Rounding to the nearest degree, the angle between the vector i + √5j and the positive direction of the x-axis is approximately 63 degrees.
The angle between a vector and the positive direction of the x-axis can be found using the inverse tangent function, also known as arctan. The formula for finding the angle θ between a vector (x, y) and the positive x-axis is given by:
θ = arctan(y/x)
In this case, the vector is i + √5j, so x = 1 and y = √5. Plugging these values into the formula, we get:
θ = arctan(√5/1) = arctan(√5)
The arctan function returns the angle in radians, so we'll need to convert it to degrees. To do this, we multiply by 180/π:
θ = arctan(√5) * (180/π) = 63.43 degrees (rounded to two decimal places)
So, Rounding to the nearest degree, the angle between the vector i + √5j and the positive direction of the x-axis is approximately 63 degrees.
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I nee help with this
Answer: MHT = 125; AHM = 55
Step-by-step explanation:
(2x + 11) + (6x - 7) = 180 since they are supplementary angles
8x + 4 = 180 ---- subtract 4 on both sides
8x = 176 ---- divide by 8 on both sides
x = 22
MHT = 6x - 7
6(22) - 7 = 132 - 7 = 125
AHM = 2x + 11
2(22) + 11 = 44 + 11 = 55
The function V(r) = ²³
can be used to find the volume of air inside a basketball given its radius. What does V(r)
represent?
The function V(r) is representing the volume of basketball when the radius is r.
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given that, the function V(r) = 4/3 πr³, can be used to find the volume of air inside a basketball given its radius (r).
We are asked to find that what does V(r) represents,
Here, V(r) is the function's output is r is the input, the only variable in the formula is r, that means the volume totally depends on the radius of the basket ball. & volume is changes with the radius.
Thus, this function represents the volume of the basketball when radius is r.
Hence, the function V(r) is representing the volume of basketball when the radius is r.
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I need help on this and it’s my last one please help
The number line is completed and attached.
What is a number line?A number line is a straight line that extends in both directions and is used to represent numbers. It is often used to visually demonstrate the relationships between numbers, including ordering and magnitude.
The number line is arranged in steps of 1/4 (fraction) or 0.25 (decimal), this represents the smallest tick marks
The medium sized marks represents the 0.5 line while the largest line mark represents the benchmark numbers chosen suitable to suit the numbers.
The negative part of the number line are numbered with the zero mark.
numbers like 1/8 (or 0.125) are converted to decimal and falls half way between each marked line.
2² = 4 and this is a benchmark number.
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Segment AD is an altitude of Triangle ABC.
The figure is not to scale.
Which of the following additional statements would allow us to prove that AB is congruent to AC?
AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.
What is the bisector of the triangle?
The bisector of a triangle is a segment that divides one of its interior angles into two equal parts and continues until it reaches the side opposite that angle. In other words, the bisector of a triangle is a line that divides each interior angle of the triangle into two equal angles.
We have given,
Segment AD is an altitude of ΔABC.
If CD ≅ BD
So, AD is the middle line of the triangle
AD is also an altitude of ΔABC.
So, AD is also an internal bisector of ΔABC
So, AB ≅ AC ............{Thereom of unity of three lines}
Hence, AD is also an internal bisector of ΔABC, this statements prove that AB is congruent to AC.
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A line contains the points P (-1, 4) and Q (-4, -2). Write the equation of the line in the slope-intercept form.
A.y = 2x + 6
B.y = 6x + 2
C.y = 3x - 4
D.y =2x + 2
Answer:
Step-by-step explanation:
Given points are P(-1,4) and Q(-4,-2)
we know that slope m between two points (x1,y1) and (x2,y2) is m=y2-y1/x2-x1
so,slope m between points P and Q is m=-2-4/-4-(-1)
m=-6/-3
m=2
Now,we know that equation of line
with slope m having points (x1,y1) and (x2,y2) is y-y1=m(x-x1)
so equation of line between P and Q is y-4=2(x+1)
y-4=2x+ 2
y=2x+6
Write an equation in point-slope form for the line that passes through the point with the given slope.
(–2,–4); m=3
Answer:
x + y = -6
Step-by-step explanation:
Just put x and y and add the number on the RHS
Its really not that hard
But i hope it helped
Solve Each System By Substitution
y=-2
4x-3y=18
Answer: x=3
Step-by-step explanation:
4x-3y=18
4x-3(-2)=18
4x+6=18
(4x=12)/4
x=3
Some wooden chest in a store. A green chest has a length out 165cm a width of 70cm and a height of 10cm. If another box, a blue box is proportional in size, what is is length if it's width is 18cm
The blue box measures about 641.667 cm in length.
What do length and width mean?The width and length of a figure indicate its breadth and length, respectively. The term "breadth" is also used to describe width. Although breadth and width are synonymous (thus the idiom hair's breadth, denoting a very small width), there are two significant differences between the two.
We are aware that the blue box's width is 18 cm, which is smaller than the green box's width (70cm).
As a result, the value of "k" must be lower than 1. By creating a proportion, we can determine the value of "k":
width of green box / width of blue box = k
70 / 18 = k
k = 70/18
k ≈ 3.8889
So the factor "k" is approximately 3.8889. To find the length of the blue box, we can use this factor to scale the length of the green box:
length of blue box = k * length of green box
length of blue box = 3.8889 * 165cm
length of blue box ≈ 641.667cm
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Dilate a square with vertices $\left(0,\ 0\right)$ , $\left(0,\ 4\right)$ , $\left(4,\ 4\right)$ , and $\left(4,\ 0\right)$ using the scale factor $k=0.5$ . What is the value of the ratio (new to original) of the perimeters? the areas?
just in case anyone was wondering
The value of the ratio (new to original) of the perimeters as required in the task content is; 0.5.
The value of the ratio (new to original) of the perimeters as required in the task content is; 0.25.
What is the constant of proportionality of the perimeter and area of the square?Recall, a dilation of a point, (x, y) using a scale factor of k is; (kx, ky).
Also; for shapes A and B;
Perimeter (A) / Perimeter (B) = k.
Also, Area (A) / Area (B) = k².
On this note, since the dilation factor of the pre-image is 0.5, it follows that the ratio of the perimeters of the new to original is; 0.5.
Also, the ratio of the area of the new to original is; 0.5² = 0.25.
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Which expressions have a constant? Select two answers.
A. 3x²
B. 2x - 4
C. 8x + y
D. 5y
E. 7+4x
Step-by-step explanation:
The constant in an expression is the number without any letters attached to it.
Looks like B and E are the only ones with constant. The other 3 only have numbers attached to numbers
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The barber cuts 61 haircuts in 4 days. Determine the rate for a ratio of the two different quantities.
61 over 65 haircuts per day
4 over 65 haircuts per day
4 over 61 haircuts per day
61 over 4 haircuts per day
Answer:
61 over 4 haircuts per day
What is a ratio?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
A way to solve for the number of haircuts per day is to use this equation:
total number of haircuts ÷ number of days = haircuts per dayYou could also use this fraction:
[tex]\frac{total-number-of-haircuts}{number-of-days}[/tex]Inserting the numbers into the fraction::
[tex]\frac{61}{4}[/tex]Therefore, the rate for a ratio using the two different quantities is 61 over 4 haircuts per day.
the mayor of a small city is trying to determine the number of judges needed to handle the judicial caseload. during each month of the year it is estimated that the number of judicial hours needed is provided in the table below. a). each judge works all 12 months and can handle as many as 120 hours per month caseload. to avoid creating a backlog all cases must be handled by the end of december. formulate an lp whose solution will determine how many judges the city needs to handle the caseload for the year.
Total hours handled by x judges in the year ≤ 12120x where x is the number of judges needed to handle the caseload for the year.
To formulate an LP for this problem, we can define the decision variables and the objective function and constraints.
Decision Variables:
Let x be the number of judges needed by the city to handle the caseload for the year.
Objective Function:
We want to minimize the number of judges needed, so our objective function is:
minimize x
Constraints:
Each judge can handle up to 120 hours of caseload per month, so the total number of hours that can be handled by x judges in a month is 120x. The total number of hours needed to handle the caseload for the year is given in the table. Therefore, we have the following constraints:
For January: 120x ≥ 100
For February: 120x ≥ 120
For March: 120x ≥ 90
For April: 120x ≥ 80
For May: 120x ≥ 110
For June: 120x ≥ 130
For July: 120x ≥ 140
For August: 120x ≥ 110
For September: 120x ≥ 100
For October: 120x ≥ 90
For November: 120x ≥ 80
For December: 120x ≥ 120
These constraints ensure that the total number of hours handled by the judges in each month is at least as much as the number of hours needed to handle the caseload in that month.
We also need to ensure that all cases are handled by the end of December. This can be expressed as follows:
Total hours handled by x judges in the year ≤ 12120x
This constraint ensures that the total number of hours handled by the judges in the year is less than or equal to the maximum possible number of hours that can be handled by x judges in a year.
Therefore, the LP can be formulated as follows:
minimize x
subject to:
120x ≥ 100
120x ≥ 120
120x ≥ 90
120x ≥ 80
120x ≥ 110
120x ≥ 130
120x ≥ 140
120x ≥ 110
120x ≥ 100
120x ≥ 90
120x ≥ 80
120x ≥ 120
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A candy store sells a brand of nuts that costs $2 per pound and a brand of chocolate coated candies that costs $0.95 per pound. Select the equation that solves for x lb of nuts that must be mixed with 32 lb of the chocolate coated candies in order to have a mixture that costs 1.48 per pound.
A. 2x + 0.95(32) = 1.48x
B. 2x + 0.95(32) = 1.48(x + 32)
C. 0.95x + 2(32) = 1.48(x + 32)
D. 0.95x + 2(32) = 1.48x
E. none of these
We know that the store sells nuts for $2 per pound and chocolate for $0.95 per pound. We also know that x represents the total pounds of nuts, and 32 represents the total pounds of chocolate.
In order to write an equation that represents a mixture that costs $1.48 per pound, we first need to find an expression to represent the total pounds in this situation, which would be (x + 32).
Now that we have this, let's just combine everything we know into one equation:
2x + 0.95(32) = 1.48(x + 32)
Therefore, the correct answer choice is option B.
Complete the table below treat each row has a different problem.
Important : the last row is sector area (a)
The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
What is sector?The sector is essentially a section of a circle, and it may be described using the following three criteria:
The area of a disc that is surrounded by two radii and an arc is known as a circular sector.
The circle is divided into the Major Sector and the Minor Sector by a sector.
The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.
Given that,
Central angle = [tex]\frac{\pi}{6}[/tex].
The arc length is given as:
l = α/360 (2πr)
Where, α is the central angle.
Substitute the value of central angle we have:
l = (π/6)/360 2πr
l = 2π²r/ 2160
The sector area is given as:
A = α/360 πr²
A = (π/6)/360 πr²
A = π²r²/ 2160
Similarly, the arc length is given as:
l = π/3
Substituting the value of l in arc length we have:
π/3 = α/360 (2πr)
α = 360(π)/ 6πr
α = 60/r
The sector area is given as:
A = α/360 πr²
A = (60/r) 360 πr²
A = πr/60
Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
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what is 13 over 16 as a decimal rounded to the nearest tenth
13/16 as a decimal rounded to the nearest tenth is 0.8.
A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.
To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).
If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.
Therefore, we leave the tenths place as is, and the final answer is 0.8.
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(-2, 2) and (4, -1) lie on a line, what is the equation of the line?
As (-2, 2) and (4, -1) lie on a line the equation of the line is: y = (-1/2)x + 1
We can use the slope-intercept form of a linear equation,
which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope of the line using the two given points. The slope formula is:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values, we get:
m = (-1 - 2) / (4 - (-2)) = -3/6 = -1/2
Now we have the slope (m = -1/2), and we can use either of the two given points to find the y-intercept (b).
Let's use the first point (-2, 2):
y = mx + b
2 = (-1/2)(-2) + b
2 = 1 + b
b = 1
So the equation of the line is:
y = (-1/2)x + 1
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4 women and 5 men are eligible to be in a committee of three. find the probability that the committee has exactly two woman.
The probability that the committee has exactly two woman is 0.1758.
Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.
Given that, 4 women and 5 men are eligible to serve on a committee.
A committee of 3 is randomly selected.
Choosing 2 women out of 3 women is
³[tex]C_{2}[/tex]
= 3
Choosing 1 men out of 5 men is
5C1
= 5
Total number of eligible person is = (4+5)=9
Choosing 3 member out of 9 member is
9C3
=84
The required probability is
=3*5/84
0.1785
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Two adjacent angles form an obtuse angle. The measure of the larger angle is six less than twice the measure of the smaller angle. Which is a possible measure for the smaller angle?
Answer:
None
Step-by-step explanation:
The reason is because none of them add up to at least 91°
62° would be your best bet but, even when you do the math 62*2= 124
124/6= 20 2/3°
62+20.66...= 82.666...
82.6666...<91°
help plssssssssssssssssssss
Answer: look at the image for the answer and solution
Step-by-step explanation:
SOLVING EQUATIONS Solve the equation. Check your solution.
50. y+4-1 = 18
52. v-7= 9+12
St 53.5+44=2+r
51. m+ 18+ 23 = 71
54. 22 +15=d-17
The solution of the equation are as follows:
y = 15
v = 28
r = 95.5
m = 30
d = 54
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The equation can be solved by finding the value of the variables.
A variable is a number represented with letter in an equation.
Therefore, let's solve the equation.
y + 4 - 1 = 18
y = 18 - 4 + 1
y = 15
v - 7 = 9 + 12
v = 12 + 9 + 7
v = 28
53.5 + 44 = 2 + r
r = 53.5 + 44 - 2
r = 95.5
m + 18 + 23 = 71
m = 71 - 18 - 23
m = 30
22 + 15 = d - 17
d = 22 + 15 + 17
d = 54
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Determine whether segments with lengths of 29, 19, and 29 form a triangle. If so, classify the triangle as acute, right, or obtuse.
Answer:
if the angle has the arrow on top pointing straight up thats a right angle if it is leaning towards the left instead it is obtuse and if is getting closer to the right side it is acute.
Step-by-step explanation:
i can't tell you anything else if there is no picture to base this question.
Graph the points, connect them in orden, find the perimeter of the polygon (-1,-1),(-1,1),(1,1),(3,-3)
Answer: the perimeter of the polygon is 29cm
Step-by-step explanation:
the mean of this distribution is 0.009 and the sd is 0.004. would you expect about 95% of the samples to have their variances within 0.008 of 0.009? why or why not?
No, we would not expect about 95% of the samples to have their variances within 0.008 of 0.009.
The variance of a normal distribution with mean μ and variance σ^2 is given by σ^2, which in this case is equal to (0.004)^2 = 0.000016.
The variance of the sample means, on the other hand, is given by σ^2/n, where n is the sample size. In order for about 95% of the samples to have variances within 0.008 of 0.009, we would need the sample size to be approximately equal to:
n ≈ σ^2 / (0.008 - 0.009)^2 = 62500
This means that we would need very large samples for this to be true. However, if the sample size is relatively small, then the distribution of sample means will not necessarily be normal and the Central Limit Theorem may not apply.
In that case, the distribution of sample variances will not necessarily follow the same pattern as the distribution of the population variance, and it may not be possible to make predictions about the sample variances based on the population parameters.
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Find the exact value of sin V in simplest radical form.
√74
7
The exact value of sin V in simplest radical form is 0.813.
What is law of sines?
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]
Remember that we took
[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]
Given;
Sin ratio √74:7
Now,
AB/sinA=BC/sinB
√74/sinA = 7/sinB
√74/sin90 = 7/sinB
sinB=7/√74
sinB=0.813
Therefore, the answer of sin V will be 0.813.
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What is the length of the other diagonal, df? 5 cm 16 cm 21 cm 32 cm
Referring to the given kite, the length of the other diagonal. DF, is 21 cm.
A kite is a quadrilateral shape, meaning it has four sides. The two pairs of adjacent sides are of equal length, while the opposite sides are not.
The shape of a kite is typically described as having two pairs of congruent adjacent sides that are connected by two diagonal lines that intersect at a right angle. The diagonal lines of a kite are perpendicular to each other, and the shorter diagonal bisects the longer diagonal.
Let's denote the point of intersection of the two diagonals as O.
Since the two diagonal intersect at a right angle, diagonal DF is perpendicular to diagonal EG.
DG = 13 cm
FG = 20 cm
OG = 1/2 EG = 1/2 x 24 = 12 cm
Using the Pythagorean Theorem:
OD = √(DG² - OG²)
= √(13² - 12²) = 5 cm
OF = √(FG² - OG²)
= √(20² - 12²) = 16 cm
DF = OD + OF
= 5 + 16 = 21 cm
The picture in your question is missing, most likely it was like on the attached picture.
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Answer: c
Step-by-step explanation: I got it right
Zoe ran a lemonade stand 5 times last summer. The numbers of lemons needed depended on
the number of customers each time
The standard deviation of the number of lemons used is equal to 14.7.
How to calculate the mean?Mathematically, the mean for these set of data would be calculated by using this formula:
Mean = [F(x)]/n
F(x) = 47 + 45 + 61 + 44 + 16
F(x) = 213.
Mean = 213/5
Mean = 42.6
Next, we would calculate the standard deviation of this data set by using this formula:
SD = √(1/n × ∑(xi - u₁)²)
SD = √(1/5 × (47 - 42.6)² + (45 - 42.6)² + (61 - 42.6)² + (44 - 42.6)² + (16 - 42.6)²)
Standard deviation, SD = √(1073.2/5)
Standard deviation, SD = 14.7.
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Write the expression as a square monomial
0.16x^2y^2
Answer: (____)^2
Answer:
0.0256x^4y^4
Step-by-step explanation:
In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet
with a diameter of 8500 kilometers, what should be the diameter of the drawing of
the planet?
In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.
What is millimeters?A millimeter, abbreviated mm, is the smallest unit for length in the metric, or Standard International, system of measurement. It is used to measure small lengths and for precise measurements. Millimeters can be converted to either units within the metric system or the customary system of measurement.
Divide 8500 kilometers by which 500 km equals 17.5 millimeters.
Therefore, In a scale drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of 8500 kilometers, 17.5 millimeters is the correct answer.
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What percent of Jemma's answers did she get incorrect?
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, then the incorrect percent is 10% .
Total number of questions in the Math's quiz is = 20 ;
Number of incorrect questions done by Jemma is = 2 ;
Number of correct questions done by Jemma are = 18 ;
So , to find the percentage she got incorrect, we divide ; (number of incorrect answers) by (total number of questions) and then multiply by 100 ;
that means ⇒ (2/20) × 100 = 10% ;
Therefore, Jemma got 10% of the questions incorrect on her most recent math quiz.
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The given question is incomplete , the complete question is
If Jemma got 2 out of 20 questions wrong on her most recent math quiz, what percent did she get incorrect ?
Say you have a 92% in a class and you do 2 assignments and they are both worth 50% of your grade. And you get a 2/5 on one of them and a 5/5 on the other. Whats the resulting grade?
Answer:
70%
Step-by-step explanation:
