What is the whole number consisting of x in the hundreds place, y in the
tens place, and 2 in the ones place?

Answers

Answer 1

The whole number consisting of x in the hundreds place, y in the tens place, and 2 in the ones place is; xy2.

What is the whole number described in the task content?

It follows from the task content that the whole number described has x in the hundreds place, y in the tens place, and 2 in the ones place.

The whole number in discuss can be broken down simply as: (x×100) + (y×10) +(2×1).

Hence, the whole number is; xy2.

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Related Questions

Hello, i am having a hard time solving this. If anyone can please explain how to solve it in order for me to solve future questions of the same type?


f(x) = 5x3 – 2x and g(x) = 3x3


perform the following :


f(g(x))


g(f(x))

----- Thank you for your help

Answers

Answer:

Step-by-step explanation:

Solve the following proportion by cross multiplying:
x / 8 = 28 / 32

Answers

Since it is an equality that means the left side of the equation (x/8) has to be equal to the right side of the equation (28/32). One way you can solve for x is to isolate it. Since it’s an equality like we said you have to do to the left side the same that you would do to the right side to isolate x. So if I multiply by 8 on the left I need to also multiply by 8 on the right. So 8* (x/8) becomes just x since 8x/8 becomes 8/8 * x which is 1 *x. On the right side we do 8 *(28/32) which becomes 28 * 8/32 which becomes 7. So x = 7.

Answer:  x = 7

Step-by-step explanation:

[tex]\frac{x}{8} =\frac{28}{32}[/tex]

We cross multiply, and we get:

32x = 8(28)

32x = 224

    x = 7

HELP HELP HELP HELP
HELP HELP HELP

Answers

Answer:  The base should be 4.

Step-by-step explanation:

1. We draw a triangle shape like the image.

(The steps was showed in the image).

two cyclists leave towns 74 miles apart at the same time and travel towards each other. one cyclist travels 3 mi/h faster than the other. If they meet in 2 hours, what is the rate of each cyclist?

Answers

The rates of each cyclist are 17mi/h and 20mi/h

What is rate?

Rate is a ratio that compares two different quantities which have different units.

In this comparison, one unit is taken to be a standard unit in which the other is compared with.

Analysis:

Let the speeds of both cyclists be x,  x+3

distance travelled by x cyclist = 2x

distance travelled by (x+3) cyclist = 2(x+3)

Total distance = 2x + 2(x+3) = 74 miles

2x +2x +6 = 74

4x + 6 = 74

4x = 74 - 6

4x = 68

x = 68/4 = 17mi/h

The other cyclist speed is x +3 = 17 +3 = 20mi/h

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Find NM=
Help me please thanks

Answers

A triangle is a three-edged polygon with three vertices. The length of the side MN is 3 cms.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

The triangle formed by MN, MO, NO is an equilateral triangle, with the length of each side of the triangle equal to the radius of the triangle. Therefore, the length of MN will be,

MN = r

Now, the length of arc MN can be written as,

2 × π × r × (60° /360°) = π

r = 360 / (60 × 2)

r = 3

Hence, the length of the side MN is 3 cms.

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Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1.08p. Using this information, which of the following represents the final price of a tablet, with the discount and taxes applied, based on its original price?

Answers

Using proportions, it is found that the expression that represents the final price is given as follows:

C(t) = 0.918t.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, we have that:

With the discount, the price is of 0.85t.With the taxes, the price is increased by 8%, hence multiplied by 1.08.

Thus the expression for the final cost is:

C(t) = t x 0.85 x 1.08 = 0.918t.

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What is the sum of the polynomials?
(6x+7+x²)+(2x²-3)
O-x²+6x+4
O3x²+6x+4
O9x + 4
O gx² +4

Answers

Answer:

3x² + 6x + 4

Step-by-step explanation:

6x + 7 + x² + 2x² - 3

→ Collect like terms

x² + 2x² + 6x + 7 - 3

→ Simplify

3x² + 6x + 4

Answer:

3x^2+6x+4

Step-by-step explanation:

We can find the sum of the polynomials by combining like terms.

(6x+7+x²)+(2x²-3)

x^2+2x^2+6x+7-3

3x^2+6x+4

In a lab experiment, the decay of a radioactive isotope is being observed. On the first day of the experiment the mass of the substance was 1400 grams and mass was decreasing by 10% per day. Write a recursive formula to represent the mass of the radioactive sample on the day of the experiment.

Answers

The recursive formula is mathematically given as

a_n=1266.77e^n

What is the recursive formula?

Generally, the equation for the decay is  mathematically given as

[tex]at=a_oe^{-\lambda t}[/tex]

Hence

a1=1400e^{-0.1 (1)}

In conclusion,

[tex]a_n=1400e^{-0.1 (n)}\\\\a_n=1266.77e^n[/tex]

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I need help pls WILL GIVE BRAINLIEST

Answers

Answer: (1, -3)

Step-by-step explanation:

[tex]8x+4y=-4\\-4x-5y=11[/tex]

[tex]2(-4x-5y)=11(2)\\-8x-10y=22[/tex]

new system:

[tex]8x+4y=-4\\-8x-10y=22[/tex]

add.

[tex]-6y=18\\y=-3[/tex]

plug in -3 for y

[tex]8x+4(-3)=-4\\8x-12=-4\\8x=8\\x=1[/tex]

system:

[tex](1,-3)[/tex]

Answer:

Make one of the variable in one of the equations the subject of the formular first.[tex]4y = - 4 - 8x[/tex]to leave y independent divide the whole equation by the coefficient of y at this point it is 4.Then divided the whole equation by 4.[tex] \frac{4y}{4} = \frac{ - 4}{4} - \frac{8x}{4} [/tex]therefore the new equation will be[tex]y = - 1 - 2x....(3)[/tex]substitute the new equation in the other equation N.B not the one you extracted the new equation from.you will use -4x-5y=11 in substituting y=-1-2y[tex] - 4x - 5( - 1 - 2x) = 11 \\ - 4x + 5 + 10x= 11 \\ \\ - 4x + 10x = 11 - 5 \\ 6x = 6 \\ \frac{6x}{6} = \frac{6}{6} \\ x = 1[/tex][tex]y = - 1 - 2(1) \\ y = - 1 - 2 \\ y = - 3[/tex]HOPE THIS HELPS!

24. A pizzeria sells a medium pizza for $5.99 plus $0.75 for each topping.
They also sell a large pizza for $6.99 plus an additional $0.50 per topping.
After how many toppings will the medium and large pizzas cost the same
amount?

The pizzas will cost the same at 4 toppings.

The pizzas will cost the same at 5 toppings.

The pizzas will cost the same at 6 toppings.

The pizzas will never cost the same amount.

Answers

Answer:

a.) The pizzas will cost the same at 4 toppings

Step-by-step explanation:

Medium Pizza:

$5.99 + $0.75x

Large Pizza:

$6.99 + $0.50x

Find x

$5.99 + $0.75x =  $6.99 + $0.50x

0.25x = 1

x = 4

A line is perpendicular to the line 3x - 4y= 2 and passes through the point (1, - 2). Which of the following
is an equation of the line?

Answers

Answer:

Last option, y = -4/3x - 2/3

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

number that describes both the direction and the steepness of the line

slope = rise/run

           b represents the y-intercept  

point where crosses the y-axis

Given:

line 3x - 4y = 2passes through the point (1, - 2)

Let change 3x - 4y = 2 into y = mx + b form,

3x - 4y = 2

subtract 3x from both sides,

3x - 3x - 4y = 2 - 3x

- 4y = 2 - 3x

divided both sides by -4 to get y alone,

- 4y / -4 = 2 - 3x / - 4

  y = (3x / 4) - (2 / 4)

→ y = (3/4)x - (1/2)

Slope of perpendicular lines to another is the negative reciprocal

(ex. slope of 2 becomes -1/2)

So for y = (3/4)x - (1/2) the slope will be,

slope = -4/3

We need to find b (y-intercept),

we know it passes through point (1, - 2)

a point is (x, y) format

y = -(4/3)x + b

plug in the point (1, - 2),

-2 = -4/3(1) + b

-2 = -4/3 + b

add 4/3 to both sides to get b alone,

-2 + 4/3 = -4/3 + 4/3 + b

-2/3 = b

the perpendicular line equation is,

y = -4/3x - 2/3

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What's the value? (yelping for help)

Answers

cos(20°) is the correct answer.

Congratulations! This is the unit circle. Literally everyone hates this. Everyone takes this in Trigonometry though, and it's required. I literally failed Trigonometry because of this and had to retake it when getting my degree in Mathematics.

So, what is the x-coordinate of this? Well, for any angle or (angle in triangle) [tex]\alpha[/tex], the coordinates are always ([tex]cos(\alpha), sin(\alpha)[/tex]).

In this case, angle [tex]\alpha[/tex] is 20°, and so the x-coordinate will be cos(20°) while the y-coordinate will be sin(20°).

Hope this helped!

Answer: cos 20

Step-by-step explanation:

Complete the following chart below.
FIll in the missing blanks.

Answers

[tex]y=2(x+1)^2+6[/tex]

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

What is graph?

A graph can be defined as a pictorial representation or a diagram that represents data or values.

[tex]y=2(x+1)^2+6[/tex]

The vertex (−1,6)

Equation of axis of symmetry is x = -1

minimum at (-1,6)

[tex]y=\frac{-(x-1)}{2} ^2-4[/tex]

The vertex (1,-4)

Equation of axis of symmetry is x = 1

maximum at (1,-4)

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Which statements are correct? Check all that apply.
One-halfQP = UT
One-halfTS = RQ
SU = PR
SU ∥ RP
UT ⊥ RP

Answers

By applying the triangle midpoint theorem to the two triangles (see attachment), the correct statements are:

A. One-halfQP = UT

D. SU ∥ RP

What is triangle midpoint theorem?

Triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the two triangles (see attachment), we can infer and logically deduce that one-half of side QP is equal to side UT and side SU is parallel to side RP (SU ∥ RP).

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Complete Question:

Points S, U, and T are the midpoints of the sides of ΔPQR. ΔSUT is inside of ΔPQR. Points S, U, and T are the midpoints of ΔPQR. Which statements are correct? Check all that apply.

A. One-half QP = UT

B. One-half TS = RQ

C. SU = PR

D. SU ∥ RP

E. UT ⊥ RP

Answer: a and d

Step-by-step explanation:

Given: x is the midpoint of MN¯¯¯¯¯¯¯¯¯¯ and MX=RX

Prove: XN=RX

Answers

A midpoint of a line segment implies a point on the line that is equidistant to its two ends. So that the required proof is shown below:

Given: line segment MN

           x, the midpoint of MN

           MX = RX

Then;

MX = XN (midpoint property of a line)

So that,

MN = MX + XN

      = MX + MX (since XN = MX)

MN = 2MX

Thus,

MX = XN = RX (given that MX = RX)

Therefore, it can be concluded that;

XN = RX

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Solve for x : log(3x) + log(x + 4) = log(15).

Please explain it to me.​

Answers

Answer:

x = 1

Explanation:

[tex]\sf \rightarrow log(3x) + log(x + 4) = log(15)[/tex]

Rule: log(a) + log(b) = log(ab)

[tex]\sf \rightarrow log(3x(x + 4)) = log(15)[/tex]

cancel out log on both sides

[tex]\sf \rightarrow 3x(x + 4) = 15[/tex]

relocate constant variable

[tex]\sf \rightarrow 3x^2 + 12x -15 = 0[/tex]

take 3 as a common factor

[tex]\sf \rightarrow 3(x^2 + 4x -5) = 0[/tex]

divide both sides by 3

[tex]\sf \rightarrow x^2 + 4x -5 = 0[/tex]

middle term split

[tex]\sf \rightarrow x^2 + 5x -x-5 = 0[/tex]

factor common terms

[tex]\sf \rightarrow x(x + 5) -1(x+5)= 0[/tex]

collect into groups

[tex]\sf \rightarrow (x-1)(x+5)= 0[/tex]

set to zero

[tex]\sf \rightarrow x-1 = 0 , \ x+5= 0[/tex]

relocate variables

[tex]\sf \rightarrow x = 1, \ x = -5[/tex]

There must be a positive solution for log, so the solution is only x = 1

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Given:

[tex]\log (3x)+\log(x+4)=\log (15)[/tex]

As the logs have no base, assume that the base is 10.

[tex]\textsf{Apply log Product law}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_{10} (3x)+\log_{10}(x+4)=\log_{10} (15)[/tex]

[tex]\implies \log_{10} \left(3x(x+4)\right)=\log_{10} (15)[/tex]

Expand the brackets:

[tex]\implies \log_{10} \left(3x^2+12x\right)=\log_{10} (15)[/tex]

[tex]\textsf{Apply the log Equality law}: \quad \textsf{if }\: \log_ax=\log_ay\:\textsf{ then }\:x=y[/tex]

[tex]\implies 3x^2+12x=15[/tex]

Subtract 15 from both sides:

[tex]\implies 3x^2+12x-15=0[/tex]

Factor out the common term 3:

[tex]\implies 3(x^2+4x-5)=0[/tex]

Divide both sides by 3:

[tex]\implies x^2+4x-5=0[/tex]

Split the middle term:

[tex]\implies x^2+5x-x-5=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x+5)-1(x+5)=0[/tex]

Factor out the common term (x + 5):

[tex]\implies (x-1)(x+5)=0[/tex]

Therefore:

[tex]x-1=0 \implies x=1[/tex]

[tex]x+5=0 \implies x=-5[/tex]

As logs cannot be taken of negative numbers, [tex]x=-5[/tex] is an extraneous solution.  Therefore, the only valid solution is:  [tex]x=1[/tex]

The expression x-y equals 0.7 if x and y have certain values. Evaluate the following expression with the same values of x and y

y-x

Answers

Answer:

-0.7

Step-by-step explanation:

Given x - y = 0.7

We will assign x and y random values that has a difference of 0.7

x = 1.3

y = 0.6

Using these 2 values,

y-x = 0.6-1.3

= -0.7

As you can see here , you will get a reversed value when you reverse the expression.

A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required

Answers

The required sample size is 694.

Given a student wants to make a guess within 0.03 of the true ratio with a 95% confidence level.

Margin of Error, E = 0.03

significance level α=0.05  {95% confidence}

A given estimate of the percentage of population p is p = 0.79.

The critical value for the significance level α = 0.05 is Zc = 1.96. This can be determined using either Excel or a normal probability table.

Use the following formula to calculate the minimum sample size required to estimate the percentage of population p within the required margin of error.

n≥p(1-p)(Zc÷E)²

n=0.796×(1-0.796)(1.96÷0.03)²

n=693.1016

Therefore, the  resample sizequired to meet the condition is n ≥ 693.1016 and must be an integer. From this, we conclude that the minimum sample size required is n = 694.

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What value of k makes the statement true?
x² (2x³ + 7x²yª) = 2xªyª + 7x³y8?

Answers

By apply the distributive property of multiplication, the value of k which makes the statement true is 1.

What is the distribution property?

Mathematically, the distributive property of multiplication is given by tis expression:

x(y + z) = xy + xz.

Next, we would apply the distributive property of multiplication to the given equation by distributing to the left-hand side using xy⁴:

k(2x⁴y⁴ + 7x³y⁸) = 2x⁴y⁴ + 7x³y⁸

Dividing both sides by the common factor, we have:

k = (2x⁴y⁴ + 7x³y⁸)/(2x⁴y⁴ + 7x³y⁸)

k = 1.

In conclusion, the value of k which makes the statement true is 1.

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Complete Question:

What value of k makes the statement true?

[tex]x^k[/tex]y⁴(2x³ + 7x²y⁴) = 2x⁴y⁴ + 7x³y⁸

One evening 1500 concert tickets were sold for the fair mount jazz festival. tickets cost 20 for covered pavilion seats and $10 for lawn seats total receipts were 23,000 how many tickets of each were sold

Answers

A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.

We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.

As a total of 1500 tickets were sold, we can form an equation:

x + y = 1500 ... (i),

as we had only those two types of tickets.

The cost of each covered pavilion ticket = $20.

Hence, the total revenue from covered pavilion tickets = $20x.

The cost of each lawn seat ticket = $10.

Hence, the total revenue from lawn seat tickets = $10y.

The total receipts were said to be $23,000.

Thus, we can represent this as an equation:

20x + 10y = 23000 ...(ii).

Combining (i) and (ii), we get a system of equations:

x + y = 1500 ... (i).

20x + 10y = 23000 ... (ii).

Dividing equation (ii) by 10, we get:

2x + y = 2300 ... (iii).

Subtracting (i) from (iii), we get:

2x + y = 2300.

 x + y = 1500.

(-)  (-)     (-)

____________

x = 800.

Substituting x = 800 in (i), we get:

x + y = 1500,

or, 800 + y = 1500,

or, y = 1500 - 800,

or, y = 700.

Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.

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Question is in the picture, please help.

Answers

Answer:

1)The equation is 3^N, where N starts at 4 and goes down 1 each time

2) 1 would be the 5th term

Step-by-step explanation:

3^4=81

3^3=27

3^2=9

3^1=3

3^0=1

What is the LCM of 24 ,40,30

Answers

Answer:

LCM(24,30,40)=120.The Least common multiple for three numbers 24,30 and 40 is 120

Step-by-step explanation:

The LCM of 24,40 and 30 = 120.

write the equations after translating the graph of y = | 1/2 x -2 | + 3 one unit to the right

Answers

Using translation concepts, the equation of the graph is:

y = |0.5x - 2.5| + 3.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The function is:

y = |0.5x - 2| + 3.

When it is shifted one unit to the right, we have that x -> x - 1, hence:

y = |0.5(x - 1) - 2| + 3

y = |0.5x - 2.5| + 3.

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PLEASE HELP
Which is the simplified form of the expression

Answers

The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²  is  [tex]\frac{1}{3^8}[/tex].

Hence, option B is the correct answer.

What is the simplified form of the expression?

Given the expression;

( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²

First, we use the properties of exponents.

( 2⁻²ˣ⁻³ × 3⁴ˣ⁻³ ) × ( 2⁻³ˣ² × 3²ˣ² )

( 2⁶ × 3⁻¹² ) × ( 2⁻⁶ × 3⁴ )

We take out the parentheses, such that;

2⁶ × 2⁻⁶ × 3⁻¹² × 3⁴

Note that: 2⁶ × 2⁻⁶ = 1, as [tex]2^6*2^{-6}=2^{6+(-6)}=2^0=1[/tex]

Hence, we have

1 × 3⁻¹² × 3⁴

3⁻¹²⁺4

3⁻⁸

Next, we express with positive exponent

[tex]\frac{1}{3^8}[/tex]

The simplified form of the expression ( (2⁻²)(3⁴) )⁻³ × ( (2⁻³)(3²) )²  is  [tex]\frac{1}{3^8}[/tex].

Hence, option B is the correct answer.

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If a soccer team made 28 penalty shots out of 100, what fraction and what
percentage of penalty shots did the team miss? Choose two answers.

Answers

.72
18/25

Please mark brainliest
28 penalty shots out of 100 = 28/100 => 7/25
Penalty shots missed:
Total - penalty shots made
= 100 - 28 = 72
72/100 missed = 72%
a. 7/25
b. 72%

Which statement about the function represented by this graph is true? A curve rises from (0, 2), (2, 3 point 9), (4, 4), (5, 4 point 1), (6, 4 point 9), (8, 5), (9, 5), and (10, 5) on the x y coordinate plane. A. The function has an inverse because it passes the vertical line test. B. The function does not have an inverse because it does not pass the horizontal line test. C. The function does not have an inverse because it never crosses the x-axis. D. The function has an inverse because it passes the horizontal line test.

Answers

The true statement about the function which is represented by this graph is: D. the function has an inverse because it passes the horizontal line test.

What is the horizontal line test?

The horizontal line test states that if the graph of function (f) is intersected by any horizontal line more than once, then, the function (f) doesn't have an inverse.

Conversely, if the graph of function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.

By critically observing the graph of the given function (f) shown in the image attached below, we can logically deduce that it has an inverse because it passed the horizontal line test.

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Answer: D. The function has an inverse because it passes the horizontal line test.

Step-by-step explanation:

Got it right on test.

Geoffrey is evaluating the expression
(-3)³(26) (2)
(-3) 5 (2²) (-3)*
C
-99
What are the values of a, b, c, and d?
O a=4, b=2, c= 16, d=9
O a=4, b= -2, c=16, d=9
O a=8, b= 8, c= 256, d=6,561
O a=8, b=8, c= 256, d=-6,561
(-3)³ (26)
(-3) (2²)
as shown below.

Answers

Answer: The values are a = 4, b = 2, c = 16, d = 9

simplified further

c = 16

d = 9

Select the correct answer.

Which function is the inverse of function f if the domain of f is ?

Answers

The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6

How to determine the inverse function?

The function is given as:

f(x) = x^2 + 6

Rewrite as:

y = x^2 + 6

Swap x and y

x = y^2 + 6

Subtract 6 from both sides

y^2 = x - 6

Take the square root

[tex]y = \sqrt{x - 6}[/tex]

Rewrite as:

[tex]f^{-1}(x) = \sqrt{x - 6}[/tex]

Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt{x - 6}[/tex] and the domain is x > 6

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3/4(2/3 + 4/3) - 9 / 1/2 x 1/3

a. -52 1/2
b. - 5 1/4
c. - 4 1/2
d. -4 7/9

Answers

Answer: a. -52 1/2

Step-by-step explanation:

    Given:

3/4(2/3 + 4/3) - 9 / 1/2 x 1/3

[tex]\displaystyle \frac{3}{4}(\frac{2}{3} +\frac{4}{3} )-\frac{9}{\frac{1}{2} *\frac{1}{3} }[/tex]

    Add and multiply:

[tex]\displaystyle \frac{3}{4}(\frac{6}{3} )-\frac{9}{\frac{1}{6} }[/tex]

    Simplify and divide:

[tex]\displaystyle \frac{3}{4}(2 )-54[/tex]

    Multiply:

[tex]\displaystyle 1.5-54[/tex]

    Subtract:

         a. -52 1/2

Which of the following is not a true bi-conditional statement?
A. A quadrilateral is a square if and only if it has 4 congruent sides and 4 right angles.
B. Jane goes to the beach if and only if it is a sunny day.
C It is the weekend if and only if today is Saturday or Sunday.
D A number is even if and only if it is divisible by two.

Answers

Answer: Choice B)

Jane goes to the beach if and only if it is a sunny day.

========================================================

Reason:

A regular conditional statement is in the form "If P, then Q" where P and Q are placeholders for other statements.

For example, we can replace "P" with "it rains" and replace "Q" with "the grass gets wet". This means "If P, then Q" becomes "If it rains, then the grass gets wet".

It's hopefully clear that the example above is a one way street. It points in only one direction. The act of raining leads directly to the grass being wet. However, we cannot go in reverse. If we see the grass is wet, it doesn't mean it rained. Perhaps someone turned on a hose or sprinkler system. P leads to Q, but Q does not lead to P.

In short, all of what is mentioned so far is considered a regular conditional statement. So far we haven't addressed bi-conditional statements.

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

Bi-conditional statements are conditionals that work in reverse.

An example would be "If a figure is a square, then it has 4 congruent sides and 4 right angles". That conditional statement works in reverse. Therefore "If a figure has 4 congruent sides and 4 right angles, then the figure is a square" is also true simply by what it means to be a square.

So the format "If P, then Q" can be reversed to "If Q, then P" to have an equivalently true statement. The common practice is to use "if and only if" to help shorten things.

We would have the template "P if and only if  Q" which is the same as "Q if and only if P". The order doesn't matter since we can reverse things just fine.

Often you'll find bi-conditional statements when it comes to definitions. The term "weekend" literally means the day is either Saturday or Sunday, which is why choice C is another bi-conditional. A very similar situation applies to choice D as well.

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

We've found that choices A, C and D are bi-conditional statements. They can be ruled out. We're left with choice B.

This is not a bi-conditional. Why not? It's assumed that Jane would go to the beach on a sunny day, but perhaps she enjoys the beach just fine on cloudy days. There's also the fact she could be doing other things on sunny days. The presence of the sun doesn't automatically mean the beach. If you said "It gets warm if and only if it's a sunny day", then I think this is more in line with a bi-conditional.

This is why choice B is the final answer.

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