1/3 Marks
These cards are put into a bag:
1 2 3 4
5 6 7 8 9 10
One card is chosen at random.
a) What is the probability of choosing the card with the number 4?
b)
What is the probability of choosing a card that has a digit 1 on it?
c) What is the probability of choosing a card that does not have a digit 1 on it?
Give your answers as fractions.

The range of the function f(x) = 3x - 4, having domain x ≥ 1 is x ≥ -1 and the graph is attached below so, option D is correct.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Given:

The function, f(x) = 3x - 4,

Domain = x ≥ 1

When domain = 1,

Range = 3 × 1 - 4 = -1

When domain = 2

Range = 3 × 2 - 4 = 2

Thus, you can conclude the range of the function as x [-1, ∞) or x ≥ -1

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Answer:2x^3+3x^2-11x-6

Step-by-step explanation:

Therefore, the numerator of the given equation comes out to be 4x+6

A fraction denotes a component of a whole or, more generally, any number of equal parts. In conversational English, a fraction, such as one-half, eight-fifths, or three-quarters, denotes the quantity of a specific size of portions.

Given

[tex]\frac{x}{x^{2} +3x+2} + \frac{3}{x+1}[/tex]

A common denominator must exist for the fractions before we can add them.

Factor the denominator of the first fraction

[tex]\frac{x}{(x+1) (x+2)} + \frac{3}{x+1}[/tex]

Subtract (x + 2) from the second fraction's numerator and denominator.

[tex]\frac{x}{(x+1) (x+2)} + \frac{3(x+2)}{(x+2)(x+1)}[/tex]  ← Currently, fractions share a common denominator.

Add the numerators leaving the denominators

= [tex]\frac{(x+2)(x+3)}{(x+2)(x+1)}[/tex]  

= [tex]\frac{x^{2} +3x+6}{(x+2)(x+1)}[/tex]

=  [tex]\frac{4x+6}{(x+2)(x+1)}[/tex]

simplified sum with numerator 4x + 6

Therefore the numerator of the given equation comes out to be 4x+6.

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The taxable income in marginal tax rates for 2016 is $44964.

What is marginal tax rate?

Gross income = $88000

Adjustments = $2000

Deductions interest = $27000

Property taxes = $4036

Charitable contribution = $2000

Taxable income = 88000 - (2000 + 27000 + 4036 + 2000)

= 88000 - 35036

= 44964

Hence, the taxable income in marginal tax rates for 2016 is $44964.

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The statement that is proportion is 3/4 = 6/8

What is statement ?

Depending on the context, the term "statement" in logic can refer to either a proposition or a coherent declarative utterance that can be true or untrue. Which is the claim a true or untrue declarative phrase makes.

A sentence that asserts something to be true is called a statement.

In the fields of law, banking, and government, there are more types of statements. Every statement makes a claim or a point. If you see an accident, you have to tell the police what you observed in a statement.

A statement is a directive issued to the computer that tells it to carry out a specific task, like display something on the screen or gather input. A succession of assertions make up a computer program.

3/4 = 5/8

3:4 ≠ 5:8

3/4 = 4/8

3/4 = 1/2

3:4 ≠ 1:2

3/4 = 6/8

3/4 = 3/4

3:4 = 3:4

3/4 = 7/8

3:4  ≠ 7/8

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Julius's Schedule C gross profit is $72,000

($97,000 sales - $2,000 returns - $25,000 cost of goods sold = $70,000 gross profit).

income from trade or business after covering the costs of generating and disbursing goods and services: Selling scraps to textile businesses brings her a sizable profit.

A business's primary goal should be to earn a profit. Understanding where your business is producing money and where you are spending it can help you assess your level of success. Calculating your profit can also provide you this information.

Income less all costs. As an illustration, Sam's Bakery collected $900 yesterday, but its expenses, including salaries, food, and power, were $650. Profit was therefore $900 divided by $650 to equal $250.

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The factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Given:

y =x³-4x²-17x+60x

Let us assume that the factors are

(x−a), (x−b) and (x- c)

So, if x is either equal to a or b or c, y=0

and a⋅ b⋅ c=−60, which means a or b and c are factors of 60.

Thus, which factor of 60 (such as 2, 3, 5, 6, 10 etc.) makes y=0.

It is given that (x−3) is a factor of y

and, When we divide y by (x−3), we get x²−x−20

Similarly x=5 makes x²−x−20 equal and Dividing x2−x−20 by (x−5), we get (x+4)

Hence, the factors of y =x³-4x²-17x+60x are (x−3), (x−5) and (x+4)

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Answer: Z=35(4)^7

Step-by-step explanation:b = multiplier = 4b = multiplier = 4a = starting amount = 35a = starting amount = 35t = time = 7 hourst = time = 7 hours. a⋅b^t

35(4)735(4)7Equivalent forms:Equivalent forms:35(4)(4)(4)(4)(4)(4)(4)35(4)(4)(4)(4)(4)(4)(4)

Answer:125=n

Step-by-step explanation: 375 divided by 3 is 125

The trains leaving atlanta for new york every 30 minutes....it takes 10 hours   so there is 20 trains on the track when YOUR

NY to ATL train leaves......during the 10 hour trip ANOTHER 20 trains will launch from ATL going to NY

  so you will pass 40 trains that are going from ATL to NY    while you are travelling to ATL  

This assumes that the trains go every 30 minutes around the clock.

If they do not go around the clock , you will only pass trains that launch for the 10 hours after your departure from NY

  that would be 20 trains

Using the concept of probability, the probability of not landing on yellow or red at all is 1/4.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Creating a square model of the two spins :

Red(R) ; Blue(B) ; Green(G) ; Yellow(Y)

___ R ___ B ___ G ___ Y

R_ RR __ RB __ RG __ RY

B_ BR __ BB __ BG __ BY

G_ GR __GB __ GG __GY

Y_ YR __ YB __ YG __ YY

Sample space = 4² = 16

Combinations without red and yellow :

{BB, BG, GB, GG}

Number of selections without red or yellow = 4

Recall :

Probability = required outcome / Total possible outcomes

P(without Red or Yellow) = 4/16 = 1/4

Hence, the probability of not landing on yellow or red at all is 1/4.

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See steps below for proving n = 2m:

An equation is formed of two equal expressions. n=2m can be proved by solving the two of the given equation for h and then equating them together as shown below.

An equation is formed when two equal expressions are equated together with the help of an equal sign ''=''.

Given the two equations, 2n=m+h, and h=n+m. Now, solve the two of the equations for h as shown below:

Equation 1.

2n = m + h

2n - m = h

h = 2n - m

Equation 2.

h = n + m

Further, equate the value of h from both the equation,

h = h

2n - m = n + m

Bring the like terms on the same side of the equation,

2n - n = m + m

n = 2m

Hence, proved n=2m.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The value of f(3) is 10.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

Given function :

f(x) = 4x - 2

We have to find the value of f(3).

Now we put x = 3 and we get

f(3) = 4 × 3 - 2

f(3) = 12 - 2

f(3) = 10

Hence, the value of f(3) is 10.

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The 20% Tony spends from his monthly salary on the wallet, the bag which cost $20 more than the wallet and the ratio of the wallet to shoe cost of 5:6, which expressed as a fraction is 5/6, indicates;

(a) Tony's monthly salary is $2,400

(b) The amount spent on the pair of shoes is (6/25) of his monthly salary

A fraction is a part of a whole item, expressed as a quotient.

Let x represent Tony's salary, from the details of the question, we get;

The amount Tony spent on the wallet = 20% of his salary

The cost of the bag Tony bought = $20 + The cost of the wallet

Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6

The amount Tony had left = $844

Therefore;

The amount Tony spent on the wallet = 20% of x = 0.2·x

Amount spent on the bag = 20 + 0.2·x

Ratio of the cost of the wallet to the cost of the pair of shoes = 5:6

Therefore;

Cost of the pair of shoes = (6/5)×(0.2·x)

Therefore;

x - 0.2·x - (20 + 0.2·x) - (6/5) ×(0.2·x) = 844

0.36·x - 20 = 844

x = (844 + 20)/0.36 = 2400

(b) The amount Tony spends on the pair of shoes = (6/5) × (0.2·x)

(6/5) × (0.2·x) = (6/5) × (2/10) × x = (12/50)·x = (6/25)·x

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Answer:

4

Step-by-step explanation:

[tex] \frac{2}{3} \times 6 = 4[/tex]

I think she can make 4 throw pillows if she should use 6 yards of fabric

i hope this helped

If fox run at speed of 10 kmph and wolf run at 11 mph , then the animal that runs faster is  wolf  .

In the question ,

it is given that ,

the speed at which the fox runs is = 10 kmph

the speed at which the wolf runs is = 11mph ,

for comparison , the units should be same ,

So , we need to convert 11 mph to kmph .

we know  that , 1 mile per hour = 1.60934 kmph ,

So , 11 mph = 17.7028 kmph .

So , the speed at which the wolf runs is = 17.7028 kmph .

On comparison , we get that speed of wolf is greater than speed of fox .

Therefore , wolf runs faster than fox .

The given question is incomplete , the complete question is

A fox can run at a speed of 10 kmph, and a wolf can run at a speed of 11 mph. Which animal is faster ?

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Answer: the Answer is wolf

Step-by-step explanation:

the wolf can peed so it is fater

Question 1

C. Congruent by ASA.

Question 2

The reason is 'definition of isosceles triangle'.

Hugo needs 15 weeks to pay back his brother completely if he pays $2 a week.

What is an equation?

An equation is written in the form of variables and constants separated by the operation of multiplication and division.

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

According to the given question:

Hugo decided to pay $2 a week to his brother to buy a bicycle.

The equation y - 10 = - 2(x – 10) models the amount of money he owes for the bike, where x is the number of weeks and y is the amount of money he still needs to pay.

To pay back to the brother he must owe no money which is y = 0.

∴ The weeks needed is,

0 - 10 = -2(x - 10).

- 10 = -2x + 20.

2x = 30.

x = 15.

He needs 15 weeks to pay back completely.

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you will be on floor no. -8 and your friend will be in floor no. 5 if you and your friend started at floor no. 0

YOU CAN ALSO VISUALISE THIS WAY

The solution to the system of equations is ( -2, 0)

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.

y = -2x - 4 ------------1

y = x + 2--------------2

Equating equation 1 and 2 we have

-2x - 4 = x + 2

collect like terms

-2x - x = 2 + 4

-3x = 6

x = 6/-3

x = -2

but y = x + 2

substitute x = -2

y = -2 + 2, y = 0

In conclusion the solution of the system of linear equations is (-2, 0 )

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In linear equation, Sofia will order 7 more rolls of sushi (84 pieces) and pay $56.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

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Answer:

x^3y^2√xy

Step-by-step explanation:

First, you calculate what's in the square root. x^2 becomes x and y^4 becomes y^2.

Then you distribute the 1/2 to the x^5 and the y so they become x^5/2 and y^1/2.

Next, you combine the like terms. x and x^5/2 becomes x^7/2. y^2 and y^1/2 become y^5/2.

So you have x^7/2 y^5/2

To get rid of the 2 on the bottom of the exponents you square root both variables.

So you get √x^7 y^5 (square rooted x^7 and y^5)

Simplify the square rooted problem to x^3 y^2 √xy

You get x to the third power y to the second power and square rooted xy.

The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).  

A quadratic equation, or quadratics, is a polynomial equation with a maximum degree of two. It will be in the form of ax² + bx + c = 0.

When a quadratic function is represented in a graph on the x and y grid, It will represent a parabola. Either it will open upwards or downwards.

The domain of a parabola is the entire set of real numbers [ Without any restrictions ]

Here we have

Ethan uses the function, f(x) = 2x² + 2x + 4

As we know all quadratic functions are parabolas

And its domain is the set of real numbers

Therefore,

The domain of f(x) = 2x² + 2x + 4  is (-∞, ∞).

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a) The equation for the volume of the cube after t hours is of: V(t) = (0.5t + 2)³.

b) The equation for the surface area of the cube after t hours is of: S(t) = 6(0.5t + 2)².

c) The surface area will be of 216 in² after 8 hours.

Considering a cube of side length s, the surface area and the volume are given as follows:

In this problem, the side length is a function of the time, as follows:

s(t) = 0.5t + 2.

Hence the equations are given as follows:

The surface area will be of 216 in³ when:

6(0.5t + 2)² = 216

(0.5t + 2)² = 216/6

(0.5t + 2)² = 36.

Taking the square root from both sides, the time is given as follows:

0.5t + 2 = 6

0.5t = 4

t = 4/0.5

t = 8 hours.

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As a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree

What is Trigonometric Ratios ?

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions.

                  The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

The expression given is

(2tan(10 degrees))/(1 - tan² (10 degrees))

By the property of Tan 2x

Tan 2x = 2tanx /(1 - tan² x)

Therefore from the formula ,

x = 10 in the given expression

Therefore as a single trigonometric ratio (2tan(10 degrees))/(1 - tan² (10 degrees)) = tan 2x = tan 20 degree

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Answer: yes tan(20°) option 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

s must be a number greater than 7

Answer:

144 + 64 =208

Step-by-step explanation:

you see the 12th square number is 12 × 12 which is 144 then the 4th cube number is 4 × 4 ×4 make it 64 and the sum of all of this is 204

Answer:

$ 7.2

Step-by-step explanation:

½ pound = $3.60

1 pound = x

just cross multiply.

½x = $ 3.60

0.5x = $ 3.60

x = $3.60/0.5

x = $7.2

Answer:

[tex]\huge\boxed{\sf \$ 7.20}[/tex]

Step-by-step explanation:

Given that,

1/2 pound of cheese = $3.60

Multiply 2 to both sides

1 pound of cheese = $3.60 × 2

[tex]\rule[225]{225}{2}[/tex]

Answer:

the answer to this should be no solution

Step-by-step explanation:

the first step would be adding seven to both sides, but all that does is leave a zero on the other side, so the equation ends up being 9x=0.

The value of x in the expression is 0.

We have,

Expression: 9x - 7 = -7

To solve for x.

Add 7 on both sides.

9x - 7 + 7 = -7 + 7

9x = 0

x = 0

Thus,

The value of x in the expression is 0.

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