\text{Nine times the difference of 8 and a number.}
Nine times the difference of 8 and a number

Step-by-step explanation:

This is the correct answer.

Even according to calculator and working.

So not quite sure why those options are incorrect?

A function f: A--B is injective if each element in A maps to a unique element in B. It is surjective if every element in B has a corresponding element in A.

A bijective function is both injective and surjective, meaning that every element in A maps to a unique element in B, and every element in B has a corresponding element in A.  If IAI = IBI, then there are the same number of elements in A and B. Therefore, if f is injective, every element in A must map to a unique element in B, leaving no elements in B without a corresponding element in A. This means that f is also surjective. Similarly, if f is surjective, then every element in B has a corresponding element in A, which means that f is also injective. Thus, f is bijective if and only if it is injective and surjective.

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The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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Answer:

\(x\) = 4.9  (1 dp)

Step-by-step explanation:

Use trig ratio \(sin(\theta)=\dfrac{O}{H}\)

where \(\theta\) is the angle, O is the side opposite the angle and H is the hypotenuse of a right triangle.

Given:

\(\implies sin(55)=\dfrac{4}{x}\)

\(\implies x=\dfrac{4}{sin(55)}\)

\(\implies x = 4.9\)   (1 dp)

Answer:

A factor of 4

Step-by-step explanation:

Since the longest side for the bigger triangle is 20cm and the smaller triangle 5cm

Hence

\( \frac{20}{5} = 4\)

Thus a factor of 4

After 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We know the decay can be as:

\(\rm C = a(1-r)^t\)

We have:

a = 470 grams

r = 3% = 0.03

t = 6 hours

\(\rm C = 470(1-0.03)^6\)

C = 391.49 grams

Thus, after 6 hours the radioactive compound with mass 470 grams becomes 391.49 grams and the equation will be C is equal to 470(1-0.03)^6.

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The points D, E, F are not collinear to points A, B, C and are coplanar. (Right choices: 6, 7, 8)

According to Euclidean geometry, three points are coplanar when they are not collinear. Three or more points are coplanar when they are contained by the same plane.

From this perspective, points A, B, C, D, E, F are coplanar, as they are contained by plane π, but points D, E, F are not collinear to points A, B, C, as they are outside the line contained by plane π.

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The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

given that,

y = 2x² + 4x

now, for, x= 0 , y = 0

for, x= 1, y = 6

for, x= 2, y = 16

Hence, The solution is, the table is, for, x= 0, 1, 2, we get, y= 0, 6, 16.

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If the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.

A constraint is a condition of an optimization problem that should be satisfied the condition.

From the we have the function,

⇒ C(x) = −0.74x² + 22x + 75

the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.

In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.

The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).

Therefore, x ≥ 5.6 and x ≤ 24.13  

⇒ 5.6 ≤ x ≤ 24.13

Hence if the company wants to keep its production costs under $175,000, then  5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.

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Answer:

0 ≤ x < 5.6 and 24.13 < x ≤ 32.82

Step-by-step explanation:

the account balance can change quickly and frequently based on transactions and fees, so it's important to keep track of your transactions carefully and reconcile your account regularly to ensure that you have an accurate balance.

Unfortunately, there is no checkbook or transaction provided in your question. Without knowing the details of the transaction and the starting balance, it is not possible to determine the account balance on January 28.
However, I can provide some general information on how to calculate account balances based on transactions in a checkbook. To determine the account balance at any given point in time, you need to start with the starting balance (which is typically the balance on the previous statement) and then add or subtract the transactions that have occurred since that time.
To do this, you would need to look at the transactions in the checkbook and classify them as either deposits or withdrawals. Deposits are amounts of money that have been added to the account, while withdrawals are amounts of money that have been taken out of the account.
For each deposit, you would add the amount to the starting balance. For each withdrawal, you would subtract the amount from the starting balance. Once you have gone through all the transactions, the resulting amount should be the account balance.

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42 pieces of candy because math

we have shown that n is divisible by d, which means that d | n.

What is Derivation ?

Derivation is a mathematical technique used to find the rate at which a function changes. In other words, it is a method for calculating the instantaneous rate of change of a function at a particular point. Derivation is an important tool in calculus, and it has a wide range of applications in fields such as physics, engineering, and economics.

We are given that dc | nc, which means that there exists an integer k such that nc = k(dc).

We need to show that d | n, which means that there exists an integer m such that n = md.

We can start by dividing both sides of the given equation nc = k(dc) by c:

n = k(d)

Since d and k are integers, their product k(d) is also an integer, which means that n is an integer.

Therefore, we have shown that n is divisible by d, which means that d | n.

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Answer:

The length of the sides are 3 feet and 4 feet, respectively.

Step-by-step explanation:

Given the fact that triangle is a right triangle, it can be represented by Pythagorean Theorem:

\(r^{2} = x^{2}+y^{2}\)

Where:

\(r\) - Hypotenuse, measured in feet.

\(x\), \(y\) - Legs, measured in feet.

In addition, each leg can be determined as functions of hypotenuse:

\(x = r-2\,ft\)

\(y = r-1\,ft\)

Hence, the Pythagorean identity can be expanded and remaining variable may be solved:

\(r^{2} = (r-2\,ft)^{2}+(r-1\,ft)^{2}\)

\(r^{2} = r^{2}-4\cdot r +4 + r^{2}-2\cdot r +1\)

\(r^{2}-6\cdot r +5 =0\)

\((r-5)\cdot (r-1) = 0\)

\(r = 5\,ft\,\vee\,r = 1\,ft\)

According to the definition of hypotenuse, it must be longer than any of legs. Hence, there is just one solution that is reasonable:

\(r = 5\,ft\)

And length of the sides are, respectively:

\(x = 5\,ft-2\,ft\)

\(x =3\,ft\)

\(y = 5\,ft-1\,ft\)

\(y = 4\,ft\)

The length of the sides are 3 feet and 4 feet, respectively.

Answer:

2^0

Step-by-step explanation:

When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.

There are two ways to go about this problem.

The first way, the generic way, is to know that,

\(\frac{a^n}{a^m}=a^{n-m},a\neq0\).

So,

\(\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}\).

The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,

\(\frac{a}{a}=1, a\neq0\)

And 1 equals to any number raised to the power of zero,

\(a^0=1,a\neq0\)

So we just have to say that the 1 we got is rewritten as some base to the power of zero.

Since our base needs to be 2, we just simply say,

\(2^0\).

Et Viola.

Hope this helps.

Answer:

doing the test rn so im pretty sure its A on edge

Step-by-step explanation:

The correct answer is (c) \((y + 4)^2 = -8(x - 2)\) which is the equation of parabola.

A parabola's standard form equation is written as\(y = ax^2 + bx + c\), where a, b, and c are constants. Depending on the sign of the coefficient a, the parabola is a U-shaped curve that can open upwards or downwards. The parabola's vertex lies at the coordinates (-b/2a, c - b2/4a). The focus and directrix of the parabola are situated a fixed distance from the vertex, and the axis of symmetry of the parabola is a vertical line passing through the vertex. Numerous practical uses for the parabola exist in the fields of optics, physics, and engineering.

To convert the equation \(-8x + y^2 - 8y = 0\)into standard form, we need to complete the square for the y terms and move the x term to the other side.

Starting with the y terms:
\(y^2 - 8y = -(8x)\)

To complete the square for y, we need to add (8/2)^2 = 16 to both sides:
\(y^2 - 8y + 16 = -(8x) + 16\)

This simplifies to:
\((y - 4)^2 = -8x + 16\)

Now we can move the constant term to the other side:
\((y - 4)^2 = -8(x - 2)\)

So the correct answer is \((c) (y + 4)^2 = -8(x - 2)\) which is equation of parabola.

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Answer: 5 inches per hour or 2.5 inches per half an hour

Step-by-step explanation:

Amount of Time Passed: 2 hours 30 minutes

Difference in Candle Height: 12.5 inches

12.5 / 2.5 = 5 inches

5 inches per hour or 2.5 inches per half an hour

If it is incorrect, please let me know.

The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Answer:

11/4

Step-by-step explanation:

3/2 can be re-written as 6/4. they now have the same denominator. 6/4 + 5/4 = 11/4

Answer:

A

Step-by-step explanation:

2x + x = 3x

y - 3y = 2y

When comparing two sample means, we can safely reject the null hypothesis if the calculated test statistic exceeds the critical value corresponding to the chosen significance level.

In hypothesis testing, when comparing two sample means, we typically perform a t-test or z-test depending on the characteristics of the data and assumptions. The null hypothesis assumes that there is no significant difference between the means of the two samples.

To determine whether we can reject the null hypothesis and conclude that there is a significant difference, we calculate a test statistic. The specific test statistic (t or z) depends on factors such as sample size and whether population parameters are known.

Next, we compare the calculated test statistic to the critical value. The critical value is determined based on the chosen significance level (commonly denoted as α). If the calculated test statistic exceeds the critical value, we reject the null hypothesis, indicating that there is evidence to support a significant difference between the two sample means.

The significance level determines the threshold for rejecting the null hypothesis and is typically set at 0.05 (5%) or lower, depending on the desired level of confidence.

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Answer:

Step-by-step explanation:

for 182 miles you need 14 gallons

???????                            8 gallons

8/14=x/182

x=182*8/14

x miles=104 miles

Step-by-step explanation:

5 = 6x

6x = 5

x = 5/6

x = 0.83

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation

y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Every point on the graph in red is 1/2 away from the x-axis as that of the equivalent position on the graph in black.

Therefore, the vertically scale factor is equal to 1/2:

=> y = (1/2)f(x)

This problem can be solved by multiplying it by two and yields the following solution:

=> 2y = f(x)

thus , option c is correct

Therefore , the solution of the given problem of equation comes out to be  option c is correct 2y = f(x) .

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To find the velocity, acceleration, and speed of a particle with a given position function, we differentiate the position function to obtain the velocity, differentiate the velocity function to obtain the acceleration, and take the magnitude of the velocity vector to obtain the speed.

To find the velocity, acceleration, and speed of a particle with a given position function, we first need to differentiate the function with respect to time.
Let's assume that the position function is given by x(t), where t is time. Then, the velocity of the particle is given by the derivative of x(t) with respect to time, which we denote as v(t). Mathematically, we can express this as:

v(t) = dx/dt

where dx/dt is the derivative of x(t) with respect to time. The velocity v(t) represents the rate of change of the position x(t) with respect to time, and is a vector quantity with magnitude and direction.
Next, to find the acceleration of the particle, we need to differentiate the velocity function v(t) with respect to time. We denote the acceleration function as a(t), and mathematically express this as:

a(t) = dv/dt = d²x/dt²

where d²x/dt² is the second derivative of the position function x(t) with respect to time. The acceleration a(t) represents the rate of change of velocity v(t) with respect to time, and is also a vector quantity with magnitude and direction.
Finally, to find the speed of the particle, we take the magnitude of the velocity vector v(t) at any given time t. The speed is simply the magnitude of the velocity vector, and is given by:

speed = |v(t)|

where |v(t)| denotes the magnitude of the velocity vector v(t).

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