The binary representation of the number 77 ten is 1001101 two . This can be found by repeatedly dividing 77 by 2 and writing down the remainders in reverse order.
What is binary representation?Binary representation is a system of representing numbers using only two digits, usually 0 and 1. It is used extensively in digital electronics and computer programming.
What is remainder?The remainder is the amount left over after dividing one number by another. It represents the part of the dividend that could not be evenly divided by the divisor.
According to the given information:
To convert the number 77 ten to base two, we need to find the binary representation of this number.
One way to do this is to repeatedly divide the number by 2 and keep track of the remainders. We continue dividing until the quotient is 0. Then, we read the remainders in reverse order to get the binary representation.
Here's how the calculation works:
77 divided by 2 is 38 with a remainder of 1. Write down the remainder (1).38 divided by 2 is 19 with a remainder of 0. Write down the remainder (0).19 divided by 2 is 9 with a remainder of 1. Write down the remainder (1).9 divided by 2 is 4 with a remainder of 1. Write down the remainder (1).4 divided by 2 is 2 with a remainder of 0. Write down the remainder (0).2 divided by 2 is 1 with a remainder of 0. Write down the remainder (0).1 divided by 2 is 0 with a remainder of 1. Write down the remainder (1).Reading the remainders in reverse order gives us 1001101, which is the binary representation of 77 ten. Therefore, 77 ten = 1001101 two .
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Let x=-[tex]\frac{16\pi }{3}[/tex]
Part A: Determine the reference angle of x. (4 points)
Part B: Find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
The reference angle of x can be found to be 13π/3.
The exact values of sin x, tan x, and sec x in simplest form:
sin x = √3/2tan x = √3sec x = -2How to find the reference angle ?Since our angle x = (10π) / -3 is in the third quadrant, we subtract π to get the reference angle:
reference angle = |x - π| = |(10π) / -3 - π| = |-13π/3|
The reference angle is 13π/3.
sin x = sin(reference angle) = sin(13π/3)
sin(π/3) = √3/2
So, sin x = √3/2
tan x = tan(reference angle) = tan(13π/3)
tan(π/3) = √3
So, tan x = √3
sec x = 1 / cos x = 1 / cos(reference angle) = 1 / cos(13π/3)
cos(π/3) = 1/2
So, sec x = 1 / (-1/2) = -2.
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Victoria wants to fill a container with sand as part of an art project. Which measurement should Victoria use to BEST determine how much sand she should buy?
Answer:
volume
Step-by-step explanation:
Victoria should use volume measurement to determine how much sand she should buy.
Selina invests £2000 in a savings account for 3 years.
The account pays compound interest at a rate of 2.5% per annum.
Calculate the total amount of interest Selina will get by the end of the 3 years.
Selina will get £153.78 of interest by the end of 3 years.
Calculate the total amount of interest Selina will get by the end of the 3 years?To calculate the total amount of interest Selina will get by the end of 3 years, we need to use the compound interest formula:
A = P[tex](1 + r/n)^{(nt)}[/tex]
where:
A = the amount of money at the end of the time period
P = the principal amount (the amount initially invested)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period (in years)
In this case, we have:
P = £2000 (the amount initially invested)
r = 2.5% per annum = 0.025 (as a decimal)
n = 1 (the interest is compounded annually)
t = 3 (the time period is 3 years)
So, plugging in the values into the formula, we get:
A = 2000[tex](1 + 0.025/1)^{(1×3)}[/tex]
= 2000[tex](1.025)^{3}[/tex]
= 2000(1.07689)
= £2,153.78 (rounded to the nearest penny)
To find the total amount of interest Selina will get, we need to subtract the principal amount from the final amount:
Total interest = £2,153.78 - £2,000
= £153.78
Therefore, Selina will get £153.78 of interest by the end of 3 years.
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Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left.Write an equation to determine the number of friends (x)left at Jack's party.
Okay so Jack started with 50 chocolates, and ended with 2.
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing [tex]48\div3=16[/tex].
Using algebra, we substitute the value we want to find with [tex]x[/tex]. Here what we want to find is the number of friends that were at Jack's party.
We know that he started with 50 chocolates, then distributed [tex]3\times[/tex] the number of friends present (which is [tex]x[/tex]).
We write that down as [tex]50-3x[/tex]
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)
We know that after this, there were only 2 chocolates left, so it's
[tex]\underline{\bold{50-3x=2}}[/tex]
Then we proceed by moving all the numbers to the right until only [tex]x[/tex] is left:
[tex]-3x=2-50[/tex]
[tex]-3x=-48[/tex]
[tex]x=\dfrac{-48}{-3}[/tex]
[tex]\boxed{\bold{x=16}}[/tex]
Conclusion: The number of people that attended the party was 16.
A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7) and no other critical points. How many real zeros does p(x) have?a) oneb) twoc) threed) foure) five
The polynomial p(x) has option (c) three real zeros because it has a relative maximum at (-2, 4), a relative minimum at (1,1), a relative maximum at (5,7), and a negative leading coefficient.
Since p(x) has a relative maximum at (-2, 4), a relative minimum at (1,1), and a relative maximum at (5,7), it means that the degree of the polynomial must be odd and at least three.
Moreover, we know that p(x) has no other critical points. This means that p(x) does not change sign between these relative extrema, which in turn implies that there are no real zeros between these extrema.
Therefore, the number of real zeros of p(x) is either one or three. To determine the answer, we need to consider the leading coefficient of p(x).
If the leading coefficient is positive, then p(x) must eventually increase on both ends, since the degree is odd. This means that there is exactly one real zero.
If the leading coefficient is negative, then p(x) must eventually decrease on both ends. In this case, since there are three relative extrema, there must be three real zeros.
Thus, we need to find the sign of the leading coefficient of p(x). This can be done by looking at the relative extrema.
Since p(x) has a relative maximum at (-2, 4), we know that the leading coefficient is negative.
Therefore, the correct option is (c) three.
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A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
A polynomial p(x) has a relative maximum at (-2, 4), a relative minimum at (1, 1), and a relative maximum at (5, 7), with no other critical points. This means there are turning points at these coordinates. Since there are two relative maxima and one relative minimum, the polynomial must have at least 3 turning points.
A polynomial with n turning points has a degree of at least n + 1. Therefore, the polynomial p(x) must have a degree of at least 4. Since a polynomial of degree 4 can have up to 4 real zeros, the answer is d) four real zeros.
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financial planner puts $3,500 into a college savings plan that pays 7.5% simple interest annually. If no additional deposits are made into the savings plan, how much interest is accumulated at the end of 5 years? A. $262.50 |B. $1,312.50* C. $ 2,625.00 D. $4,812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
Define about the term simple interest:Simple interest (SI) is calculated as a percentage added to the principle amount deposited or borrowed for a given period of time. SI is typically expressed as years.
As a result, it represents the real expense incurred on the main sum. The accrued interest is not included in this. SI and CI are very dissimilar to one another. CI is the interest rate applied to both the principal amount and the total amount of unpaid interest.Given data:
Principal P = $3,500Simple Interest rate R = 7.5%Time T = 5 yearsSimple interest formula:
SI = PRT / 100
SI = 3500*7.5*5 / 100
SI = 1312.5
Now,
Amount = principal + simple interest
Amount = 3500 + 1312.5
Amount = $4812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
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a) Work out the bearing of A from B.
b) Work out the bearing of B from A.
(Hint: bearings are written with three digits.)
306°
54°
126°
N
B
234⁰
Not drawn accurately
a).The bearing of point A from B is 234°.
b). The bearing of point B from point A is 054°.
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
The bearing of point A from B is the angle measured from the north of B to the straight line distance between A and B which is 234°. While the bearing of point B from point A is the angle measure starting from the north of A to the straight line distance between A and B which is 054°.
Therefore, the bearing of point A from B is 234° while the bearing of point B from point A is 054°.
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Which model is appropriate for the set {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}
We can conclude that a quadratic model is appropriate for the given set of points {(-2,4. 5),(0,8),(1,10. 67),(3,18. 96)}.
To determine which model is appropriate for the given set of points {(-2,4.5),(0,8),(1,10.67),(3,18.96)}, we need to examine the pattern in the data and choose a model that fits the pattern well.
One common approach to fitting a model to data is to use regression analysis. In this case, we can start by plotting the points on a graph and visually examining the pattern.
When we plot the points, we see that they form a curved shape that resembles a quadratic function. To confirm this, we can use regression analysis to fit a quadratic model to the data.
Using a quadratic regression model, we obtain an equation of the form y = ax^2 + bx + c, where a, b, and c are constants to be determined. The regression analysis yields the following coefficients: a = 2.138, b = 1.959, and c = 5.48.
We can now use this quadratic equation to predict y for any given value of x within the range of the data.
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A line passes through the points (−4, 50) and (5, −31). What is the equation of the line in slope-intercept form?
Answer:
y = - 9x + 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )
m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then
y = - 9x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (5, - 31 )
- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )
14 = c
y = - 9x + 14 ← equation of line
x2=441 -1
what wouod it be
Answer:
The answer for x is 11
Step-by-step explanation:
x²=144-1
Square root of both sides
√x²=√144-1
x=12-1
x=11
What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth. –26, –9.81, 1.94 –26 –2 –2, 0.11, 4.39
The polynomial equation with roots -26, -2, and 4.39 is:
x³ + 15.22x² - 239.44x + 1049.44 = 0
The given root of 0.11 is not a root of this equation.
What are polynomial equation?Any equation with a sum of terms that includes constant coefficients multiplied by one or more variables raised to a non-negative integer power constitutes a polynomial equation.
If the roots of a polynomial equation are -26, -2, and 4.39, then the factored form of the polynomial equation can be written as:
(x + 26)(x + 2)(x - 4.39) = 0
Expanding this equation gives us:
(x + 26)(x² - 2x - 8.78x + 8.78×2) = 0
Simplifying further, we get:
(x + 26)(x² - 10.78x + 38.44) = 0
Multiplying out the second factor, we get:
x³ - 10.78x² + 38.44x + 26x² - 277.88x + 1049.44 = 0
Combining like terms, we get:
x³ + 15.22x² - 239.44x + 1049.44 = 0
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find the equation of a line which passes through the point (0,3) and (6,0)
Answer:
y=-0.5x+3
Step-by-step explanation:
The equation of a line is
y=mx+b, with m being the slope, and b being the y-intercept
The slope is -0.5, and the y intercept is 3
so:
y=-0.5x+3
Answer:
y= -1/2x+3
Expiation:
you can find the equation between two points by using the slope formula and the slope intercept form which is y=mx+b.
Select and use the most direct method to solve 2x(x + 1.5) = -1.
The solutions to the equation 2x(x + 1.5) = -1 are x = -1/2 and x = -1.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We can use the distributive property to simplify the left-hand side of the equation:
2x(x + 1.5) = -1
2x^2 + 3x = -1
Now we can move all the terms to one side of the equation:
2x² + 3x + 1 = 0
This is a quadratic equation in standard form, where a = 2, b = 3, and c = 1. We can use the quadratic formula to solve for x:
x = (-b ± √(b² - 4ac)) / 2a
Plugging in the values for a, b, and c, we get:
x = (-3 ± √(3² - 4(2)(1))) / 2(2)
Simplifying this expression, we get:
x = (-3 ± √(1)) / 4
x = (-3 ± 1) / 4
x = -1/2 or x = -1
Therefore,
The solutions to the equation 2x(x + 1.5) = -1 are x = -1/2 and x = -1.
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HELP AGAIN LOL
Subtract.
(8h + 7) - (7h + 6)
The simplified form of the expression (8h + 7) - (7h + 6) is h + 1. We subtract this by using the distributive law.
What is an expression?An expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.) that represents a mathematical quantity or value. Expressions can be simple, consisting of just a single number or variable, or they can be complex, involving multiple numbers, variables, and operations.
What is distributive law?The distributive law, also known as the distributive property or distributive property of multiplication over addition, is a fundamental property of arithmetic and algebra that allows the distribution of a multiplication operation over an addition or subtraction operation.
The distributive law states that for any three numbers a, b, and c:
a × (b + c) = (a × b) + (a × c)
According to the given information:
To subtract (8h + 7) - (7h + 6), we can use the distributive property of multiplication over addition to simplify the expression.
(8h + 7) - (7h + 6)
= 8h + 7 - 7h - 6 (Applying the distributive property)
Now, we can combine like terms by adding or subtracting coefficients of the same variable:
= (8h - 7h) + (7 - 6) (Grouping-like terms)
= h + 1 (Simplifying)
So, the simplified form of the expression (8h + 7) - (7h + 6) is h + 1.
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There are 11 athletes at a track meet. How many different ways can they finish first, second, and third?
HELP IS VERY MUCH APPRECIATED PLS just tell me what box and number belongs where pls
The area of figures are calculated a follows:
1. 78.5 m² 2. 66.5 m² 3. 35 m² 4. 153.86 m² 5. 70 m²
How to Find the Area of the Figures?1. The area of the circle = πr²
= 3.14 * 5²
= 78.5 m²
2. The figure is a trapezoid, therefore:
Area of the trapezoid = 1/2 * (a + b) * h
= 7(5 + 14)/2
= 66.5 m²
3. Area of triangle = 1/2 * base * height = 1/2 * 14 * 5 = 35 m²
4. The area of the circle = πr²
= 3.14 * 7²
= 153.86 m²
5. Area of parallelogram = base * height = 14 * 5 = 70 m²
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standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is [tex]SE = \frac{σ }{\sqrt{n}}[/tex]
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
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Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size
y=400(0.99)x growth or decay
The given function of the growth decay is decreasing.
What in mathematics is an exponential?
The formula for an exponential function, often known as an exponential function, is f (x) = axe, where "x" is a variable and "a" is a constant that serves as the function's basis and must be greater than 0.The transcendental number, abbreviated e, which is roughly equivalent to 2.71828, is the most often used exponential function basis.
We have given that,
Y=400(.99)^x
Exponential growth is a process that increases quantity over time. decreases over time, and is said to be undergoing exponential decay instead.
Therefore, The given function of the growth decay is decreasing.
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Classify each number below as an integer or not.
Whoever answers it first ill give u brainliest
And if you dont figure the question ill report you so please help me
Answer:-91 is an integer
1/2 is not an integer
51 is an integer
-6/2 is not an integer
-99.34 is an integer
Step-by-step explanation: An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Answer:
-91 - yes
1/2 - no
51 - yes
-6/2 - yes
-99.34 - no
The graph shows f(x). The absolute value function g(x) is described in the table.
The graph shows a v-shaped graph, labeled f of x, with a vertex at 0 comma 1, a point at negative 1 comma 2, and a point at 1 comma 2.
x g(x)
−4 0
−2 −2
0 −4
2 −2
4 0
If g(x) = f(x) + k, what is the value of k?
k = −5
k = −4
k = 4
k = 5
The value of k given the absolute value functions is (a) k = -5
Given that
graph = f(x)
table = g(x)
Since the vertex of the function f(x) is at (0,1), we have f(0) = 1.
Also, from the given table, we have g(0) = -4.
Therefore, if g(x) = f(x) + k, we must have g(0) = f(0) + k = 1 + k.
But we also know that g(0) = -4. Thus, we have:
1 + k = -4
Solving for k, we get:
k = -5
Therefore, the value of k is -5.
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How can I find the length of AB
To find line segment AB, you'd have to use the principle of proportions. Thus, Line AB is 10.5.
What is the explanation for the above response?To derive line segment AB,
6/4 = AB/7
To solve for AB, we can cross-multiply and simplify:
6/4 = AB/7
Multiply both sides by 7:
(6/4) * 7 = AB
Simplify:
10.5 = AB
Therefore, AB is equal to 10.5.
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Please help this is due today
Using multiplication we know that after 141 min there will be 400,000 bacteria present.
What is multiplication?One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.
A product is the output of a multiplication operation.
When you take a single number and multiply it by several, you are multiplying.
A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).
We multiplied the number five by four times.
Multiplication is commonly referred to as "times" because of this.
So, in the given situation:
At the initial stage, the number of bacteria is: 50,000
Then, after 47 min: 50,000 * 2 = 100,000
Then, after 47 min which is after 94 min: 100,000 * 2 = 200,000
Then, after 47 min which is after 141 min: 200,000 * 2 = 400,000
Therefore, using multiplication we know that after 141 min there will be 400,000 bacteria present.
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What is the polynomial factor for X4-36
Answer:
(2x+6),(2x-6)
Step-by-step explanation:
This instance is DOTS or the difference of 2 squares so (2x+6),(2x-6). it states [tex]a^{2} - b^{2} = (a+b)(a-b)[/tex]
Britney had a math quiz yesterday. She got 7 questions correct for every 2 that she got incorrect.
If Britney got 10 more questions correct than she got incorrect, how many questions were on the quiz?
Answer:18
Step-by-step explanation:
Use your shapes to create a new shape with an area of 4 square units. Trace your shape.
We can construct a shape of area 4 square meters using the four shapes square, rectangle, triangle and parallelogram.
What are your knowledge of area ?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
The area of a plane figure is the area that its perimeter encloses. The amount of units in a figure determines its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.
Area of a square = side² (a²)
Area of a triangle = 1/2 × base length × height (1/2×b×h)
Area of a rectangle = length × breadth ( l×b )
Area of a parallelogram = base length × height ( b×h)
Consider the square of side 1 m
Area = 1 × 1 = 1 m²
Now consider the triangle of base length , b = 1/2 m and height, h = 2 m
∴ Area = 1/2×1/2×2 = 1/2 m²
Once more , area of the parallelogram of side 1 m and height 2 m is given by
Area = 1×2= 2 m²
For the rectangle of length 1/2 m and breadth 1 m
Area = l × b = 1/2 × 1 = 1/2 m²
∴ Total area = 1 + 1/2 + 2 + 1/2 = 4 square meter.
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Prueba de unidad Stacia necesita3 9bombillas para cada3candelabros que ella hace Completa la tabla usando razones equivalentes. Número de bombillas Número de candelabros 39 3 4 10 Informar d
The simplified ratio is 3 light bulbs for every 1 chandelier.
How to explain the ratioIt should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.
In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:
9 light bulbs ÷ 3 = 3 light bulbs
3 chandeliers ÷ 3 = 1 chandelier
So the simplified ratio is 3 light bulbs for every 1 chandelier.
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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.
Find the perimeter and area of a regular octagon that has a radius of 10m.
AC is the perpendicular bisector of G . Determine the length of the following sides.
A. GH
B. CH
The requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.
Here,
AC is the perpendicular bisector of side GH, But this bisector also bisects the triangle in two equal halves.
So,
GH =2GB
FH = 2 * 8 = 16
CH = CG
CH = 12
Thus, the requried length of measure of GH and CH in triangle GCH is 16 and 12 respectively.
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how would you solve this equation?
Answer:
19,188
Step-by-step explanation:
hope this helps ;)
Help me calculate this integral!
Answer:
Step-by-step explan 456
