An event manager is tracking participation in a tournament by age group. The manager created the following histogram:


Histogram with title Tournament Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 30, the second goes to 50, the third goes to 40, and the last goes to 10.


What percentage of the tournament participants are under the age of 20? Round to the nearest whole percent.


10%

23%

30%

77%

The equation of the circle centered at (−5, 8) and having a radius of 7 is (x + 5)² + (y - 8)² = 49.

The standard form of the equation of a circle is expressed as;

x² + y² = r²

The horizontal (h) and vertical (k) translations represents the center of the circle.

Hence;

(x - h)² + (y - k)² = r²

Given the data in the question;

Center of the circle: (−5, 8)

Now, plug the values of h, k and r into the equation above and simplify,

(x - h)² + (y - k)² = r²

( x - (-5) )² + ( y - 8 )² = 7²

(x + 5)² + (y - 8)² = 49

Therefore, the equation of the circle is (x + 5)² + (y - 8)² = 49.

Hence, option A is the correct answer.

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The required value of V for the given equation is 115.34

What is a simple equation?

A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. It primarily consists of a variable, sometimes with a numerical constant in addition. There cannot be a simple equation without a variable. A known, fixed quantity that is used in a straightforward equation is referred to as a constant.

Given an expression, V/7.9 equals 14.6

or, V/7.9 = 14.6

or, V = 14.6*7.9

or, V = 115.34

Hence, the required value of V is 115.34

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Answer: x-18

Step-by-step explanation:

the alternative hypothesis will state that the proportion is not significantly different than 0.75.

This should be researched with a hypothesis test on the proportion of tourists visiting Rock City.

The claim that want to be tested is if the proportion has increased from the past proportion (π=0.75).

Then, the alternative hypothesis will state that the proportion is significantly higher than 0.75.

On the contrary, the alternative hypothesis will state that the proportion is not significantly different than 0.75.

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The bottom of the ladder is at 8 feet from the wall.

The position of the ladder will form a right angled triangle with the wall. The perpendicular is 15 feet. Let the distance between ladder and wall be x. Thus, the length of the ladder will be 2x + 1. Forming a equation according to Pythagoras theorem.

(2x + 1)² = x² + 15²

Expanding the equation

4x² + 1 + 4x = x² + 225

Rewriting the equation

4x² - x² + 4x = 225 - 1

Performing subtraction

3x² + 4x = 224

3x² + 4x - 224 = 0

Factorizing the quadratic equation, we get -

x = -9.3 and 8

The distance can not be negative. Hence, the value of x is 8.

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The probabilities are given as follows:

The probabilities are called identifying the desired outcomes from the distribution of the number of children per parent.

Hence the probability of fewer than 4 siblings is of:

P(X < 4) = P(X = 1) + P(X = 2) + P(X = 3) = 0.266 + 0.322 + 0.149 = 0.737.

The probability of at least 5 siblings is of:

P(X >= 5) = P(X = 5) + P(X = 6) + P(X > 6) = 0.059 + 0.032 + 0.02 = 0.111.

The probability that the student is not an only child is given as follows:

P(X > 1) = 1 - P(X = 1) = 1 - 0.266 = 0.734.

The distribution is given as follows:

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It will take 51.9 seconds to return to sea level.

The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Using the speed - distance relationship, the time taken for the scientist to travel back to sea level would be 51.9 seconds

Distance = Speed × time

First travel :

Distance covered = 90 × 3.5 = 315 feet

Second travel :

Distance covered = 30 × 2.2 = 66 feet

Net change in position from sea level :

(315 - 66) feet = 249 feet

Maximum speed = 4.8 feet per second

Time taken = Distance / speed

Time taken = 249 ÷ 4.8 = 51.875 seconds

Hence, it will take 51.9 seconds to return to sea level.

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The volume of the solid S in the given question is 5.48unit³.

A three-dimensional space's occupied volume is measured.

It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.

The definition of length and volume are connected.

So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.

An equilateral triangle's height is determined by:

[tex]h = sSin60 = \frac{\sqrt{3} }{2} s[/tex]

Consequently, one triangle's area is:

[tex]A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2[/tex]

The line equation that depicts the diagonal is:

[tex]\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}[/tex]

This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.

[tex]\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}[/tex]

Therefore, the volume of the solid S in the given question is 5.48unit³.

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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.

Answer:

Solution = (5, 2)

Step-by-step explanation:

Step 1: Solve for y in 9x + 2y = 49

    1. 9x + 2y = 49 → 2y = -9x + 49 → y = -4.5x + 24.5

Step 2: Substitute -4.5x + 24.5 for y in -3x + 5y = -5

    2. -3x + 5(-4.5x + 24.5) = -5

Step 3: Solve for x

    3. -3x - 22.5x + 122.5 = -5 → -25.5x + 122.5 = -5 → -25.5x = -127.5 → x = 5

Step 4: Substitute 5 for x in -3x + 5y = -5

    4. -3(5) + 5y = -5 → -15 + 5y = -5 → 5y = 10 → y = 2

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The best buy will be;

''28 pounds for $49.56''

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The two options are,

16 pounds for $31.68

28 pounds for $49.56

Now,

Since, The two options are,

16 pounds for $31.68

28 pounds for $49.56

Hence, The unit rate for each are;

Since, The cost of 16 pounds = $31.68

Hence, The cost of 1 pounds = $31.68/16

                                            = $1.98

And, The cost of 28 pounds = $49.56

Hence, The cost of 1 pounds = $49.56/28

                                            = $1.77

Thus, The best buy will be;

''28 pounds for $49.56''

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Answer:

All the best

The answer is fully correct

The probability that the marksman hits the target at most 13 times is 11.57.

Define binomial probability.

The likelihood of precisely x successes on n further trials in an experiment with two possible outcomes is known as a binomial probability (commonly called a binomial experiment). A random variable's binomial probability is indicated by the notation X B(n, p) (where the prefix stands for "has distribution..."). The distribution's parameters are known as n and p.

The binomial probability is nCx⋅px⋅(1−p)n−x when the probability of success on a given trial is p. In this case, nCx denotes the number of various combinations of x objects chosen from a set of n objects.

Solution Explained:

Given,
P(HT) = 0.89

so if we multiply the chances of hitting he target with 13, we get

P(H13) = 0.89 X 13 = 11.57

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a) The student's work is False and the strategy is incorrect as the fraction should be 1/16

b) The fraction 1/16  as decimal is 0.0625

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be = A

Now the value of A is A = 6 1/4 %

The value of A = 6.25 %

Now , the value of 6.25 % = 6.25 / 100

The fractional form can be substituted by dividing the numerator and denominator by 25 , we get

A = 6.25 / 100

A = ( ( 6.25 ) / 25 ) / ( 100 / 25 )

A = ( 0.25 ) / 4

The value of A = 0.25 / 4

The value of A = 0.0625

And it can be represented in the fractional form as

A = 0.25 / 4

The value of 0.25 = 1/4

Substituting the value of 0.25 in the equation , we get

A = ( 1/4 ) / 4

A = 1/16

Therefore , the value of A = 1/16

b)

The decimal from of the number 1/16 is 0.0625

The mistake the student did was while dividing the number by 100 to convert the percentage , the student evaluated the number 625 instead of 6.25 , so after avoiding the error , we get the fraction as 1/16

The decimal from of the number 1/16 is 0.0625

Hence ,

a) The student's work is False and the strategy is incorrect as the fraction should be 1/16

b) The fraction 1/16  as decimal is 0.0625

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Both the pairs of opposite sides in a parallelogram are parallel and congruent.

According to the question,

We've proved that one pair of sides in parallelogram must be congruent

Let ABCD is a parallelogram ,

We know that AB // CD

Here, AC is transversal for the parallel lines AB and CD

So, ∠BAC = ∠DCA    (Using interior angle property) --------(1)

Similarly , We also know that BC // AD

=> ∠BCA = ∠DAC -----------(2)

Now , In ΔABC and ΔADC,

Therefore , ΔABC ≅ ΔADC    (as per ASA congruence rule)

Therefore , AB = CD and BC=AD   (Corresponding sides of congruent triangles are equal)

Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.

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The Wason selection test measures a person's ability to recognize information that challenges a certain hypothesis, in this case, a type of conditional hypothesis. if P, then Q.

Given,

Wason's Card;

A popular tool for studying problem resolution that was developed in 1966 by English psychologist Peter C(athcart) Wason (1924–2003). The uppermost faces of the four cards, which are arranged on a table, display the letters and numerals E, K, 4, and 7.

What is demonstrated by the Wason selection task?

As a result, the Wason selection test gauges how well people can spot evidence that refutes a certain hypothesis, in this case, a conditional hypothesis of the type. P, then Q if.

For example;-

The majority of people have no trouble choosing the proper cards ("16" and "drinking beer") if the rule is "If you are drinking alcohol, then you must be over 18" and the cards contain an age and beverage on one side, respectively.

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Answer:

The slope is y=-2x.

If solving the equation for the line it is y=-2x-1

Answer: x ∈ {-0.5, -5, -12.5}

Step-by-step explanation: To solve the inequality 2x³ + 21x² + 60x + 25 > 0, we first need to find the values of x that make the inequality true. We can do this by setting the expression equal to 0 and solving for x.

We can start by factoring the expression to make it easier to solve. Notice that 2x³ + 21x² + 60x + 25 is a polynomial with a leading coefficient of 2 and a constant term of 25. This means that it has the form (x + a)(x + b)(x + c), where a, b, and c are constants.

We can start by factoring out the common factor of 2x from the first two terms: 2x³ + 21x² + 60x + 25 = 2x(x² + 10.5x + 12.5). Now we can see that the expression has the form (x + a)(x + b)(x + c), where a = 0.5, b = 5, and c = 12.5.

So, we can rewrite the expression as (x + 0.5)(x + 5)(x + 12.5) = 0. Now we can solve for x by setting each factor equal to 0 and solving for x:

x + 0.5 = 0 => x = -0.5

x + 5 = 0 => x = -5

x + 12.5 = 0 => x = -12.5

Therefore, the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5.

Now we need to determine which of these values make the inequality 2x³ + 21x² + 60x + 25 > 0 true. To do this, we can substitute each of the values of x into the inequality and see which ones make the inequality true.

When x = -0.5, the inequality becomes 2(-0.5)³ + 21(-0.5)² + 60(-0.5) + 25 > 0, which simplifies to -0.5 + 5.25 - 15 + 25 > 0. This is true, because the left-hand side is 29 > 0.

When x = -5, the inequality becomes 2(-5)³ + 21(-5)² + 60(-5) + 25 > 0, which simplifies to -125 + 525 - 300 + 25 > 0. This is also true, because the left-hand side is 225 > 0.

When x = -12.5, the inequality becomes 2(-12.5)³ + 21(-12.5)² + 60(-12.5) + 25 > 0, which simplifies to -391.25 + 1181.25 - 750 + 25 > 0. This is also true, because the left-hand side is 1147.5 > 0.

Therefore, the solution to the inequality is x ∈ {-0.5, -5, -12.5}. This means that the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5. The inequality is satisfied when x is any of these values.

The probability that the couple will have more than 2 girls is 1/2.

Here, we are given that a couple is planning to have 3 children.

Let us list down all the possible combination of outcomes-

GGG, GGB, GBB, BBB

Here G stands for a girl and B for a boy.

Thus, there are a total of 4 outcomes. We need to find the probability that the number of girls is greater than or equal to 2.

Out of the listed outcomes, 2 combinations- GGG and GGB have number of girls ≥ 2.

We know that probability = Number of favorable outcomes/ total number of outcomes

P(x ≥ 2) = 2/4

= 1/2

Thus, the probability that the couple will have more than 2 girls is 1/2.

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There are 201376 ways can a group of 5 lucky students be selected to sit in the front of the classroom.

What are combinations?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

Permutations and combinations are often mistaken. The chosen components' order is crucial in permutations, though. For instance, whereas permutations treat the arrangements differently, combinations treat the arrangements ab and ba equally (as one arrangement).

Use the combinations formula:

n = 32, r=5

[tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex]

[tex]^{32}C_{5}=\frac{32!}{(32-5)! 5!}[/tex]

       = (32*31*30*29*28*27!)/(5!*27!)

       = (32*31*30*29*28)/ (5*4*3*2*1)

       = 201376

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As per the concept of z - score, the percentile would this client's score is 0.4772

Z - score:

In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.

Given,

A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.

Here we need to find at what percentile (rounded off) would this client's score place her.

As per the formula of z score, here we have the values,

mean = 100

standard deviation = 15

Score = 130

Therefore, the z score is calculated as,

=> z score = (130 - 100) / 15

=> z score = 30 / 15

=> z score = 2

According to the z score table the resulting value is 0.4772.

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The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..

The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).

We have given that,

A sample of manufacturing process.

Sample size, n = 5

Mean of sample ranges = 0.50

we have to calculate the estimate of standard deviations of population.

thus , we estimate the standard deviations as fourth of the mean of the sample ranges is

S = Mean of sample ranges/4

=> S = 0.50/4

=> S = 0.125

Hence, the standard deviation of the population is estimated as 0.125..

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Answer:

Step-by-step explanation:

x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.

Given that,

Pens and notebooks used to cost the same, however recently the price of the pen went up by $4 while the price of the notebook went down by $6 from its previous value of $5.

We have to find what might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.

We know that,

We get the equation as

x+4>5x-6

By solving the x

The inequality with x<2.5

So, natural number, n=2

x>2

Therefore, x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.

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The slope of both functions remains the same, there is no effect of the value of k on a slope.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The given functions are :

f(x) = 2x + 5

g(x) = ( 2x + 5) -3

From the graph of both functions,

Let us consider two pairs of coordinates to find the slope,

For f(x)

(0,5) and ( -2, 1)

The slope of f(x)

m= ( 1- 5) / (-2 -0)

m= 2

For g(x) at (0,2) and (-1, 0) slope of g(x),

m = ( 0-2) / (-1-0)

m = 2

The slope remains unaffected.

y-intercept of f(x) , put x = 0

⇒ y = 5

y-intercept of g(x) , put x = 0

y =(0+ 5) -3

y = 2

Change in the value of y-intercept due to the value of k = -3.

Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:

The slope of both functions remains the same, there is no effect of the value of k on a slope.

Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.

The graph is attached.

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The equivalent expressions of each number are respectively;

1) 2(x - 2) = -7 + 6x - 4x + 3

2) (x + 14) - (8 - 2x) = 9x - 2(3x - 3)

3) 3(x + 5) = -2x + 9 + 5x + 6

4) -4(x + 1) + 5x =  (7 - 2x) + (3x - 11)

5) (7 + 5x) + (4x - 1) = -3x + 6 + 4x

The properties of algebra include associative property, distributive property, Identity property, Inverse property, e.t.c.

Now, let us simplify the terms on the right;

a) (7 - 2x) + (3x - 11)

Expanding the brackets gives us;

7 - 2x + 3x - 11

= x - 4

This can also be expressed as;

-4(x + 1) + 5x

b) -7 + 6x - 4x + 3

Simplifying gives;

2x - 4

= 2(x - 2)

c) 9x - 2(3x - 3)

Simplifying gives;

9x - 6x + 6

3x + 6

It can also be written as;

(x + 14) - (8 - 2x)

d) -3x + 6 + 4x

Simplifying gives;

x + 6

This can also be expressed as;

(7 + 5x) + (4x - 1)

e) -2x + 9 + 5x + 6

This can also be expressed as;

3x + 15

3(x + 5)

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Answer:

[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]

[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]

[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]

[tex]\boxed{5.} \quad -3x+6+4x[/tex]

[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]

Step-by-step explanation:

Simplify the given expressions numbered 1 through 5:

[tex]\begin{aligned}\textsf{1.} \quad 2(x-2)&=2 \cdot x + 2 \cdot (-2)\\&=2x-4\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{2.} \quad (x+14)-(8-2x)&=x+14-8+2x\\&=x+2x+14-8\\&=3x+6\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{3.} \quad 3(x+5)&=3 \cdot x + 3 \cdot 5\\&=3x+15\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{4.} \quad -4(x+1)+5x&=-4 \cdot x -4 \cdot 1+5x\\&=-4x-4+5x\\&=5x-4x-4\\&=x-4\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{5.} \quad (7+5x)+(-4x-1)&=7+5x-4x-1\\&=5x-4x+7-1\\&=x+6\end{aligned}[/tex]

Simplify the given answer expressions:

[tex]\begin{aligned}(7-2x)+(3x-11)&=7-2x+3x-11\\&=3x-2x+11-11\\&=x-4\end{aligned}[/tex]

[tex]\begin{aligned}-7+6x-4x+3&=6x-4x+3-7\\&=2x-4\end{aligned}[/tex]

[tex]\begin{aligned}9x-2(3x-3)&=9x-2 \cdot 3x-2 \cdot (-3)\\&=9x-6x+6\\&=3x+6\end{aligned}[/tex]

[tex]\begin{aligned}-3x+6+4x&=4x-3x+6\\&=x+6\end{aligned}[/tex]

[tex]\begin{aligned}-2x+9+5x+6&=5x-2x+9+6\\&=3x+15\end{aligned}[/tex]

Therefore, the matching pairs of equivalent expressions are:

[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]

[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]

[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]

[tex]\boxed{5.} \quad -3x+6+4x[/tex]

[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]

Answer:

4x + 15

Step-by-step explanation:

1. Add the numbers

4x + 2(2 + 5) + 1

4x + 2(7) + 1

2. Multiply the numbers

4x + 2(7) + 1

4x + 14 + 1

3. Add the numbers

4x + 14 + 1

4x + 15

Solution:

4x + 15

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The solution to the system equation  is (x, y, z, w) = (23, 12, 3, 1).

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

Here is a system of linear equations that represents the situation.

x +5y +10z +20w = 133 . . . total amount earned

x +y +z +w = 39 . . . . . . . . . total number of bills

y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s

x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s

_____

We can substitute for x and z in the first two equations:

... (2y-1) +5y +10(y/4) +20w = 133

... (2y-1) +y +(y/4) +w = 39

These simplify to

... 9.5y +20w = 134

... 3.25y +w = 40

Solving by your favorite method, you get

... y = 12

... w = 1

So the other values can be found to be

... x = 2·12 -1 = 23

... z = 12/4 = 3

hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).

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The shape of the molecule having formula ab2 has been linear or trigonal planar. Hence, the correct option will be e) linear or trigonal planar

The hybridization is been given as the combining of the valence shells with the formation of the given hybridized shell which have equal energy distribution.

The molecule that has A as a central atom, and B bonded to the fixed central atom. The molecular hybridization of the given molecule will be sp hybridization and that accounts for the linear shape of the molecule according to VSEPR theory.

Hybridization of A having the lone pair, and the shape of the molecule will be trigonal planar.

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Answer: 32

Step-by-step explanation:

50% = x/2

50% of 64 = 64/2

50%=32

Answer:  The correct answer is 32 tickets were early admission

Step-by-step explanation:

T = Total tickets sold

E = Early admission tickets

If 50% of the total tickets are for early admission, then our equation would be:

E = T * 50% (or .5)

Substitute 64 for the total tickets

E = 64 * .5

E = 32

Answer: C

Step-by-step explanation:

-2 and 2 add up to 0

Answer:

c

Step-by-step explanation:

-2 + 2 =0