(Score for Question 4: of 4 points)
4. Write the indicated conditional statements for the given statement.
Conditional Statement:
Converse Statement:
Inverse Statement:
Contrapositive Statement:
Biconditional Statement:
If a car is out of gas, then it will not run.
Assuming the original statement is biconditional, write the biconditional version of the statement:

The wholesale price of the TV will be 0.40 x where x represents the retail price.

Percentage :

In mathematics, it is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Let the retail price of TV be x

Now, we are given that it is sold off at 60 percent discount.

Whole sale price = x - 60 % of x

Whole sale price = x - 60 / 100 x

Whole sale price = x - 0.60 x

Whole sale price = 0.40 x.

Therefore, the wholesale price of the TV will be 0.40 x where x represents the retail price of the TV.

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Answer:

  (d)  c = ab/x

Step-by-step explanation:

You want to solve the proportion x/a = b/c for the variable c.

The usual method recommended for solving almost any kind of proportion is to first clear the fractions. You do this by multiplying both sides by the product of the denominators. This has the appearance of "cross multiplication."

  [tex]\dfrac{x}{a}=\dfrac{b}{c}\qquad\text{given}\\\\\\\dfrac{x}{a}\cdot ac=\dfrac{b}{c}\cdot ac\qquad\text{multiply by $ac$}\\\\xc=ba\qquad\text{simplify; each numerator times the opposite denominator}[/tex]

At this point, it is a "one-step" linear equation in c, so is solved by dividing by the coefficient of c, which is x.

  [tex]\dfrac{xc}{x}=\dfrac{ab}{x}\\\\\boxed{c=\dfrac{ab}{x}}[/tex]

Answer:

$5.30 for two gallons

Step-by-step explanation:

Answer:

[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex] Whatever this number may be

Step-by-step explanation:

The distance will be on the plane containing the point, and perpendicular to the line - which exists as long as the point doesn't sit on the line, but in that case our distance will simply be zero. Good news, since the line is given in parametric equation, the equation of the plane is easy to write by simply computing the dot product between the vector generating the line - or any multiple of it! - and the vector joining a random point x y z of the space with our given point, and setting it equal to zero. The equation of our plane is thus

[tex]6(x-(-8)) + 3(y-9) -7(z-8) = 0\\6(x+8)+3(y-9)-7(z-8)=0[/tex]

We could multiply now or later, doesn't matter, so let's wait. Now, we need to know when the line passes through the plane, so let's plug the (parametric) coordinate of the line and let's see for which value of t that happens:

[tex]6(-2-6t+8) +3(1-3t -9) -7(-5+7t-8) =0\\6(6-6t) -3(8+3t)+7(13-7t)=0\\36-36t-24-9t+91-49t = 0\\t=103/94[/tex]

Found this value of t, we can use it to find the coordinate of the point in common between the line and the plane:

[tex](-2-6\frac {103}{94};1-3\frac {103}{94}; -5+7\frac {103}{94}) = (-\frac{806}{94};-\frac{215}{94};-\frac{251}{94})[/tex]

At this point it's simply a matter of calculating the distance between two points in 3D space, given by the usual [tex]\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}[/tex], whatever abomination of a number it might become:

[tex]\sqrt{(-\frac{806}{94}+8)^2+(-\frac{215}{94}-9)^2+ (-\frac{251}{94}-8)^2}[/tex]

At this point is a simple exercise in number crunching which I refuse to entertain more - but please double check all calculation above in case I didn't notice something.

Answer:

x = 2.638

Step-by-step explanation:

Answer

Unless you need a different version of this answer?

Step-by-step explanation:

(27in(3)

x=___4_______ True

In(3)

Using proportions, it is found that Jen planned to spend 19/4 hours paddleboarding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

In this problem, we have that:

4 + 3/4 = 4.75 hours = 19/4.

Jen planned to spent 19/4 hours paddleboarding.

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Answer:

[tex]3.4196 \times 10^{7}[/tex]

Step-by-step explanation:

Given expression:

[tex](4.12 \times 10^{-9})(8.3 \times 10^{15})[/tex]

Remove the parentheses:

[tex]\implies 4.12\times 10^{-9} \times 8.3 \times 10^{15}[/tex]

Collect like terms:

[tex]\implies 4.12 \times 8.3 \times 10^{-9} \times 10^{15}[/tex]

Multiply the numbers 4.12 and 8.3:

[tex]\implies 34.196 \times 10^{-9} \times 10^{15}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 34.196 \times 10^{(-9+15)}[/tex]

[tex]\implies 34.196 \times 10^{6}[/tex]

Scientific notation is written in the form  [tex]\boxed{a \times 10^n}[/tex]

where [tex]1\leq a < 10[/tex]  and [tex]n[/tex] is any positive or negative whole number.

To convert 34.196 × 10⁶ into scientific notation, move the decimal point to the left by one place and increase the power of 10 by 1:

[tex]\implies 34.196 \times 10^{6}=3.4196 \times 10^{7}[/tex]

Answer:

No, I do not agree with Simon's reasoning.

Step-by-step explanation:

7*2=14

8*1=8

BUT

7+2=9

8+1=9

YET

Simon isn't properly solving the equation with the right basic operation of arithmetic. He must multiply, not use addition.

Hope this helps.

Maria need 12 fiction books.

Multiplication table: A multiplication chart is a table that shows the products of two numbers. Usually, one set of numbers is written on the left column and another set is written as the top row. The products are listed as a rectangular array of numbers.

Given that She wants to make packages that have 3 fiction books and 4 nonfiction books. She already has 9 fiction books

Step 1

Complete the rows for 3 and 4 on multiplication table

Fraction           : 3,6,9,12, 15, 18, 21, 24,27,30.

Notification     : 4,8,12,16,20,24,28,32,36,40.

Step 2

Read across the top until you reach 9. The corresponding number bottom row.

The top untill you reach 9 the corresponding number bottom row is 12

Maria need 12 fiction books.

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Answer:

0.000345 in standard form would be:

3.45 times 10 to the -4 power

Step-by-step explanation:

The number tells use that we have to divide by 10 and we are working with a negativenumber equal to the power of 4.

Answer:

3.45 × 10^-4

Step-by-step explanation:

Move from the decimal point till you you get to after the first number.

Then you put the decimal point there and because it's starts with 0. i.e it is not up to one

You put minus in front of it when raising it to the power of 10

The height of the building is 23.09m.

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The value of the constant π is located between 3 and 4 on a number line

The value is given as

Value = π

As a general rule, the value of π is

π = 22/7

So, we have

Value = 22/7

Evaluate the quotient of 22/7

So, we have

Value = 3.143

The number 3.143 is greater than 3 but less than 4

This means that, 3.143 is between 3 and 4

In other words, the value of the constant π is located between 3 and 4 on a number line

Hence, the value of the constant π is located between 3 and 4 on a number line

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According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

A quadratic equation seems to be a second-order polynomial equation in a variable, x ax2+bx+c=0, with a 0 as the coefficient. The fundamental theorem of algebra ensures that it has at least one solution as it is a second-order polynomial problem. The solution could be straightforward or difficult.

Equivalent equations are those that have the same solutions or roots. An equivalent equation is produced by adding or subtracting the identical number or expression from both sides of an equation. Equivalent equations are produced by multiplying and dividing both sides of such an equation by the same non-zero value.

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

Simplifying this equation:

3 ⁢X² + 5 x − 7 +  X² + 4

= 4X² + 5x - 3

According to the solving the non of the quadratic equations equivalent.

4X² + 5x - 3.

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I understand that the question you are looking for is:

Which expression is equivalent to the given expression?

3 ⁢X² + 5 x − 7 ⁢+ ( X² + 4 ).

A. - 4X² + 5X − 4

B. X² + 4

C. X² + 28

D. - 4 ⁢X² + 5x − 28

Answer:

18

Step-by-step explanation:

5*(6)-10(2)+8 = 18

Substitute k = 6 and c = 2 into the equation and solve it.

Answer:

2.3(2.99)=$6.877

Step-by-step explanation:

Multiply the pounds (2.3) by the price of apples per pound.

Hope this helps! :)

Answer:

2.3(2.99)=$6.877

Step-by-step explanation:

Hope this helps!

Answer:

No

Step-by-step explanation:

1/10 = 0.1

0.05 x 0.1 = 0.005

The correct inequality will be 53.46d + 45.5 ≤ 260

What does a math inequality look like?

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Given That:

She plan to drive 350 miles and each mile cost $0.13 which is total $45.5

and she have to pay $53.46 for each day

So the correct inequality will be 53.46d + 45.5 ≤ 260

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Answer:

It's 0.4

Step-by-step explanation:

2/5 = 40/100 = 4/10 = 0.4

Hope that helps :)

The bagel costs $0.89 and a muffin costs $0.75

Let B = Bagel cost

Let M = Muffin cost

Thus, from the given question parameters, the system of equations that can be used to determine the cost x is;

3B + 4M = 5.67     ------(1)

5B + 3M = 6.70    ------(2)

Multiply the 1st equation by 3 and the 2nd equation by (-4) to get;

9B +12M =  17.01     ------(3)

-20B - 12M = -26.80   ------(3)

Add equations 3 and 4 together to get;

-11B = -9.79

B = 0.89  

Plug this value for B in to the 1st equation and solve for M to get;

3(0.89) + 4M = 5.67

2.67 + 4M = 5.67

4M = 3.00

M = 0.75

Thus, a bagel costs $0.89 and a muffin costs $0.75

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Answer:

The answer to the inequality is

x < -5

x > 15

The value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.

As per the given relation in the question, we see that b is calculated once and m is calculated based on the variable value x, which is the number of students. Hence, for correct calculation, value of m is $25 and value of b is $100.

The cost if 8 students are passengers will be calculated by keeping the value of x and other constants as per the above answer.

Cost = 25×8 + 100

Cost = 200 + 100

Cost = $300

Number of students will again be found as the value of x, by keeping the values as specified above.

400 = 25x + 100

25x = 400 - 100

25x = 300

x = 300 ÷ 25

x = 12

Hence, value of m is $25 and value of b is $100, the cost is $300 and the number of students is 12.

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The complete question is attached in figure.

So the correct answer is a. f(-3)=-5.

Solution :

Cartesian coordinate system

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.

Cartesian Plane:

A plane consists of axes and quadrants. Thus, we call the plane the Cartesian Plane, or the Coordinate Plane, or the x-y plane. The axes are called the coordinate axes.

Abscissa and Ordinate

The x-coordinate of a point is its perpendicular distance from the y-axis measured along the x-axis and it is known as Abscissa.

The y-coordinate of a point is its perpendicular distance from the x-axis measured along the y-axis and it is known as the Ordinate.

So,

the point (-3, -5) corresponds to the graph of the function.

A point on a graph in the Cartesian coordinate system then that point consists of coordinates (x, y).

In, y=f(x) and x so (x, f(x))

x is a x-coordinate and y=f(x) is y-coordinate.

So if we have a point (-3, -5) the corresponding coordinates are x=-3 and

y=f(x)=-5. So it must be true that y=f(-3)=-5.

So the correct answer is a. f(-3)=-5.

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The linear functions for this problem are given as follows:

13. y = 2x/3 + 8/3.

14. y = -3x + 5.

15. y = -1/3x - 2.

16. y = 5/4x - 1/4.

17. y = 7/4x + 19/2.

A linear function is modeled by the following rule:

y = mx + b

In which:

The slope is also related with parallel and perpendicular lines, as follows:

In item 13, the line in slope-intercept form is:

y = 2x/3.

The line we want to find is parallel, hence it has the same slope, that is:

y = 2x/3 + b.

When x = -1, y = 2, hence:

2 = -2/3 + b

b = 8/3.

Hence the line is:

y = 2x/3 + 8/3.

For item 14, the line is perpendicular to:

y = 1/3x + 4.

Hence the slope is found as follows:

1/3m = -1

m = -3.

Then:

y = -3x + b.

When x = 0, y = 5, hence b = 5 and the line is:

y = -3x + 5.

For item 15, the line is perpendicular to:

y = 3x + 4.

Then the slope is found as follows:

3m = -1

m = -1/3.

Then:

y = -1/3x + b.

When x = 0, y = -2, hence b = -2 and the line is:

y = -1/3x - 2.

For item 16, the line is perpendicular to:

y = 4 - 4/5x.

Then the slope is found as follows:

-4m/5 = -1

m = 5/4.

Hence:

y = 5/4x + b.

When x = 1, y = 1, hence:

1 = 5/4 + b

b = -1/4.

Then the line is:

y = 5/4x - 1/4.

For item 17, the line is perpendicular to:

y = 13/7 - 4/7x

Then the slope is found as follows:

-4m/7 = -1

m = 7/4.

Hence:

y = 7/4x + b.

When x = -2, y = 6, hence:

6 = -14/4 + b

b = 19/2.

Hence the line is given by:

y = 7/4x + 19/2.

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Because the angles are vertical angles, the value of x is 1

The angles are given as

A = 7x + 26

B = 4x + 29

The angles are vertical angles

So, we have

A = B

This gives

7x + 26 = 4x + 29

Evaluate the like terms

3x = 3

Divide by 3

x = 1

Hence, the value of x is 1

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Answer:58.73

Step-by-step explanation:

28.37+30.36=58.73