Part a
Two parts:
a) How would decimal 86 be represented in base 8? What about in hex?
b) What is the number 10110.01 in decimal?
The given decimal number = 86
The procedure to convert decimal to base 8 is :-
Divide the given number by 8.
keep track of the remainder and quotient
Again divide the quotient by 8 and get remainder and next quotient.
Repeat step 3 untill the quotie

Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

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Answer:she will need around 9 weeks and she will have enuogh

Step-by-step explanation:

9  

The equation of P in the given equation is P = 100N/W

The equation is given as:

W = 100N/P

Multiply both sides by P

WP = 100N

Divide both sides by W

P = 100N/W

Hence, the equation of P in the given equation is P = 100N/W

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The arc of a circle is 6.285 radians

For given question,

we have been given a radius of a circle r = 5 and a central angle θ = 72°

We need to find  the arc of a circle.

We know the formula for arc length of the circle is,

s = rθ

where  θ is in radians.

First we convert θ = 72° into radians.

72° × π/180 = 1.257 Rad

So,  the arc of a circle would be,

⇒ s = r × θ

⇒ s = 5 × 1.257

⇒ s = 6.285 radians

Therefore, the arc of a circle is 6.285 radians

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Answer:38

Step-by-step explanation:

sense it subteact between

Answer: 38

Step-by-step explanation: subtract between

Answer:

(9,6)

Step-by-step explanation:

So, if we're thinking about a (fair in amount, related to something else/properly sized compared to something else) relationship, or the graph of a (fair in amount, related to something else/properly sized compared to something else) relationship, there should be two things that we're looking for. One, it should be a line. It should be a linear relationship between the two (numbers that change/things that change). Y should be some constant, some (fair in amount, related to something else/properly sized compared to something else)ity constant, times X.

rise/run

2/3 is the proportionality

(6,4) is the last point so if we apply the proportionality the next point should be located at (9,6)

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Using the continuity concept, it is found that the discontinuities of the functions are given as follows:

A function f(x) is continuous at x = a if it is defined at x = a, and:

\(\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)\)

In a graph, a function is discontinuous at open intervals, with examples for this problem given by:

For both functions, the lateral limits are the same, however, since the functions are not defined at these points, they have discontinuities.

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Answer:

Answer down below!

Step-by-step explanation:

Lets start off by finding a point we can start off at!

Since (2,0) lands perfectly on the number line, we can use that one!

From there, use the rise/run method to find your slope

We go up 2 and over -2

Thus our fraction is -2/2 BUT WE AREN'T DONE!

We can simplify this to be -1/1 or -1

Thus, our slope is -1

It's negative one, starting from the y intercept you're going down one right one and so on.

Answer:

Supplementary angles add up to 180°

180=7x-9+4x+3

180=7x+4x-9+3

180=11x-7

180+7=11x

187=11x

11x=187

x=187/11

x=17

Therefore x = 17

1) The polynomial of the given equation (5 + 5n^3) - (1 - 3n^3) is \(8n^{3} + 4\\\).

To find the answer we will first arrange each polynomial with the term with the highest degree first then in decreasing order of degree, then group the like terms and lastly we will simplify by combining like terms.

= (5 + 5n^3) - (1 - 3n^3)

= \(5 + 5n^{3} - 1 + 3n^3\)

= \(5n^3 + 3n^3 +5 -1\\\)

= \(8n^{3} + 4\\\)

So, the answer is \(8n^{3} + 4\\\).

2) The polynomial of the given equation  (6a - 3a^2) + (2a^2 - 3a) is \(-a^2 + 3a\).

To find the answer we will first arrange each polynomial with the term with the highest degree first then in decreasing order of degree, then group the like terms and lastly we will simplify by combining like terms.

=  (6a - 3a^2) + (2a^2 - 3a)

= \(6a - 3a^2 + 2a^2 -3a\\\)

= \(-3a^2 + 2a^2 +6a - 3a\)

= \(-a^2 + 3a\\\)

So, the answer is \(-a^2 + 3a\\\\\).

3) The polynomial of the given equation (x^2 - x) + (8x - 2x^2) is  \(-x^2 +7x\\\).

To find the answer we will first arrange each polynomial with the term with the highest degree first then in decreasing order of degree, then group the like terms and lastly we will simplify by combining like terms.

= (x^2 - x) + (8x - 2x^2)

= \(x^2 - x + 8x - 2x^2\)

= \(x^2 - 2x^2 -x + 8x\\\)

= \(-x^2 +7x\)

So, the answer is \(-x^2 +7x\).

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Answer:

It is True

Step-by-step explanation:

Hope it helps :)

Answer:

True

Step-by-step explanation:

You can only combine like terms when they are EXACTLY the same including the variables and exponents

for ex.

5a+1a+2\(a^{2}\)+5b+7\(b^{4}\)

the simplified answer after combining like terms would be

6a+2\(a^{2}\)+5b+\(7b^{4}\)

the 5b and exponent 4, 7b would not be able to combine because they are not exactly the same

Answer:

125 small boxes

Step-by-step explanation:

\(n = { \tt{ \frac{volume \: of \: big \: box}{volume \: of \: small \: boxes} }} \\ \\ { \tt{n = \frac{(20 \times 10 \times 5)}{(2 \times 2 \times 2)} }} \\ \\ { \tt{n = \frac{5 \times 5 \times 5}{1} }} \\ \\ { \tt{n = 5 {}^{3} }} \\ \\ { \tt{n = 125}}\)

Answer:

The correct answer is 5b²-b-2

To find the unit rate for Start Fraction 182 dollars Over 14 feet End Fraction,

c. divide both 182 and 14 by 182.

A fraction is a mathematical concept that refers to a component of a whole or, more broadly, any number of equal parts.

An element of the whole is a fraction. The number is shown as a quotient in mathematics, where the numerator and denominator are split.Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction.

Step 1: Divide 182 by 182

182 / 182 = 1

Step 2: Divide 14 by 182

14 / 182 = 0.07660818713450292

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Answer:

7 nickels

20 dimes

5 quarters

Step-by-step explanation:

n=nickels. d=dimes. q=quarters

n+d+q=32

0.05n+0.1d+0.25q=3.60

d=8+n+q

Solve for number of dimes:

d-8=8-8+n+q

d-8=n+q

d-d-8=n+q-d

-8=n+q-d

  32=n+q+d

-  (-8=n+q-d)

32 - (-8) = n-n + q-q + d-(-d)

32 + 8 = d + d

40 = 2d

d = 20  => simplify

20=8+n+q  ==> substitute 20 for d (d=8+n+q)

20-8 = 8-8+n+q

n+q = 12

0.05n+0.1(20)+0.25q=3.60  ==> substitute 20 for d

0.05n + 2 + 0.25q = 3.60

(0.05n + 2 + 0.25q = 3.60)*100 ->remove the decimals by multiplying by 100

5n + 200 + 25q = 360

5n + 200 - 200 + 25q = 360 - 200

5n + 25q = 160

Solve for number of quarters:

(5n + 25q)/5 = 160/5  ==> simplify the equation

  n + 5q = 32

- (n + q = 12)

n-n + 5q-q = 32-12

0 + 4q = 20

4q = 20

q = 5  ==> simplify

Solve for number of nickels:

n+20+5=32  ==> plug in 20 for d and 5 for q  (n+d+q=32)

n+25=32

n+25-25=32-25  ==> solve for n

n=7 ==> simplify

n=7: 7 nickels

d = 20: 20 dimes

q = 5: 5 quarters

The values of A and B that would give the best scales if height is plotted on the horizontal axis and mass on the vertical axis is 10:10.

The values of A and B that would give the best scales if mass is plotted on the horizontal axis and height on the vertical axis is 5:20.

In this scenario and exercise, you are required to determine if the values of A and B that would give the best scales if height (in millimeters) is plotted on the horizontal axis while mass (in grams) is plotted on the vertical axis.

Based on the table, we can reasonably infer and logically deduce that the height (in millimeters) ranges from 0 to 60 and the mass ranges from 0 to 30.

When x-axis: height and y-axis: mass

A = 60/6 = 10

B = 30/3 = 10

When x-axis: mass and y-axis: height

A = 30/6 = 5

B = 60/3 = 20

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Answer:

C. Y=2x

Step-by-step explanation:

I hope this help you

The standard error of the proportion decreases as the sample size increases. This means that larger sample sizes provide more accurate estimates of the population proportion.

To calculate the standard error of the proportion, we can use the formula:
SE = √(p(1-p)/n)
Where:
SE = standard error
p = proportion of the population
n = sample size
For each sample size, we can plug in the values and calculate the standard error:
A. For a sample size of 30:
SE = √(0.39(1-0.39)/30) = 0.088
B. For a sample size of 60:
SE = √(0.39(1-0.39)/60) = 0.062
C. For a sample size of 90:
SE = √(0.39(1-0.39)/90) = 0.051

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Answer:

1 and 7

Step-by-step explanation:

Answer:

The variable expression equation of the situation is;

x + 5 + x + 3·x - 7 = $73

The amount of money Jadah collects = $15

The amount of money Martez collects = $20

The amount of money Roana collects = $38

Step-by-step explanation:

The given parameters are;

The total amount of money they collect together = $73

The amount of money Martez collects = 5 + The amount of money Jadah collects

The amount of money Roana collects = 3 × The amount of money Jadah collects - 7

Let x represent the amount of money Jadah collects

Therefore, we have;

The amount of money Martez collects = 5 + x

The amount of money Roana collects = 3 × x - 7

The variable expression equation of the situation is given as follows;

The total amount of money the three collected = x + 5 + x + 3 × x - 7 = $73

∴ 5 × x - 2 = $73

5 × x - 2 = 73

5 × x  = 73 + 2 = 75

x = 75/5 = 15

x = 15

The amount of money Jadah collects = x = $15

The amount of money Martez collects = 5 + x = 5 + 15 = 20

The amount of money Martez collects = $20

The amount of money Roana collects = 3 × x - 7 = 3 × 15 - 7 = 38

The amount of money Roana collects = $38

Answer: Yes. for each input there is exactly

ONE output

Step-by-step explanation:

I did the test and it was true.

Answer:

2 seconds

Step-by-step explanation:

\(y=-5t^2+20\) (Given)

When acorn will hit the the ground, at that moment y = 0

\(\implies 0= -5t^2+20\)

\(\implies 5t^2=20\)

\(\implies t^2=\frac{20}{5}\)

\(\implies t^2=4\)

\(\implies t=\pm\sqrt4\)

\(\implies t=\pm 2\)

Time can not be negative.

\(\implies t\neq-2\)

\(\implies t=2\:seconds\)

Answer:

A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things

Venn diagrams help to visually represent the similarities and differences between two concepts.

Quick sort will be guaranteed to run in O(n log n) time when the pivot element is chosen in a way that partitions the array into approximately equal halves.

Quick sort is a sorting algorithm that uses divide-and-conquer to sort an array or list of elements. The algorithm works by partitioning the array into two subarrays, one containing all elements smaller than a chosen pivot element, and the other containing all elements larger than the pivot.

The pivot element is then placed between the two subarrays and the process is repeated recursively on each subarray until the entire array is sorted.

Quick sort is generally considered to have an average case time complexity of O(n log n), which means that the algorithm will take proportional to n log n time to sort an array of n elements on average. However, in the worst case, the time complexity of quick sort can be O(n^2), which can occur when the pivot is consistently chosen as the smallest or largest element in the array, leading to an unbalanced partitioning of the array.

To guarantee that quick sort will run in O(n log n) time, it is important to choose a good pivot element that is representative of the entire array and leads to a balanced partitioning of the elements. This can be done by using a randomized pivot selection or by choosing a median-of-three pivot selection that takes the median of the first, middle, and last elements of the array as the pivot. Additionally, choosing a good partitioning scheme that minimizes the number of comparisons and swaps required can also improve the time complexity of the algorithm.

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Answer:10.75

Step-by-step explanation:

3/4 as a decimal is 0.75. add that to the 10 gives you 10.75

Answer:

3:6

Step-by-step explanation:

8:24 and 24:72 reduce down to 1:3. 3:6 is 1:2.

The error interval for the combined mass, m, of the car and the person is: \($$2067.65 kg \leq m \leq 2068.75 kg$$\).

The mass of the car is given as 2006 kg rounded to the nearest kilogram, which means its actual mass could be as low as 2005.5 kg or as high as 2006.5 kg.

The mass of the person is given as 62.2 kg rounded to one decimal place, which means their actual mass could be as low as 62.15 kg or as high as 62.25 kg.

To find the error interval for the combined mass of the car and the person, we need to add the upper and lower bounds of each mass:

Lower bound of combined mass: 2005.5 kg + 62.15 kg = 2067.65 kg

Upper bound of combined mass: 2006.5 kg + 62.25 kg = 2068.75 kg

Therefore, the error interval for the combined mass, m, of the car and the person is: \($$2067.65 kg \leq m \leq 2068.75 kg$$\).

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Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.