Andrea is travelling by bus at an average speed of 85km/h The equation relating distance,d and time t, is d= 85t

Ian works part-time at a movie theatre. He
earns $8.25/h. The relationship between his
pay, p, and the time he works, t, can be
modelled with the equation p = 8.25t.
a) Show the relationship on a graph.
b) Explain how you know the graph
represents the equation.

Considering the depreciation rate of 11%, the value of car is $11800 in 4.1 years.

Depreciation is the reduction in the value of an asset over time due to wear and tear, age, or obsolescence.

The most basic and widely used method of calculating depreciation is Annual depreciation = (Cost of asset - Salvage value) / Useful life

To find the time it will take for the value of the car to depreciate to $11,800, we can set up the following equation:

24900 - 11800 = 11000

24900 * .11 = 2679

11000 / 2679 = 4.09 years

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The terminal point is 0.36 radii to the right of the circle's center.

The terminal point is 0.93 radii above the circle's center.

Here, the 3 O'clock line is OA and the terminal point is on the line OP.

The angle θ = 1.2 radians

Let the radius = r

The distance of the terminal point to the right of the center = OQ

= r × cos θ

= r × cos 1.2  

= r × 0.36

So, it is equal to 0.36 radii

The distance of the terminal point above the center = PQ

= r × sin θ

= r × sin 1.2

= r × 0.93

So, it is equal to 0.93 radii.

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The worst case complexity for the algorithm is O(n²)

In the worst case, every time we call the function findmin(list)

where list of length n, it will take  O(n)  operations.

For simplicity we can assume it will take n operations.

Since in each call , list decreases in one element  until it is finally empty.

the number of operations in the while loop is:

n(n-1)+(n-2)+....2+1 = n(n+1)/2= (n²+n)/2

Therefore the worst case complexity for the algorithm is O(n²).

Thus, time complexity is the number of activities a calculation performs to get done with its responsibility (taking into account that every activity requires some investment). The calculation that plays out the undertaking in the most modest number of activities is viewed as the most effective one regarding the time complexity.

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Answer:

x = - 5 , x = 7

Step-by-step explanation:

to find the zeros, let y = 0 , that is

x² - 2x - 35 = 0

consider the factors of the constant term (- 35) which sum to give the coefficient of the x- term (- 2)

the factors are - 7 and + 5 , since

- 7 × + 5 = - 35 and - 7 + 5 = - 2 , then

x² - 2x - 35 = (x - 7)(x + 5) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 7 = 0 ⇒ x = 7

A point on the graph is (30, 4) and the meaning is that the cost of 30 units of electricity is £4

From the question, we have the graph that can be used in our computation:

From the graph, we have the following ordered pairs

(0, 0) and (30, 4)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (0, 0) and (30, 4)

The gradient of the line is then calculated using the following slope equation

gradient = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (30, 4)

Substitute the known values in the above equation

So, we have the following equation

gradient  = (4 - 0)/(30 - 0)

Evaluate

gradient  = 4/30

So, the gradient of the line is 4/30

As a general rule:

Generally, slope or gradient means rate

This means that the gradient of this line represent the rate

i.e. the amount for each unit is 4/30

So, we can conclude that the point (30, 4) on the graph means that the cost of 30 units is £4

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Complete question

An electricity company charges the same fixed amount for each unit of electricity used. David uses this graph to work out the total cost of the electricity he has used.

See attachment for graph

The unit rate for miles per gallon for each​ car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

You are running an efficiency study. One of the vehicles you find is blue. It can travel 45 ¹/₂ miles on 1 ¹/₄ gallon of fuel. Another vehicle is red. It can travel 24 ⁴/₅ on ⁴/₅ gallons of fuel.

The rate of blue cars is given as,

⇒ (45 ¹/₂) / (1 ¹/₄)

⇒ 45.5 / 1.25

⇒ 36.4 miles per gallon

The rate of red cars is given as,

⇒ (24 ⁴/₅) / (⁴/₅)

⇒ 24.8 / 0.8

⇒ 31 miles per hour

The unit rate for miles per gallon for each​ car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

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The mean is 66, the median is 75 and the mode is None.

The center or typical value of a dataset is represented by summary statistics known as measures of central tendency. These metrics, such as the mean, median, and mode, are examples. These statistics, often known as the central location of a distribution, show where the majority of values in a distribution fall.

Given,

No. of observations = 5

Mean = Total observations/ no. of observations = 20+73+75+80+82/5 = 66

Median = Middle most observation arranged from smallest to largest = 75

Mode = Observation which occurs at least twice = None

Mean describes the data the best because it takes the average of all the given data.

The distribution of the data set is scattered and the shape of the frequency graph is going upwards.

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The solved inverse matrices.

(9x - 2y = 12

3x + 4y = 18

([2],[3 ])

To solve a system of linear equations using inverse matrices, we can express the system in matrix form as follows:

[9 -2] [x] = [12]

[3 4] [y] [18]

Then we can find the inverse of the coefficient matrix, which is the matrix containing the coefficients of the variables in the system:

[9 -2]^⁻¹ = 1/((9)(4) - (-2)(3)) * [ 4 2]

[3 4] [ -3 9]

= 1/14 * [ 4 2] = [2/7  1/7]

[ -3 9] [-3/7  2/7]

We can then multiply both sides of the equation by the inverse matrix to obtain the solution:

[2/7   1/7] [9 -2] [x] = [2/7   1/7] [12]

[-3/7   2/7] [3 4] [y] [-3/7   2/7] [18]

[x] = [2/7   1/7]^-1 [2/7   1/7] [9  -2] [x]

[y] [-3/7   2/7] [-3/7    2/7] [3   4] [y]

[x] = [1  0] [9  -2] [x]

[y] [0  1] [3  4] [y]

This simplifies to the following system of equations:

9x - 2y = 12

3x + 4y = 18

Therefore in solving this system, we find that x = 2 and y = 3. So, the solution to the original system is (x, y) = (2, 3).

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The entry to record this payment when the company’s estimated taxes for the first quarter total $50,000 will be:

Debit Income taxes payable $50000

Credit Cash $50000.

A journal is a book in which all of a company's transactions are recorded for the first time. Journaling is the process of recording transactions in a journal. Every transaction has two effects: one is debited and the other is credited.

The act of keeping or making records of any transaction, economic or non-economic, is referred to as a journal entry. An accounting journal, which shows a company's debit and credit balances, records transactions. The journal entry may include multiple recordings, each of which is either a debit or a credit. A journal entry's purpose is to physically or digitally record every business transaction properly and accurately.

The journal entry based on the information is illustrated.

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The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

Average population = 240

Standard deviation for the population; 3

Z-score can be calculated as ,

z = (x' - μ)/σ

Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.

Z-score is 1.96 at significance level 0.025.

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Getting close to a whole number results ,

x' = 246

The two z-score tables are as follows:

Positive Z Score Table: The observed value is greater than the average of all values.

An observed value that is below the mean of all values is shown by a negative Z score table.

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The expressions is equivalent to z + z+z + z would be 4z. so option A is correct.

What are equivalent expressions?

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

Given expression

z + z+z + z

All the terms are like terms, by adding all of them

z + z+z + z

= 4z

Thus, The expressions is equivalent to z + z+z + z would be 4z. so option A is correct.

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On solving the provided question, we got to know that ∠ H + ∠ K = 45°.

K therefore has a 135° measure.

A unique kind of quadrilateral created by parallel lines is a parallelogram. A parallelogram might have different angles between its neighboring sides, but it must have parallel opposite sides in order to be considered one. If a quadrilateral's opposite sides are parallel and congruent, it is a parallelogram. As a result, a parallelogram is a quadrilateral with both pairs of opposite sides being parallel and equal.

the K-value of the angle.

First of all, we should be aware that the sum of the adjacent angles in the parallelogram ABCD, which has the angles A, B, C, and D, is 180°.

[tex]angle A + angle B = 180\\ angle B + angle C = 180\\ angle C + angle D = 180\\ angle A + angle D = 180[/tex]

They're considered to be a linear pair.

As a result, the parallelogram HIJK, whose angle H = 45°, is what we have.

Therefore, ∠ H +∠K = 180° (linear pair),

∠ K = 180° - 45°

∠ K = 135°,

and

∠ H + ∠ K = 45°.

K therefore has a 135° measure.

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1. The number of baseball cards from Gene is 321.

2. An equation that represents finding the number of baseball cards that come from Gene is g = 758 - a.

An equation is a mathematical statement that shows the equality of two or more mathematical expressions.

Equations are solved to solve mathematical problems with unknown variables, combining numbers and variables with mathematical operands.

We depict equations using the equation symbol (=).

The total number of baseball cards with Aaron and Gene = 758

The number of cards from Aaron, a = 437

The number of cards from Gene = g

g = 758 - a.

= 758 - 437

= 321

Thus, using the above equation, we can use the subtraction operation to find that Gene brought 321 baseball cards.

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The measure of the central angles of the circle are, respectively:

m ∠ BOC = 60°

m ∠ COD = 120°

m ∠ AOD = 60°

m ∠ AOB = 120°

m ∠ DOB = 180°

In this problem we find a geometric system formed by a circle, two parallel lines and two additional lines that intersect each other at the center of the circle. Then, the angles DOC, COB, AOB and DOB are central angles of the circle such that:

m ∠ DOC + m ∠ COB + m ∠ AOB + m ∠ DOB = 360°

Then, by direct inspection, we find that the measures of the central angles are, respectively:

m ∠ BOC = 60°

m ∠ COD = 120°

m ∠ AOD = 60°

m ∠ AOB = 120°

m ∠ DOB = m ∠ COD + m ∠ BOC = 120° + 60° = 180°

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Answer:

27 vidoe are actions adventure.

Step-by-step explanation:

1005 would we all of the vidoes.  100% - 40 % = 60%

60% is the same as .6

.6 x 45 = 27

Answer:

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

40% of 45 DVD's are comedies.

It is in number:

The rest are action-adventures:

Gail's friends does not reject the null hypothesis.

What is null and alternate hypothesis?

Statisticians test hypotheses using null and alternate hypotheses. The alternative hypothesis of a test states your research's prediction of an effect or relationship, whereas the null hypothesis of a test consistently predicts no effect or no relationship between variables.

Given:

H0: p = 0.4

Ha: p ≠ 0.4

Gail uses a level of significance of α = 0.05, she does not reject the null hypothesis.

Therefore the p-value she obtained is greater than 0.05

Andrew uses a level of significance of α = 0.1

Since from given information we can not say if p value is > 0.1 or less, hence

it is impossible to tell from the information given.

Ben uses α = 0.01

Since p-value  is greater than 0.05 hence definitely greater than 0.01

Hence, Gail's friends does not reject the null hypothesis.

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Complete question:

Gail is a student in a class that has been asked to conduct a hypothesis test for a population proportion. The null and alternative hypotheses are: H0: p = 0.4 Ha: p ≠ 0.4 Gail is given a sample and calculates the test statistic. Using a level of significance of α = 0.05, she does not reject the null hypothesis. Gail's friends, Andrew and Ben, also use the sample to calculate a test statistic. However, they differ in the level of significance they use. Andrew uses a level of significance of α = 0.1, while Ben uses α = 0.01. All three students perform their calculations correctly. For each of Gail's friends, select whether or not they reject the null hypothesis, or whether it is impossible to tell from the information given.

35% of the fuel Capacity did not use on this flight.

Step 1: Calculate the change i.e., subtract old value from the new value

Step 2: Divide that change by the old value.

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

 Percentage change = ((final value - initial value) ÷final value) ×100

Given: Total capacity in a fuel tank of a jet = 200000 liters

Used fuel =130000 liters

% Of fuel which is not used = ((total capacity of fuel tank - used fuel) ÷total capacity of fuel tank) ×100

[tex]=\frac{200000-130000}{200000}*100\\=\frac{70000}{2000}[/tex]

=35%

Therefore, 35% of the fuel capacity did not used in this flight.

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Here we want to find all the zeros of the function f(x) = 16*x^4 - 81.

Function is a relation or expression involving one or more variables.

The zeros are:

x = 3/2

x = -3/2

x = (3/2)*i

x = (-3/2)*i

First, for a given function f(x), we define the zeros as the values of x such that:

f(x) = 0.

Then we must solve:

f(x) = 16*x^4 - 81 = 0

Solving this for x leads to:

16*x^4 = 81

x^4 =  81/16

x^2 = ±√(81/16) = 9/4

x = ±√±(9/4) = ±3/2 and ±(3/2)*i

So there are 4 zeros, and these are:

x = 3/2

x = -3/2

x = (3/2)*i

x = (-3/2)*i

Where the two complex zeros come from evaluating the second square root on

-9/4.

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The probability is 0.8427.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Here we are total number of insurance agents = 89

And  number of insurance agents do own a handgun = 75

So we asked probability that a insurance agent will own a handgun  

Probability = no.of insurance agents/no.of insurance agents who owns a handgun

Probability = 75/89 = 0.8427

The probability that the agent will own a handgun is .84

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Answer:

14

Step By Step

22/4= 5.5 77/5.5= 14

Answer:

Step-by-step explanation:

slope intercept is y=mx+b

y+4=2(x-3)

y=2(x-3)-4

y=2x-6-4

y=2x-10

Answer:

36x⁵ y² ÷ w¹

= 36x⁵ y² w⁻¹

Thus, The simplified form is 36x⁵ y² w⁻¹

Answer:

9

Step-by-step explanation:

8x - 4x = 36

4x = 36

x = 36/4 = 9

Answer:

9

Step-by-step explanation:

8n-4n=36

n=9

8(9)-4(9)=36

The amount must be $164,313.82 deposited in her local bank. which is the correct answer would be an option (C).

For yearly payments of $18,000 for 20 years at a current rate of 9% compounded annually.

Let's assume that the amount would be P deposited in her local bank

As per the given question, the required solution would be as:

P = 18000[1 - (1 + 9/100)⁻²⁰]/0.09

P = 18000[1 - (1 + 0.09)⁻²⁰]/0.09

P = $164,313.82

Therefore, the required amount must be $164,313.82 deposited in her local bank.

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Answer:

Option B

Step-by-step explanation:

Use the formula

[tex]x = \frac{-b\±\sqrt{b^{2}-4ac } }{2a}[/tex]

now input the values. In equation [tex]x^{2} - 5x + 7 = 0[/tex], a = 1, b = -5 & c = 7

By taking positive sign we get,

[tex]x = \frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]

⇒[tex]x = \frac{-(-5)+\sqrt{(-5)^{2}-4.1.7 } }{2.1}[/tex]

⇒[tex]x = \frac{5+\sqrt{25-28 } }{2}[/tex]

⇒[tex]x = \frac{5+\sqrt{-3 } }{2}[/tex]

In the same way, by taking minus sign, we get [tex]x = \frac{5-\sqrt{-3 } }{2}[/tex]

The probability that the next chew would be a lime chew is 5%.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the next chew would be a lime chew = number of lime chews / total number of chews

Total number of chews = 34 + 5 + 2 = 41

The probability that the next chew would be a lime chew = (2 / 41) x 100 = 5%

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There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

The solution set is x ≤ 0.4.

The graph of the solution is

<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>

                      <------------------o

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

8(12 - 4x) ≥ 82

96 - 32x ≥ 82

96 - 82 ≥ 32x

14 ≥ 32x

x ≤ 14/32

x ≤ 7/16

x ≤ 0.4

This can be graphed using a number line.

<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>

                      <------------------o

Thus,

The solution set is x ≤ 0.4.

The graph of the solution is given above.

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After solving the given equations the value obtained for x and y will be equal to 2 and 14 respectively.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

The given equations are:

y = 9x - 4 and,

y = -2x + 18

Equate both equations,

9x - 4 = -2x + 18

9x + 2x = 18 + 4

11x = 22

x = 2

Substitute x = 2 in the first equation,

y = 9x - 4

y = 9(2) - 4

y = 14

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For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

In the given question, we have to state true or false for the given statement.

In our programs, we frequently want to be able to "conditionally" execute certain actions, i.e., "if this is true, then do X, but if this other thing is true, then do Y." It's similar to how we dress when we get out of bed: "If it's sunny, I wear sunglasses, but if it's raining, I take an umbrella." In our programs, we can use if statements, if/else statements, and conditional expressions to do things conditionally.

If a condition is true, an if statement instructs the computer to run a certain piece of code. Only if x is bigger than 0 do we output a message in the following code:

We would be able to see the message on the canvas since x is 5, which is bigger than 0. If we modified x to -1, the message wouldn't appear at all because x wouldn't be greater than 0.

A conditional expression is one that can only be evaluated as either true or false, and the x > 0 qualifies as one. A boolean value is one that can only be either true or false (as opposed to a number or a string). For instance, we might simply show the following conditional statement:

1. Return true if the array's size is zero or one.

2. Verify the last two members of the array; if they are sorted, call n-1 times in a recursive fashion; otherwise, return false.

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The right question is:

State in predicate calculus that an array of int, say a, is sorted. You may use the Java expression syntax (e.g., a.length, a[i], ==, and <) and logical operators (&&).