 and y = -1.

So that is not a function.

Now, for the given one:

[tex]y = f(x) = 3x^4 - 5x^2[/tex]

This is a polynomial of degree 4, for each value of x, we get only one value of y, so we conclude that this is a function.

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the answer would be 9.88372093e-7

1 )Simplify.

[tex]\frac{850000000000000000}{8.6E}[/tex]+23

2 )Answer

9.88372093e-7

Answer:

D, C

Step-by-step explanation:

for part a, there is a negative slope with the graph shifted two units upwards

for part b, if you plug in C, you get an answer that works

Amy is correct, -7.1 is between -7 and -8.  

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Two students were asked to graph a rational number -7.1.

Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.

In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.

But -7.1 has a whole number of 7 then it is in between -7 and -8.

Thus, Amy is correct, -7.1 is between -7 and -8.  

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Answer:

C

Step-by-step explanation:

The y intercept is 3, so eliminate B and D.

Also, the slope is less than 1, so this eliminates A.

This leaves us with C.

Answer:

I exactly don't have or know the answer

Answer:

12 is the correct answer

Answer:

5. y = 2/3x + 1

8. y = 4/7x - 4

Step-by-step explanation:

5. (-6, -3) and (6, 5)

You can use the slope formula which is (y2-y1)/(x2-x1) to find the slope and plug it back into the slope-intercept form to find the y-intercept

(5-(-3)) / (6-(-6)) = 8 / 12 = 2/3

slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

to find b you can plug in one of the coordinates and the slope

5 = 6(2/3) + b

5 = 4 + b

1 = b

y = 2/3x + 1

8. (-7, -8), (21, 8)

m = (8 -  (-8)) / (21 - (-7)) = 16 / 28 = 4/7

plug in one of the coordinates and the slope to find b or the y-intercept

8 = 21(4/7) + b

8 = 12 + b

-4 = b

y = 4/7x - 4

Answer:

- 24

Step-by-step explanation:

4(m + 2p) ← substitute m = 2 and p = - 4 into the expression

= 4(2 + 2(- 4) )

= 4(2 - 8)

= 4(- 6)

= - 24

The difference of the fractions as given in the task content is; (4-2x) / (x²-16).

According to the task content, the fractions whose difference is to be evaluated are as indicated below;

[tex] \frac{x}{( {x}^{2 } - 16)} - \frac{3}{x - 4} [/tex]

Hence, the LCM of the denominators of both fractions can be evaluated as;

x -3(x+4)/(x²-16).

(4-2x) / (x²-16)

Hence, the difference of the two fractions is; (4-2x) / (x²-16).

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Answer:

[tex]\fbox {False}[/tex]

Step-by-step explanation:

To convert a degree measure to radian measure, multiply with π/180.

⇒ 180 × π/180

⇒ π radians

false is the answers

please mark me as brainlest

Answer:

  a) positive real zeros: 2 or 0; negative real zeros: 2 or 0; complex zeros: 0, 2, or 4. (rule of signs)

  b) ∪-shaped, as for an even-degree polynomial with positive leading coefficient. See attached.

  c, d) See attached

Step-by-step explanation:

Descarte's rule of signs gives bounds on the number of positive and negative real roots. The numbers it gives may be reduced by multiples of 2, as complex roots will come in conjugate pairs. The total number of roots of all kinds will match the degree of the polynomial.

Synthetic division is essentially polynomial long division with some modifications:

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The signs of the terms of the given polynomial are + - - - +. There are two sign changes, so 2 possible positive real roots.

When the signs of the odd-degree terms are changed, the signs become + + - + +. There are still two sign changes, so 2 possible negative real roots.

Either or both of these numbers can be reduced by 2 if the roots include a conjugate pair. That is, there may also be 0 possible positive real roots, and 0 possible negative real roots.

The number of non-real (complex) zeros may be any multiple of 2 up to the degree of the polynomial. The may be 0, 2, or 4 possible non-real zeros.

__

The graph is the first attachment. It shows 4 real zeros: x = -4, -2, 1, 6.

Since the polynomial is of even degree (4) and has a positive leading coefficient (+1), we expect the general shape to be ∪-shaped. It is.

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The second attachment shows synthetic division using x = -4. (The binomial divisor is (x+4).) The remainder (lower right value in the tableau) is the value of y when x=-4. The third attachment shows synthetic division using the value x=3. (y is -210 when x=3.)

Maybe this is the table you want:

  [tex]\begin{array}{|c|c|c|}\cline{1-3}x&-4&3\\\cline{1-3}y&0&-210\\\cline{1-3}\end{array}[/tex]

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The second attachment shows synthetic division by the factor (x+4).

_____

Additional comment

The synthetic division attachments show instructions for carrying out the synthetic division and interpreting the results. As we said above, "the entry on the left" is the opposite of the constant in the binomial divisor. It is the actual value of x you want to use to evaluate the function.

The equations shown are merely for the purpose of indicating the operations that are used. An actual synthetic division tableau is simply a 3-row table of numbers, with the bottom row being the quotient coefficients and remainder.