When we construct the confidence interval their sample must have some conditions which are as follows,
The data should be a random sample from the population of interest.np^ ≥ 10 n(1 - p^) ≥ 10Individual observations can be taken as independent.Therefore , these are the conditions which the administrator should use to construct a one-sample z interval for a proportion.
When two ratios are equivalent to each other , they are said to be in a state called proportion. The proportion formula is used to see whether the given ratios or fractions are equal or not . The proportion formula can be given as, The product of means is equal to the the product of extremes. This can be written as ad = bc.
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What would the answer be?
Answer:
[tex]w^{2}[/tex]
Step-by-step explanation:
Is the triangle with sides of length 5 cm 3 cm and 4 cm a right angled triangle If yes why?
The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.
We know that if non zero real numbers a, b, c follows Pythagoras theorem c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.
And these numbers are nothing but the sides of right triangle.
Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm
Assume that p = 5 cm, q = 3 cm and r = 4 cm
p² = 25
q² = 9
and r² = 16
Consider q² + r² = 16 + 9
q² + r² = 25
q² + r² = r²
Since given numbers follows Pythagoras theorem, (3, 4, 5) is a Pythagorean triple.
And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.
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Let X_0, Y and Z be integers greater than 0. Let A_n be the product of the unique prime factors of X_n. What condition is needed to be met for the equation X_(n+1) = YA_n + Z to have X_p = X_q, where p =/= q?
On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
the prime factors of
32 are 2 × 2 x 2 x 2 x 2
64 are - 2 x 2 × 2 x 2 x 2 x 2
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Carlos saves aluminum cans to sell to the recycling center. He recently recycled 43 pounds of cans and received $23. 65. How many dollars would he get at this rate for recycling 200 pounds of cans?
The rate of recycling 200 pounds of cans based on the mentioned information is $110.
Firstly calculating the cost of cans per pounds. Then we will proceed to actual calculation about rate of recycling 200 pounds.
Cost of recycling one pound of can = total cost ÷ number of recycled cans
Keep the values in formula
Cost of recycling one pound of can = 23.65/43
Performing division
Cost of recycling one pound of can = 0.55
Cost of recycling 200 pounds of cans = 0.55 × 200
Performing multiplication
Cost of recycling 200 pounds of cans = 110
Therefore, the required rate is $110.
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WHAT?
Never in my life have I ever wanted to kill math
Answer:
Y-intercept: 15
Slope: 1.3
Equation: y = 1.3x + 15
Step-by-step explanation:
Base on the table:
# of haircuts = x
Cost ($) = y
Knowing that;
y-intercept = The starting point (y)
Thus, based on the table the y-intercept is 15.
Y-intercept: 15.
To find the slope.
We first have to pick two points on the line & determine their coordinates.
Then subtract y-coordinates of these two points and also subtract x-coordinates for these two points.
After that divide the y by the x.
Shown below:
I'm going to use;
(0,15) and (1,20.5)
0 = x₁
15 = x₂
1 = y₁
20.5 = y₂
Now we do;
20.5 - 1 = 19.5
15 - 0 = 15
19.5 / 15 = 1.3
Hence, Slope = 1.3
Slope: 1.3
The equation - y = mx + b
Knowing that;
b = y-intercept
m = Slope
Substitute it in we have;
y = 1.3x + 15
Equation: y = 1.3x + 15
RevyBreeze
Find the nth term of the following sentence
-5,-2,3,10,19
On solving the provided question, we can say that An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
what is arithmetic sequence?Arithmetic sequences are groups of integers that are arranged in a certain order and share a common difference between each term. The tolerance, for instance, is six in the mathematical progression 3, 9, 15, 21, and 27. Arithmetic progression can also be referred to as such. a series that is produced by adding the same value repeatedly. for instance, 1, 4, 7, 10, 13, 16, 19, 22, and 25. Sequences that have an arithmetic difference between two successive phrases are known as arithmetic sequences. A progression in math with a tolerance of 2 is 2,4,6,8,10.
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. 2,4,6,8,10….is an arithmetic sequence with the common difference 2.
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Thirty one divided by seven
Answer:
4.42857142857
Rounded:
4.4
Please can someone help me with this circle theorem question and explain which rule would apply as I can’t seem to find which one I should be using please? :)
Answer:
∠LOP = 96°
Step-by-step explanation:
Given an inscribed angle of 48°, you want to know the measure of the central angle that subtends the same arc.
Inscribed angleThe measure of an inscribed angle is half the measure of the arc it subtends.
∠LMP = 1/2(arc LP)
48° = 1/2(arc LP) . . . . . . use the given value
96° = arc LP . . . . . . . . . multiply by 2
Central angleThe measure of an arc of a circle is the same as the measure of the central angle it subtends: the arc measure and its central angle measure are identical.
arc LP = ∠LOP
96° = ∠LOP
__
Additional comment
That's a long way of saying the central angle is twice the inscribed angle that subtends the same arc. ∠LOP = 2×∠LMP.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Step-by-step explanation:
4/56\8
Mrs. Johnson lets her students choose between two word problems:
Problem A: If you are digging for dinosaurs and need to fence off your dig site, what's the biggest site you can fence off with 40 ft. of fence?
Problem B: What is the largest area you can create with 20 inches of rope?
Mrs. Johnson finds a significant majority of her students chose to work Problem A. Which of the following is the most likely reason more students chose Problem A instead of Problem B?
The reason to choose problem B over A is simple - it is more relatable to them.
Problem A involves dinosaurs, which may be more interesting to students than the abstract concept of creating an area with rope. Additionally, the use of feet as a unit of measurement in Problem A may be more familiar to students than inches.
Finding a number that represents the quantity of anything is called measurement. An accepted quantity that is used to represent a physical quantity is called a measurement unit. Let's learn about some of the standard units used to measure physical quantities.
The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.
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what is the area of the shaded part, in square meters, below?
Check the picture below.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]
`y=7/(1,000)-(9x)/8` whats the y incercept
On a certain hot summer's day, 311 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $525 How many children and how many adults swam at the public pool that day?
The number of children that swam in the public pool that day is 194
and the number of adult that swam in the public pool that day is 117
Let x represent the number of children that swam in the public pool that day.
Let y represent the number of adult that swam in the public pool that day.
On a certain hot summer day, 311 people used the public swimming pool. This means that
x + y = 311
The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled to $525. This means that
$1.50x + $2.00y = $525 - - - - - - - -1
Substituting x = 311 - y into equation 1, it becomes
1.50(311 - y) + 2.00y = 525
466.5 - 1.50y + 2.00y = 525
0.5 y = 58.5
y = 117
Substituting y = 117 into x = 311 - y, it becomes
x = 311 - 117
x = 194
Hence , the number of children that swam in the public pool that day is 194 and the number of adult that swam in the public pool that day is 117.
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what is the legend of variables of combined gas law
The combined gas law for a gas is discussed below.
What is a gas?Gas is one of the four fundamental states of matter – the others being solid, liquid, and plasma. A pure gas may be made up of individual atoms, elemental molecules made from one type of atom, or compound molecules made from a variety of atoms.Given is the combined gas law.
The ideal combined gas law is given by →
PV = nRT
Where -
{P} = pressure {T} = temperature {V} = volume
{n} = number of moles {R} = gas constant
Non ideal gases are often modelled by the Van der Waals equation as →
(p + n²a/V²)(V - nb) = nRT
Where -
{a} and {b} = constants for a particular gas
{p} = pressure {v} = volume
{n} = number of moles {t} = temperature
{R} = gas constant
Therefore, the combined gas law for a gas is discussed above.
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PLEASE HELP f(x)=x^2-12x+35 g(x)=x−5, find(f⋅g)(x)
Step-by-step explanation:
this is a multiplication dot, right ?
so,
(f.g)(x)
or
(f×g)(x)
any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.
(f×g)(x) = (x² - 12x + 35)(x - 5) =
= x³ - 5x² - 12x² + 60x + 35x -175 =
= x³ - 17x² + 95x - 175
Step-by-step explanation:
(f.g)(x) = f(x) . g(x)
= (x² - 12x + 35)(x - 5)
=x(x²-12x+35) - 5(x²-12x+35)
= x³-12x²+35x-5x²+60x-175
(f.g)(x)=x³-17x²+95x-175
How do I do this function stuff I’m been kinda confused
Explanation:
When solving a function, you plug in the given [tex]x[/tex]-value (what's inside the parentheses next to the [tex]g[/tex] or [tex]f[/tex]) into the corresponding equation (what [tex]f(x)[/tex] and [tex]g(x)[/tex] are set equal to).
Before starting the worksheet, take a simpler example:
Given the function [tex]h(x) = x + 2[/tex],
the following work solves for [tex]h(3)[/tex].
[tex]h(3) = 3 + 2[/tex]
[tex]h(3) = 5[/tex]
Essentially, to solve for the value of a function for a given [tex]x[/tex]-value, simply plug in that value in for [tex]x[/tex] and simplify the resulting expression.
Onto problem 14 from the given worksheet:
We are given [tex]f(x) = 3x + 2[/tex] and are asked to solve for [tex]f(4)[/tex].
Hence, all we have to do is plug [tex]4[/tex] in for [tex]x[/tex]:
[tex]f(4) = 3(4) + 2[/tex]
[tex]f(4) = 12 + 2[/tex]
[tex]f(4) = 14[/tex]
You can apply this concept to the rest of the problems.
Owen is designing a rectangular garden whose length is 25 feet he needs to put fencing all around the exterior of the garden and wants to use less than 8 feet of fencing
Answer:
To enclose the rectangular garden, Owen will need to put fencing along the length of the garden, which is 25 feet, and along the width of the garden. He wants to use less than 8 feet of fencing, so the width of the garden must be less than 8 feet.
The total amount of fencing needed will be equal to the length of the garden plus the width of the garden, multiplied by 2 (since there are two sides to the garden for each of the length and width).
For example, if the width of the garden is 5 feet, the total amount of fencing needed will be 25 + 5 + 25 + 5 = 60 feet, which is less than 8 feet.
So, the width of the garden can be any value less than 8 feet.
Step-by-step explanation:
Type the correct answer in each box. The coordinates of the point that corresponds to an angle of radians in the unit circle are (, ).
On solving the provided question, we can say that coordinates of the point in the unit circle S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )
What is circle?Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.
S = (0, -1 )
coordinates of the point in the unit circle
S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )
S= ( 0 , -1 )
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How do you find the longest side of an acute triangle?
The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.
Triangle
A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Angle
A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
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By choosing an appropriate line, use the
diagram to estimate the solutions to these
simultaneous equations:
2
y = -x +1.5
y = 1.5x2.5
So on solving the provided question, here we can say that by is a simultaneous equations the value of x = - 3/5 and y = 9/10
What is the simultaneous equation formula?Multiple algebraic equations that have the same unknowna as the give in the variables and the same answer are referred to as simultaneous equations. This suggests that there is a single solution to the simultaneous equations. Examples of simultaneous equations include: 2x - 4y = 4, 5x + 8y = 3, and others. This implies that the simultaneous equations have a single solution. The simultaneous equations 2x - 4y = 4, 5x + 8y = 3, and others are examples.
y = -x + 1.5
y = 1.5x + 2.5
x = -3/5
y = 9/10
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What value is X in math?
Answer:
Any value
Step-by-step explanation:
X is a variable, meaning it can be any number, and they are just using our variable, x, as a little mask to hide the exact value. In math, we will usually need to find x by solving different equations.
Examples:
x + 4 = 7
Know, x in this case is 3 because we just know 3 + 4 = 7, but x can be any value, and sometimes it gets more complicated than this. For example, we can have something like:
2x + 8 = 16
In this case, we need to have multiple steps to solve for x. First, we minus 8 from both sides:
2x = 8
Then we divide by 2:
x = 4
So, we know x = 4. In conclusion, x is a variable that is hiding a value, and you will need to either solve or substitute x. Meaning x can be any value.
Hope this Helped!
Find the midpoint of the line segment with end coordinates of:
(
−
4
,
−
2
)
and
(
−
2
,
−
10
)
Answer:
this is the answer (-3,-6)
Jackson is trying to find the density, in g/cm", of a block of wood.
The block of wood is in the shape of a cuboid.
He measures
the length as 13. 2 cm, correct to the nearest mm
the width as 16. 0 cm, correct to the nearest mm
the height as 21. 7 cm, correct to the nearest mm
He measures the mass as 1970 g, correct to the nearest 5 g.
By considering bounds, work out the density of the wood.
Give your answer to a suitable degree of accuracy.
You must show all your working and give a reason for your final answer.
The density of the wood is between 0.35 g/cm^3
The density of a substance can be calculated using the formula:
density = mass / volume
To calculate the volume of the cuboid, we can use the formula:
volume = length x width x height
So, using the measurements provided:
volume = 13.2 cm x 16.0 cm x 21.7 cm = 5541.44 cm^3
To calculate the density of the wood, we divide the mass by the volume:
density = 1970 g / 5541.44 cm^3
We can convert cm^3 to g/cm^3 by converting the volume to g
1cm^3 = 1g/cm^3
density = 1970 g / 5541.44 g/cm^3
density = 0.3555 g/cm^3
However, as the measurements provided have a degree of uncertainty, we should consider bounds to find the range of possible densities.
The lower bound for the length is 13.2 cm - 0.1 cm = 13.1 cm
The upper bound for the length is 13.2 cm + 0.1 cm = 13.3 cm
The lower bound for the width is 16.0 cm - 0.1 cm = 15.9 cm
The upper bound for the width is 16.0 cm + 0.1 cm = 16.1 cm
The lower bound for the height is 21.7 cm - 0.1 cm = 21.6 cm
The upper bound for the height is 21.7 cm + 0.1 cm = 21.8 cm
The lower bound for the mass is 1970 g - 5 g = 1965 g
The upper bound for the mass is 1970 g + 5 g = 1975 g
We can now use these bounds to calculate the range of possible densities:
Density lower bound = 1965 g / (13.3 cm x 16.1 cm x 21.8 cm) = 0.350 g/cm^3
Density upper bound = 1975 g / (13.1 cm x 15.9 cm x 21.6 cm) = 0.360 g/cm^3
So the density of the wood is between 0.35 and 0.36 g/cm^3 to one decimal place.
So the density is 0.35 g/cm^3 with an uncertainty of 0.01 g/cm^3
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Which quantity is proportional to 12/4?
Check all that are true.
48/18
36/12
35/15
2416
3/1
The quantities which are proportional to 12/4 are 36/12 and 3/1 .
What is proportional ?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
12/4 ⇒ 3/1
48/18= 24/9
= 8/3
The quantity 12/4 is not proportional to 48/18
36/12= 18/6
= 3/1
The quantity 12/4 is proportional to 36/12
35/15= 7/3
The quantity 12/4 is not proportional to 35/15
24/16= 12/8
= 6/4
= 3/2
The quantity 12/4 is not proportional to 24/16
3/1The quantity 12/4 is proportional to 3/1
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I need help with these 4 problems
As a result, using the values provided, we can turn these data into a bar graph.
What is a graph?A graph is a type of non-linear data structure that consists of nodes, also called vertices, and edges. Any two edges can connect the nodes, which are also known as vertices in a graph. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 5, and 4, 50.
Here,
The gene contributes to the development of pigment.
Yes, factors such as temperature, light cycle, and the presence of mutagens can affect the color of the fur.
In the evolution chart, Mcl provided has ullets that it runs. In mature solutions, the dominating truit moderate is thus always present.
Therefore, using the supplied numbers, we may convert these data into a bar graph.
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Hey guys so I NEEEEEED HELP ON THIS MATH QUESTION, so here it is please help me P.S: LIMITED TIME, P.P.S: LIKE IN 40-74 MINUTES!!! HELP
The approximate diameters of Uranus and Mars are listed below:
Uranus: 5.11×10^4
kilometers
Mars: 6.79×10^3
kilometers
How many times larger is the diameter of Uranus? Write your answer in standard notation, rounding to the nearest tenth.
The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times
How to determine the number of times larger is the diameter of UranusFrom the question, we have the following parameters that can be used in our computation:
The diameters of Uranus and Mars
These diameters are given as
Diameter of Uranus: 5.11×10^4 kilometers
Diameter of Mars: 6.79×10^3 kilometers
Express the diameters properly
So, we have the following representation
Diameter of Uranus: 5.11 × 10⁴ kilometers
Diameter of Mars: 6.79 × 10³ kilometers
This means that
Number of times larger = Diameter of Uranus/Diameter of Mars
Substitute the known values in the above equation, so, we have the following representation
Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers
Evaluate the quotient
So, we have the following representation
Number of times larger = 7.5
Hence, the number of times is 7.5
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Write a polynomial in intercept form so that P(x)=0 has the given roots.
7. 2, √√3
8. -i, -5
9. i, √7
11. --√6, √3
10. 2i, -i
12. 4DR, VII
The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
What is polynomial?
A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.
We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.
Let 2 and √3 are the roots of the polynomial so,
x = 2, x = √3
⇒ x - 2 = 0, x - √3 = 0
⇒ (x - 2)(x - √3) = 0
x^2 - √3x - 2x + 2√3 = 0
Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.
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Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish
On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Month / Brent / Gretel
0/4/ 128
1/ 16 / 256
2 / 64 / 512
3 / 256 / 1024
4 / 1024 / 2048
5 / 4096 / 4096
They will have the same amount of fish in 5 months.
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Multiply using the distributive property
D) Simplify the expression:
8(1 + 7d) =
Answer:
8 + 56d
Step-by-step explanation:
We will open the parentheses, multiplying the stuff outside by the stuff inside. So, we get:
8*1 + 8*7d
Then, we can simplify by giving us:
8 + 56d
Hope this helped!