Which property justifies the work between steps 7 and 8

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

-2x-7y=-4

Step-by-step explanation:

5x+-7x=-2x

-9y+2y=-7y

1+-5=-4

So -2x-7y=-4

Answer:

C

Step-by-step explanation:

if we are equidistant and in the upper part of a whole number, we round up. if in the lower part of a whole number, we round down.

so,

3/4 gets rounded up to 1 as the nearest 1/2 (as 1 = 2/2).

1/4 would get rounded down to 0 as the nearest 1/2 (as 0 = 0/2).

Answer:

we conclude that the intervals in which the function P(t) is decreasing are:

Step-by-step explanation:

At x< 1, the function P(t) is decreasing

From the figure, it is clear that the function seems to be increasing

from (1, 3) and then 4 to onwards.

But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).

Therefore, we conclude that the intervals in which the function P(t) is decreasing are:

The opposie angles are equal

c is opposite to a, so

The angle p is opposite to that of n, so

The total angle of rotation in a line is 180°. so,

This o is the oppsite to m, and hence m=o.

similarly,

And hence, b=d=146

The square of a binomial, when the binomials are subtracted, is defined as follows:

(a - b)² = a² - 2ab + b².

When the two binomials are added, the square is given as follows:

(a + b)².

Expanding the square, we have that:

(a + b)² = (a + b) x (a + b).

(a + b)² = a² + ab + ab + b².

(a + b)² = a² + 2ab + b².

Which is the result presented in this problem.

Now, when the binomial has a minus sign, involving a subtraction, the pattern is obtained as follows:

(a - b)² = (a - b) x (a - b).

(a - b)² = a² - ab - ab + b².

(a - b)² = a² - 2ab + b².

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Answer:

\(\huge\boxed{x=\sqrt{66}}\)

Step-by-step explanation:

ΔADC and ΔABD are similar (AAA)

Therefore the cooresponging sides are in proportion:

\(\dfrac{AD}{AC}=\dfrac{AB}{AD}\)

Substitute

\(AD=x;\ AC=6+5=11;\ AB=6\)

\(\dfrac{x}{11}=\dfrac{6}{x}\)          cross multiply

\((x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}\)

Collin's gross salary, after the 7% raise, for each 2-week pay period, will be approximately $1,159.17.

To calculate Collin's gross salary after the 7% raise for each 2-week pay period, we need to find the raise amount and add it to his current gross salary.

Collin's current gross salary is $1,083.34.

To find the raise amount, we multiply his current gross salary by 7% (or 0.07):

Raise amount = $1,083.34 \(\times\) 0.07

= $75.8338 (rounded to two decimal places)

Now, we add the raise amount to his current gross salary to find the new gross salary:

New gross salary = $1,083.34 + $75.8338 = $1,159.1738 (rounded to two decimal places)

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Answer:6.25

Step-by-step explanation:

The solution to find the five number summary shown below.

When conducting descriptive analyses or conducting an initial analysis of a sizable data set, a five-number summary is particularly helpful. The maximum and minimum values in the data set, the lower and upper quartiles, and the median make up a summary's five values.

To find a five number summary we have follow:

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The average change as a simplified mixed number would be,

⇒ 1 3/4

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The running back for the Bulldogs football team carried the ball 7 times for a total loss of 12 1/4 yards.

Now, The average change as a simplified mixed number would be,

⇒ (12 1/4) / 7

⇒ (49/4) / 7

⇒ (49 / 4×7)

⇒ 7/4

⇒ 1 3/4

Therefore, The average change is,

⇒ 1 3/4

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Option (c) In the given Poem "Hope is the thing with a feather" Hope symbolizes a Strong-willed bird

"Hope" is described by the speaker as a winged creature that resides within the human spirit. This feathered monster sings a tune without any words and never stops. Its song is most enjoyable when heard in strong gusts. This bird's chirping could only be silenced by a storm that was quite intense. Many people have experienced warmth from the "Hope" bird. The narrator has heard the song of the bird in the coldest climates and on the most unusual seas. But even in the most extreme instances, according to the speaker, the bird never demanded anything in return.

The well-known poem "Hope is the thing with feathers" by American poet Emily Dickinson was composed sometime about 1861. In the poem, "Hope" is figuratively changed into a tenacious bird that dwells inside the human soul and sings its song despite everything. The poem basically aims to remind readers of the strength of optimism and how little it demands of people. Hope, according to the speaker, has always been a comfort in trying times and has never required anything in return. The poem "Hope is the Thing with Feathers" is one of many by Emily Dickinson that reinterprets an abstract idea using novel imagery and figurative language.

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The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population.

The population parameter is the true value of the statistic for the entire population. The probability that the statistic is obtained is the probability that it will be obtained in a single sample from the population. The variance of the values is the amount of variation among the values of the statistic in the sample. The formula for calculating the variance is the sum of the squared deviations from the mean, divided by the number of values in the sample. This can be written mathematically as: Variance = Σ (x - X)2/ n, where x is each value in the sample, X is the mean value, and n is the number of values in the sample.

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Answer:

4-3x=0

-3x=-4

x=4/3

tip:- it should always be equal to 0

x+-2*2-3x-7

x+4-3x-7

x+1.x-7

x.x-7

2x-7

The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

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The answer is -53.8

Step-by-step explanation:

jSubtract

Answer:

Step-by-step explaination:

The hypotenuse of a right triangle will be $561$.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Lengths of legs of a right triangle are given that are $264$ and $495$.

According to The Pythagorean Theorem,

\(hypotenuse^{2} = lenght^{2} + lenght^{2}\\hypotenuse^{2} = 264^{2} + 495^{2}\\\\hypotenuse^{2} = 69,696 + 245,025\\ hypotenuse^{2} = 314,721\\hypotenuse = 561\)

The hypotenuse of a right triangle will be $561$.

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Answer:

first blank is "Permutation", i dont know what the second blank is but its not 17550

Step-by-step explanation:

This is an example of a permutation. There are 421,200 possible arrangements of first through fourth place winners.

"A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order."

We need to arrange 27 swimmers for 4 positions

Hence, the numbers are 27P4

= \(\frac{27!}{(27-4)!}\)

\(=\frac{27.26.25.24.23!}{23!}\)

\(=421,200\)

Hence, the given situation is an example of permutation with 421,200 possible arrangements.

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Answer:

I think answer is D but it could be wrong not sure

Answer:

Step-by-step explanation:

Given function:

\(y=\sqrt{x-2}\)

The domain is the set of all possible input values (x-values).

As the square root of a negative number cannot be taken, the domain of the given function is restricted.

\(x-2\geq 0 \implies x\geq 2\)

Therefore, the domain of the given function is [2, ∞).

The range is the set of all possible output values (y-values).

As the square root of a negative number cannot be taken, the range of the given function is restricted.  

Therefore, the range of the given function is [0, ∞).

A function f(x) is continuous when, for every value \(c\) in its domain:

\(\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}\)

Therefore, the function is continuous on its domain [2, ∞).

Stationary points occur when the gradient of a graph is zero.

Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.

\(\begin{aligned}y & = \sqrt{x-2}\\& = (x-2)^{\frac{1}{2}\\\implies \dfrac{\text{d}y}{\text{d}x} & = \dfrac{1}{2}(x-2)^{-\frac{1}{2}}\\ & = \dfrac{1}{2\sqrt{x-2}}\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies \dfrac{1}{2\sqrt{x-2}} &= 0\\\dfrac{1}{2} &\neq 0\end{aligned}\)

Therefore, there are no stationary points.

As the domain is restricted and f(x) ≥ 0, the minimum point of the function is at point (2, 0).

\(\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0\)

\(\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0\)

Increasing

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & > 0 \\ \dfrac{1}{\sqrt{x-2}} & > 0\\ \textsf{If $\frac{1}{a} > 0$ then $a > 0$}: \\ \implies \sqrt{x-2} & > 0\\ x-2 & > 0\\ x & > 2\end{aligned}\)

Decreasing

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies \dfrac{1}{2\sqrt{x-2}} & < 0 \\ \dfrac{1}{\sqrt{x-2}} & < 0\\ \textsf{If $\frac{1}{a} < 0$ then $a < 0$}: \\ \implies \sqrt{x-2} & < 0\\ \textsf{As $\sqrt{x}\geq 0$, no solution.}\end{aligned}\)

Therefore:

\(\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}\)

\(\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}\)

As there is no symmetry about the y-axis (even symmetry) and no origin symmetry (odd symmetry), the symmetry of the function is neither.

Answer:

Domain: [2, ∞)

Range: [0, ∞)

Continuity: Function is continuous on its domain [2, ∞).

Minimum point at (2, 0).

Increasing function: (2, ∞)

Symmetry: Neither as there is no symmetry about the y-axis and no origin symmetry.

A ray with an endpoint B is shown in option C.

A ray is a line that has only one endpoint defined, and it extends continuously away from the other (endpoint B in this case).

The ray in the question has one endpoint B, and endpoint A is extending away continuously (as shown by the arrowhead).

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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The graph of the population equation is on the image at the end.

Here we know that the function p(h) models the population of bacteria as the function of h, the number of hours.

And we can write this as the exponential function:

p(h) = 150*(3)^h

The graph of this will be an exponential that starts at 150 and triples for each increase in the horizontal variable, then the graph of this will be like the one you can see at the end of the answer.

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9514 1404 393

Answer:

  te, tm, (m-e), t

Step-by-step explanation:

The problem statement tells you how to interpret the expressions and their parts.

Swap the top two expressions on the right and the list will be in the appropriate order:

Answer:

The answer would be y > 2/-1x - 5. This is in slope-intercept form, y = mx + b. The letter m would be the slope meaning the rise/run. The letter b would be the y-intercept, meaning where the line crosses the y-intercept.  As we can see, the line crosses the y-intercept at -5, so that would replace b. From -5, we would go up positive 2 spaces and left 1 space since that is where the next point is on the line, so it would be the slope. Lastly, since it is a solid line, we would use a partial equal sign. And since the shaded area is above the line, we know to use a greater than or equal to sign. Hope this helped!      

Step-by-step explanation:

The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.