You have $14 in your pocket. A bike rental costs $5 plus $2.50 per hour. What is maximum amount of time you can rent a bike for without spending all of your money? ​

Answer:  2 abd the answer is that

Step-by-step explanation:

The difference between lagging strand and leading strand based on DNA replication is.

What is DNA?

DNA stands for deoxyribonucleic acid.

Main body:

The major difference between a lagging and leading strand is that the lagging strand replicates discontinuously forming short fragments, whereas the leading strand replicates continuously. Find out more such differences between a lagging and leading strand, in the table below.

Lagging Strand  

Description:                                                      

Leading Strand

Description:                

Therefore the difference between lagging strand and leading strand are as follows.

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Answer:

9 = 20

7 = 10

Step-by-step explanation:

Answer:

Step-by-step explanation:

(4i)·(-8i)·(5+5i) = 160+ 160i

We take into account that (i)²  = -1

1)

(4i)·(-8i) = (-32)·i² = (-32)·(-1) = 32

2)

32·(5 + 5i) = 32·5 + 32·(5i)  = 160 + 160 i

The machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test using the normal distribution.

What is Normal Distribution?

The Normal Distribution, often known as the Gaussian Distribution, is the most important continuous probability distribution in probability theory and statistics. It is also referred to as a bell curve on occasion. In every physical science and in economics, a huge number of random variables are either closely or precisely described by the normal distribution. Additionally, it may be used to roughly represent various probability distributions, reinforcing the notion that the term "normal" refers to the most common distribution.

Let X denotes the scores.

In the question, It is given that:

Normal distribution with p=400 and 60.

[tex]X \sim N(\mu=400, \sigma=60)\\$$$\frac{X-\mu}{\sigma}(=Z) \sim N(0,1)$\\i.e. $P(Z \leq z)=\Phi(z)$[/tex]

Let 'a' be the score to be in the top 10% of all machinists.

[tex]\begin{aligned}&P(X \leq a)=1-0.10=0.90 \\&\text { or, } P\left(\frac{X-\mu}{\sigma} \leq \frac{a-400}{60}\right)=0.90 \\&\text { or, } \Phi\left(\frac{a-400}{60}\right)=0.90=\Phi(1.282) \\&\text { or, } \frac{a-400}{60}=1.282 \\&\text { or, } \mathbf{a}=\mathbf{4 7 6 . 9 2}\end{aligned}[/tex]

So,

The score a machinist need in order to be in the top 10% is 476.92.  

Hence,

a machinist would score 476.92 in order to be in the top 10% of all machinists who would take this test.

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The value of the expression given as 26 + 15 is -11.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, the value of -26 + 15 will be:

= -26 + 15

= -11

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The 8 bushels of apples cost is $63.60 i.e, option(A.)

What do you mean by Cost ?

           Cost (c) : is the total cost of the purchase.

           Rate (r) : is the cost of each individual item.

            Number (n) : is the number of items you want to purchase.

      These are related in the following way:

      c = n * r

Given,

Bushels of apples cost = $7.95

8 bushels of apples cost will be = $7.95 * 8

                                                     = $63.6 or $63.60

Hence, the 8 bushels of apples cost is $63.60 i.e, option(A.)

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Area of rectangle is the product of Length and Width, so by using this the length of garden will be 13 feet.

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a type of quadrilateral. As a result, it is also referred to as an equiangular quadrilateral. The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

suppose x = width of rectangular garden.

length of the garden is  5 feet longer than width.

now, x+5 = Length

Area of rectangle L X B = [tex]x X(x+5)[/tex]

Garden's area is = 104 square feet

Then,

[tex]x X (x +5) = 104\\x^{2} + 5x - 104=0\\(x-8)(x+13)=0\\x=8,-13[/tex]

Now, width ==8

Therefore, Length = x+5= 13

13feet is the length of the garden.

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Answer: [tex]\frac{8.1}{5}[/tex]

Step-by-step explanation:

First of all, I multiplied both sides by 5.

8 x 5 is 40, and 13 x 5 is 65.

This gives 65/40

Now, I divide 65 and 40 by 8.

65/8 is 8.1

and 40 divided by 8 is 5.

So the answer is 8.1/5

Answer: 40k⁶-15k⁴

Step-by-step explanation:

[tex](8k^4-3k^2)(5k^2)=\\\\8k^4(5k^2)-3k^2(5k^2)=\\\\8(5)(k^{4+2})-3(5)(k^{2+2})=\\\\40k^6-15k^4[/tex]

Result of [tex]8k^{4} -3k^{2}[/tex] multiplied by [tex]5k^{2}[/tex] is [tex]40k^{6}-15 k^{4}[/tex]

Algebra and Exponent

To answer this question you need to know about algebra and exponent rule.

[tex]8k^{4} -3k^{2}[/tex] multiplied by [tex]5k^{2}[/tex]

It means the operation will become:

[tex]5k^{2} (8k^{4} -3k^{2} )=[/tex]

The way to calculate algebraic multiplication with 2 or more variables is the way I call 'rainbow'.

[tex]5k^{2} (8k^{4} -3k^{2} )=[/tex]

[tex]5k^{2}[/tex] multiplied by [tex]8k^{4}[/tex],  [tex]5k^{2}[/tex] multiplied by [tex]-3k^{2}[/tex] first, then the two are added.

[tex](5k^{2}) (8k^{4} )=[/tex]

The way to multiply this is by: numbers multiplied by numbers and letters multiplied by letters

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )[/tex]

Then how to multiply the letters, this uses the rule of exponents. If there are 2 same variables are multiplied, then the result is a variable with the power of the sum of the two powers.

[tex]a^{m} a^{n} =a^{m+n}[/tex]

Which means,

[tex]k^{2}k^{4} =k^{6}[/tex]

Then,

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5)(8))((k^{2} )(k^{4} ))\\=40((k^{2} )(k^{4} )\\=40k^{6}[/tex]

Also same with above,

[tex]=(5k^{2} )(-3k^{2} )\\=((5)(-3))((k^{2} )(k^{2} )\\=-15k^{4}[/tex]

[tex]=5k^{2} (8k^{4} -3k^{2} )\\=((5k^{2})(8k^{4})+((5k^{2})(-3k^{2})\\=(40k^{6})+(-15k^{4} )\\=40k^{6}-15k^{4}[/tex]

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In the given function the rate of change is -2 and the initial value is 7. Therefore, Harry is incorrect.

The given function is y=7-2x.

The rate of change, or the slope, is calculated as Δy/Δx , or (y2−y1)/(x2−x1). The slope-intercept equation of a line is y=mx+b , where m is the slope and b is the initial value.

Given that, the rate of change is 7 and the initial value is -2.

In the given function y=7-2x

Here, slope or the rate of change is -2 and the y-intercept or initial value is 7.

In the given function the rate of change is -2 and the initial value is 7. Therefore, Harry is incorrect.

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The Number of Associates and Number of Partners assigned to the case by the law firm is 5 and 9 respectively. We can solve this by using the concept of Linear Equation.

Given that,

Daily rate charged to the client for each Associate = $ 800

Daily rate charged to the client for each Partner = $ 1700

Let number of Associates assigned to case = X

And number of Partners assigned to case = Y

So, According to Question

X + Y = 14    ----(1)

800X + 1700Y = 19300        ---(2)

From the equation (1) , Y = 14 – X

Substituting the value of Y into equation (2) we get,

800X + 1700(14-X) = 19300

800X + 23800 – 1700X = 19300

23800 – 900X = 19300

23800 – 19300 = 900X

4500=900X

4500/900 = X

X = 5

Put the value of X into equation (1),

5 + Y = 14

Y = 14 -5

Y = 9

So we let the number of Associates assigned to case X and number of partners assigned to case Y and the value of X is 5 and Y is 9 .

Hence the number of Associates assigned to the case is 5 and the number of Partners assigned to the case is 9.

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If 15% of 500 is equal to 7.5% of the number, the number is equals to 1000.

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.

Therefore, let's find the number if 15% of 500 is equal to 7.5% of the number.

Let

x = the number

Hence,

15% of 500 = 7.5% of x

15 / 100 × 500 = 7.5 / 100 × x

75 = 7.5x / 100

cross multiply

7500 = 7.5x

divide both sides by 7.5

x = 7500 / 7.5

x = 1000

Therefore, the number is 100.

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Answer:

( 3 , 0 )

Step-by-step explanation:

When the reflection is over the y-axis , the y-coordinate is the same

and x-coordinate changes its Sign

So for ( -3 , 0) is reflected over y-axis

Then x-coordinate = 3

Then y-coordinate =0

So the new point = ( 3 , 0 )

Answer:

Step-by-step explanation:

a; i

b; i

The amount owed by the debtor is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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For each pair of fractions, following fraction is larger

a) 5/6 > 5/7

b) 2/9 < 5/9

c) 3/4 < 9/10

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given,

Fraction:

a) 5/6 or 5/7

Taking LCM,

LCM = 42

5/6 × 7/7

35/42

5/7 × 6/6

30/42

5/6 > 5/7

b) 2/9 or 5/9

They have same denominator,

So,

2/9 < 5/9

c) 3/4 or 9/10

Taking LCM:

LCM = 20

3/4 ×5/5

15/20

9/10 × 2

18/20

3/4 < 9/10

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Answer: B

Step-by-step explanation:

2.5/4.5 = x/2.25

x = 1.25 in

The polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

So, the equation of the curve with a leading coefficient of 1 or the polynomial function with a leading coefficient of 1 f(x) can be expressed as (x-a)* (x-b)* if a, b, and c are the zeros of a polynomial (x-c).

Now, calculate as follows:

Therefore, the polynomial function with the lowest degree with a leading coefficient of 1 and zeros is 1, -1(multiplicity 3), and 3i is [x³+(2-3i)x²-(3+6i)x+9i].

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If the angle A and angle B are supplementary then the measure of angle A is = 93° .

In the question ,

it is given that

the two angles A and B are supplementary ,

we know that when two angles are supplementary their sum is 180° .

So , the sum of measure of angle A and angle B will be 180° ,

that is ,

given that measure of angle A = (7x - 12)°

measure of angle B = (7x - 18)°

So , according to the question ,

(7x - 12) + (7x - 18) = 180°

7x + 7x - 12 - 18 = 180

14x - 30 = 180

14x = 180 + 30

14x = 210

x = 210/14

x = 15

So , the measure of angle A = (7*15 - 12) = 105 - 12 = 93°

Therefore , If the angle A and angle B are supplementary then the measure of angle A is = 93° .

The given question is incomplete , the complete question is

Angle A and angle B are supplementary angle. If angle A = (7x - 12)° and angle B = (7x - 18)° , then find the measure of angle A ?

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Here is the proof:

1. Length AB = Length DC

2. Angle BAC = Angle ACD (AB is parallel to CD, so the opposite interior angles are equal)

3. AC length = AC length (2 lines coincide)

Principle of Side - Angle - Side

then the two triangles are said to be congruent

So Length BC = Length DA

Congruence is a condition where two flat shapes have the same size and are said to be congruent.

The characteristics of two triangles that are said to be congruent are:

1. When the pairs of corresponding sides are equal in length. Usually called the side-by-side criterion.

2. Two pairs of corresponding sides are equal in length and the angles between them are equal. Commonly referred to as the side-angle-side criterion.

3. Two pairs of congruent angles and the same side lengths. Also known as angle-side-angle

Answer:

4. d = 4

5. d = 8.8

6. d = 6

7. d = 10

8. d = 3

9. d = 1

Step-by-step explanation:

4. (-5, 2), (-5, 6)

    (x₁, y₁)  (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5 - (-5))² + (6 - 2)²

d = √(-5 + 5)² + (4)²

d = √(4)²

d = √16

d = 4

5. (4.5, -3.3), (4.5, 5.5)

       (x₁, y₁)      (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(4.5 - 4.5)² + (5.5 - (-3.3)²

d = √(0)² + (5.5 + 3.3)²

d = √(8.8)²

d = √77.44

d = 8.8

6. ((5(1/2), (-7(1/2)) and ((5(1/2), (-1(1/2))

         (x₁,     y₁)                   (x₂,     y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(11/2) - (11/2)² + (-3/2) - (-15/2))²

d = √(d)² + ((-3/2) + (15/2)²

d = √(6)²

d = √36

d = 6

7. (-2(1/4)), -8) and (7(3/4), -8)

        (x₁,   y₁)               (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(31/4) - (-9/4))² + (-8 - (-8))²

d = √(31/4) + (9/4))² + (-8 + 8)²

d = √(10)²

d = √100

d = 10

8. (5(1/4)), (-3(1/4) and ((5(1/4), (-6(1/4))

         (x₁,     y₁)                    (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(21/4) - (21/4))² + (-25/4) - (-13/4))²

d = √(-25/4) + (13/4))²

d = √(-3)²

d = √9

d = 3

9. (-1(1/2)), (-6(1/2) and ((-2(1/2), (-6(1/2))

          (x₁, y₁)                        (x₂, y₂)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-5/2) - (-3/2))² + (-13/2) - (-13/2))²

d = √(-5/2) + (3/2))²

d = √(-1)²

d = √1

d = 1

I hope this helps!

The equation of the line perpendicular to the line 3x - 6y = - 8 is y = - 2x - 15 and of line parallel to the line 3x - 6y = - 8 is y = x/2.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a line 3x - 6y = - 8.

We have -

3x - 6y = - 8

3x = 6y - 8

6y = 3x - 8

y = x/2 - 4/3

For a parallel line -

slope = 1/2

y = x/2 + c

for the point (- 6, - 3), we can write -

-3 = -6/2 + c

-3 = -3 + c

c = 0

Equation : y = x/2

For a perpendicular line -

y = - 2x + c

for the point (- 6, - 3)

- 3 = - 2 x - 6 + c

- 3 = 12 + c

c = - 15

Equation : y = - 2x - 15

Therefore, the equation of the line perpendicular to the line 3x - 6y = - 8 is y = - 2x - 15 and of line parallel to the line 3x - 6y = - 8 is y = x/2.

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The linear function is 2/3 x=y-1. Therefore, option D is the correct answer.

A linear function is a function that represents a straight line on the coordinate plane. The standard form of a linear function is y = mx + b.

Here, 'm' is the slope of the line, 'b' is the y-intercept of the line, 'x' is the independent variable and 'y' (or f(x)) is the dependent variable.

Option A:

In the function y=3x², the highest degree is 2, so it is quadratic function.

Option B:

The function y=1/3x is not a linear function.

Option C:

In the function y=x³+5, the highest degree is 3, so it is cubic function.

Option D:

In the function 2/3 x=y-1, the highest degree is 1, so it is linear function.

The linear function is 2/3 x=y-1. Therefore, option D is the correct answer.

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Answer:

∴ x = 10.7 (to 3sf), y = 18

Step-by-step explanation:

(3x)° + (4x-15)° = 90° (right angle given) ------ equation (1)

(3x)° + (4x-15)° + (5y)° = 180° (adjacent angles on a straight line) ------ equation (2)

From equation (1),

3x + 4x - 15 = 90

              7x = 75

             ∴ x = 10.7 (to 3sf)

Subtract equation (1) from equation (2):

(3x+4x-15+5y) - (3x+4x-15) = 180 - 90

                                      5y = 90

                                     ∴ y = 18

The probability an athlete plays golf or tennis but not both = 0.75  

The ratio of favorable outcomes to all possible outcomes of an event is known as probability.  

The formula to calculate the probability of an event is given by

Probability(E) = Favorable Outcomes/Total Outcomes  

Here we have 40 athletes,  

Number of athletes who plays both tennis and golf = 5

Number of athletes who plays tennis = 30

=> Number of athletes who plays only tennis = 30 - 5 = 25  

Number of athletes who plays golf = 10  

Number of athletes who plays only golf = 10 - 5 = 5

From the above calculations,

Number of athletes who plays tennis or golf but not both = 25 + 5 = 30

Probability that athletes play golf or tennis but not both = 30/40 = 0.75

Therefore,

The probability an athlete plays golf or tennis but not both = 0.75

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The percentage is the measure of the portion of a quantity present in the whole. The remaining computers are 75.

Percentage of quantity is proportional to its portion or fraction in a whole.

To convert the percentage into fraction divide the percentage value by 100.

Suppose the total number of employee's computer be x.

Then, as per the question after adding 25 more computers, the following equation can be written,

85% of x = 80% of x + 25

=> 85x/100 = 80x/100 + 25

=> 85x/100 - 80x/100 = 25

=> 5x/100 = 25

=> x = 500.

The remaining computers are  given as

15% of x = 15/100 × 500

              = 75

Hence, the number of remaining employee's computer after adding 25 more computers are 750.

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