Which of the following statements represents a function?
A. Students of their current age?
B. Countries to its capital?
C. A store to its merchandise
D. Teacher and student’s relationship

The price of one pound is $0.8.

This problem can be solved by unitary method. To understand this we must know that in this method we need to calculate the value of a unit of product and then multiply that value with the required value for which we have to calculate the value.

Given, that the weight of the apple is 5.2 pounds.

Cost of the apple is = $4.16

Therefore the cost of one pound of apple = [tex]\frac{4.16}{5.2}[/tex]

                                                                 = $0.8

So, to buy a pound of apple one must pay $0.8.

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The nail protrudes 5[tex]\frac{9}{15}[/tex] inches from the other side of the board having a thickness of  2[tex]\frac{2}{5}[/tex] inches

Given that A nail 6 [tex]\frac{1}{3}[/tex] inches long is driven into a board 2 [tex]\frac{2}{5}[/tex] inches thick and asked to find out how much the nail protrudes into the board.

To calculate the nail protrudes, need to subtract the length of the nail and the thickness of the board.

Length of nail protrudes= 6 [tex]\frac{1}{3}[/tex] - 6 [tex]\frac{1}{3}[/tex]

Length of nail protrudes=[tex]\frac{19}{3}[/tex]-[tex]\frac{12}{5}[/tex]

Length of nail protrudes=[tex]\frac{59}{15}[/tex]

Length of nail protrudes= 5[tex]\frac{9}{15}[/tex] .

Therefore,The nail protrudes 5[tex]\frac{9}{15}[/tex] inches from the other side of the board having a thickness of  2[tex]\frac{2}{5}[/tex] inches

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The number 4.1818181818... is a rational number because the number is terminating. Then the correct option is D.

If the value of a numerical expression is terminating then they are the rational number then they are called a rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

Let's check all the options, then we have

A 1.4142135623..., the number is an irrational number because the number is non-terminating.

B. 2.7182818284..., the number is an irrational number because the number is non-terminating.

C 3.1415926535..., the number is an irrational number because the number is non-terminating.

D 4.1818181818..., the number is a rational number because the number is terminating.

The number 4.1818181818... is a rational number because the number is terminating. Then the correct option is D.

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Value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.

As given in the question,

Given data :

sin(3x-35)°-cos(x+20)° = 0     __(1)

As we know  x is an acute angle  ,

cos (90 - α)° =sinα°

⇒ sin (3x -35)° =cos (90 -(3x - 35))°

⇒ sin (3x -35)°=cos (55 -3x )° ___(2)

Substitute the value of sin (3x -35)° from (2) to (1),

cos(55 -3x)° -cos(x+20)°=0

⇒cos(55 -3x)° =cos(x+20)°

⇒55 -3x=x+20

⇒x=8.75°

Therefore, value of x for the given data sin(3x-35)°-cos(x+20)°=0, where x is an acute angle is equal to 8.75°.

The complete question is :

Given that sin(3x-35)°-cos(x+20)° =0 and x is an acute angle, find it's value.

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Marty will have to pay $18,000 for his $15,000 car.

While taking out a loan, the amount taken has to be repaid along with an interest. Thus, the amount paid back by the borrower is always greater than the initial amount that the borrower gets from the lender as a loan.

Here, we are given that Marty has to pay $500 per month for 3 years to repay the loan for his $15,000 car.

Thus, for one month he pays = $500

and also we know that 1 year = 12 months

⇒ 3 years = 12(3) = 36 months

Therefore, for 36 months Marty will have to pay,

500 × 36 = 18,000

Thus, Marty will have to pay $18,000 for his $15,000 car.

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The systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6 mm Hg

We are given the equation that gives a person's blood pressure, p at the age y year is;

p = 0.007y² - 0.003y + 122

To find the systolic pressure for a person of age 41 years, just plug in y = 41 into the given quadratic equation to get;

p(41) = 0.007(41)² - 0.003(41) + 122

p(41) = 11.767 - 0.123 + 122

p(41) = 133.6

Thus, the systolic pressure, to the nearest tenth of a millimeter, for a person of age 41 years is; 133.6

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Answer:

Step-by-step explanation:

Solve for x

7/8 of x is 14

7/8x = 14

x = 14 : 7/8

x = 14 * 8/7

x =16

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

check

7/8 * 16 = 14

14 = 14

the answer is good

Answer:

$25.70 (nearest cent)

Step-by-step explanation:

Given:

[tex]\begin{aligned} \textsf{Net Asset Value}_{\textsf{(Per Share)}} & =\dfrac{\textsf{Fund Assets}-\textsf{Fund Liabilities}}{\textsf{Total number of Outstanding Shares}}\\\\\implies \textsf{Net Asset Value}_{\textsf{(Per Share)}} & = \dfrac{\$39,400,000-\$3,940,000}{\$1,380,000}\\\\& = \dfrac{\$35,460,000}{\$1,380,000}\\\\& = \$25.69565217...\\\\\end{aligned}[/tex]

Therefore, the Net Asset Value (NAV) per share is $25.70 (nearest cent).

The given information is,

→ x = $39,400,000

→ y = $3,940,000

→ z = 1,380,000

Formula we use is,

→ (x - y)/z

Now the net asset value per share is,

→ (x - y)/z

→ (39400000 - 3940000)/1380000

→ 35460000/1380000

→ 25.6956521739

→ ≈ $25.70

Hence, the net asset value is $25.70.

The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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The first flight is 2 hours and second flight is 2 hours and 48 minutes

The two distances are the same (out and back),

so set them equal.

That distance is cover by having one is (rate)(time) equal to other is (rate)(time).

Let,

One time is “x” and the other is “4.8-x.”

One average rate  is 460 per hour

and the other average rate is 500 per hour.

we know , Speed = [tex]\frac{distance}{time}[/tex]

so , distance = speed × time

put in this formula we get the value of X

⇒460 x = 500 (4.8 -x)

⇒460 x = 2400 - 500x

⇒900 x = 2400

⇒x = 2.5 hours for the slower plane.

⇒4.8- x = 2.3 hours for the faster plane.

The formula speed = distance ÷ time can be rearranged, just like any other equation.

Here detail explanation about relation between speed distance and time :

The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

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Answer:

1/6 is greater than 0.16

Step-by-step explanation:

0.16 as a fraction is 4/25

4/25 < 1/6

Answer: Answer  2, Triangle A is dilated from the origin by a scale of 1/2 to obtain triangle B

Step-by-step explanation:

Answer:

7/10, 12/40, 2/20, -10

Answer:

x=±7; y=12.25.

Step-by-step explanation:

1) x-interception:
(y=0): x²=49, ⇒ x=±7;

2) y-interception:

(x=0):  4y=49; ⇒ y=12.25.

Answer:

Linear?

Step-by-step explanation:

its been years since I've seen this so I'm not sure

Answer:

c

Step-by-step explanation:

7x²-36x+5= 7x²-x-35x+5

=x(7x-1)-5(7x-1)

=(7x-1)(x-5)

The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.

The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.

The set notation of the numbers is {x | x < 50 ∪ x > 50}

The set is given as

The set of all real numbers less than 50 or greater than 50

Let the number be represented by x

So, we have

x less than 50 or x greater than 50

When represented as an inequality, we have

x < 50 or x > 50

Using set notation, we have

{x | x < 50 ∪ x > 50}

Hence, the set notation of the numbers is {x | x < 50 ∪ x > 50}

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Answer:

Step 1. The perimeter P means adding up all four sides of a rectangle.

Step 2. Let w be the width

Step 3. Let 3w be the length since the width is one-third the length

Step 4. Then P=w+w+3w+3w=8w=20 since the perimeter P is 20 cm.

Step 5. Solving the equation in Step 4 leads to the following steps

Divide by 8 to both sides of the equation

8w%2F8=20%2F8

w=5%2F2 and 3w=15/2 and P=2(5/2+15/2)=20 which is a true statement.

Step 6. ANSWER: The width is 5/2 cm.

Step-by-step explanation:

I hope the above steps and explanation were helpful.

Using a proportional relationship, the fewest number of vegetables that can be used to make this salad is:

C. 4

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For this problem, looming at the table, we have that the number of Broccoli is triple the number of carrots, hence the proportional function is:

B = 3C.

When there is one carrot, the number of broccoli is given by:

B = 3 x 1 = 3.

Hence the fewest number of vegetables is of 4, as 1 carrot + 3 broccoli = 4 vegetables, hence option C is correct.

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The triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

It is given that:

In Euclidean geometry, the interior angles of any triangle add up to 180 degrees.

As we know,

Spherical trigonometry, which departs from conventional trigonometry in many ways, is created when angles between great circles are defined.

For instance, the total of the sides and angles of a hemispheric triangle is more than 180 degrees.

In spherical geometry, triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.

Thus, the triangles are subject to this law. If another number were present, their sum would always be greater than 180 degrees.

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Given that the between 16 and 20 minutes driving times to the campus is uniformly distributed, the mean driving time is 18 minutes

The correct option is therefore;

The time it takes to drive from the apartment to the campus = Between 16 and 20 minutes

The mean of a continuous uniform distribution between two boundaries, a and b is given by the formula;

[tex] \mu = \frac{a+b}{2} [/tex]

The mean amount of time it takes to drive to campus is therefore;

[tex] \mu = \mathbf{\frac{16+20}{2}} = 18 [/tex]

The correct mean driving time is the option;

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Simplifying  the quantity 10 minus three fourths times the square root of 16 end quantity squared plus the quantity 2 minus 7 end quantity squared is: c. 74.

The given expression:

(10 - 3/4 × ✓16)² + (2 - 7)²

Hence,

Now let simplify the expression

(10 - 3/4 × ✓16)² + (2 - 7)²

=(10 - 3)² + (-5)²

= 7² + 5²

= 49+ 25

= 74

Therefore simplifying  the quantity 10 minus three fourths times the square root of 16 end quantity squared plus the quantity 2 minus 7 end quantity squared is: option c. 74.

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The equation which represents the height of the books is  [tex]s(b)=\frac{5}{4} b[/tex]

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation between two sums of monomials of degree 0 or 1 is known as a linear equation.

The books are stacked one above the other and each book is [tex]1\frac{1}{4}[/tex] inches thick.

So to calculate the total height of the stack we have to multiply the number of books in the stack with the thickness of each book.

The total thickness is represented in the from of a function as

s(b) and the thickness of each book is [tex]1\frac{1}{4}=\frac{5}{4}[/tex] inches

total height=[tex]\frac{5}{4}\times b[/tex]

Therefore the required equation is  [tex]s(b)=\frac{5}{4} b[/tex].

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Answer:

[tex]y=-\frac{5}{7}x+5[/tex]

Step-by-step explanation:

The equation of a line can be written in the form of y= mx +c, where m is the slope and c is the y-intercept. This is also known as the slope-intercept form.

Identify the value of the slope, m:

Given that the slope is [tex]-\frac{5}{7}[/tex], m= [tex]-\frac{5}{7}[/tex].

Substituting the value of m into the equation:

[tex]y=-\frac{5}{7} x+c[/tex]

Identify the value of the y-intercept:

Given that the y-intercept is 5, c= 5.

Substitute c= 5:

[tex]\bf{y=-\frac{5}{7}x+5}[/tex]

Thus, the equation of the line is [tex]\bf{y=-\frac{5}{7} x+5}[/tex].

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The answer is that 80 people will build the same road in 160 days.

Given that 50 people take 256 days to build a road.

And we need to find out how many days will 80 people take to build the same road.

Disclaimer: Assuming that the work done by all the people are same.

If the number of people increases, the time taken to build the road decreases in the same proportion. Clearly, the number of people varies inversely to the number of days.

Let x denote the number of days required to build the road for 80 people.

Then the ratio, 80/50 = 256/x

⇒ x = (256×50)/80 = 160

Therefore, 80 people will build the same road in 160 days.

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