The vector <5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.
How to determine the unit vector in the direction of a given vector
Vectors are described by two features: (i) magnitude, (ii) direction. The magnitude is the quantity associated with a vector and determine by Pythagorean theorem, and the direction indicates the "distribution" of the magnitude along the ortogonal axes of the vector. Unit vectors are vectors of magnitude 1 and we can determine it by using the following definition:
[tex]\vec u[/tex] = <x, y> / ||<x, y>||
Where ||<x, y>|| = √(x² + y²)
Please notice that [tex]\vec u[/tex] represents the unit vector.
If we know that <x, y> = <5, - 7>, then the unit vector is:
Magnitude
||<x, y>|| = √[5² + (- 7)²]
||<x, y>|| = √74
Unit vector
[tex]\vec u[/tex] = <5, - 7> / √74
[tex]\vec u[/tex] = <5 / √74, - 7 / √74>
[tex]\vec u[/tex] = <5√74 / 74, - 7√74 / 74>
<5√74 / 74, - 7√74 / 74> is the unit vector in the direction of <5, - 7>.
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70% of the class has a pet.
There are 30 kids in the class.
How many kids have a pet?
Answer: 21
Step-by-step explanation:
70x30/100
= 21
Hope this helps! :)
Yesterday was the first playoff game for the Culver City Cyclones baseball team. The
stadium's manager predicted attendance at the game would be 5,600 fans. Unfortunately, the
threat of a storm caused many to stay home, and his prediction wound up being 28% higher
than the actual attendance. What was the actual attendance at the baseball game?
The actual attendance at the baseball game is 7168 fans
What is meant by percentage?A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. The abbreviations "pct," "pct," and occasionally "pc" are also used to represent percentage in addition to the symbol "%". A% has neither a recognized unit of measurement nor any dimensions. Take this as an example: There will be 50 men in the class if there are 100 students total and there are 50 men in the class. There are 250 male students overall, or 250 out of 500.
Given,
The actual attendance at the game=5600 fans
Also given that, the threat of a storm caused many to stay home, and his prediction wound up being 28% higher than the actual attendance.
Then,
28% of 5600
=5600×(28/100)
=1568
Total=5600+1568
Total=7168
Therefore, the actual attendance at the baseball game is 7168 fans.
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Answer:
4,375 fans
Step-by-step explanation:
percent error= amount of error/correct amount
1.28x=5600
1.28x/1.28= 5000/1.28
x=4375
SOME HELP FAST!! What is the slope of this line?
Answer:
-2/3
Step-by-step explanation:
x varies inversely as the square of y. If x= 6 when y = 2, then the value of x when y = 8 will be
Answer: 24
Step-by-step explanation:
You can use proportions to calculate this:
[tex]\frac{6}{2} =\frac{x}{8} \\\\2x=6*8\\\\2x=48\\\\x=\frac{48}{2} =24[/tex]
Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
C
Step-by-step explanation:
Prime numbers are only divisible by themselves and 1 ....all even numbers are divisible by '2' , so all primes are odd numbers
Select the correct answer.
Which graph is the graph of f(x) = x³ - 10x² + 16x?
OA.
B.
-5
4
-3 -2
-3
-2
-3
-4
-5
2
-3
5
The graph of the cubic equation, f(x) = x³ - 10x² + 16x, is shown below
Graph of Cubic equationFrom the question, we are to determine graph of the given cubic equation.
The given cubic function is
f(x) = x³ - 10x² + 16x
To graph the equation, we will determine the value of f(x) for certain values of x
When x = 0
f(x) = x³ - 10x² + 16x
f(x) = (0)³ - 10(0)² + 16(0)
f(x) = 0
When x = 2
f(x) = x³ - 10x² + 16x
f(x) = (2)³ - 10(2)² + 16(2)
f(x) = 0
When x = 5
f(x) = x³ - 10x² + 16x
f(x) = (5)³ - 10(5)² + 16(5)
f(x) = -45
When x = 8
f(x) = x³ - 10x² + 16x
f(x) = (8)³ - 10(8)² + 16(8)
f(x) = 0
When x = 10
f(x) = x³ - 10x² + 16x
f(x) = (10)³ - 10(10)² + 16(10)
f(x) = 160
Using the determined points above, the graph of the cubic equation is shown below
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APProximate the following numbers to The nereast thousand.
1• 6203
Answer:
the answer should be 6000
HELP!!!!!PLEASE!! ASAPPP
By calculating the percentage of earnings, we find out that Gary earns more money in one week as compared to Tara. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.
It is given to us that -
Gary and Tara work as tutors at two different test prep companies
In a week, Gary earns 45% of the $2000 collected from the pupils
In the same week, Tara earns 20% of the $3,525 collected from the pupils
We have to find out who earns more money in a week.
We know that, in a week, Gary earns 45% of the $2000 collected from the pupils. This implies earning of Gary in a week
= 45% of 2000
= $900
Similarly, we know that, in the same week, Tara earns 20% of the $3,525 collected from the pupils. This implies earning of Tara in the same week
= 20% of 3,525
= $705
Thus, by calculating the percentage of earnings, we can see that Gary earns more money in one week. Gary earns $900 and Tara earns $705 in one week. Therefore, the last option is correct.
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pls check and see if i'm wrong
Answer:
I think you are right.Because im sure
Given: (GH) is a midsegment of ∆DEF. Show all work.
a. Find the value of x and y.
b. What is the length of DF?
Applying the triangle midsegment theorem:
a. x = 17; y = 2
b. Length of DF = 20 units.
What is the Triangle Midsegment Theorem?The triangle midsegment theorem states that the midsegment of a triangle is always parallel to the third side, and has a length that is half the length of the third side of the triangle.
GH is said to be the midsegment of triangle DEF, therefore:
a. GH = 1/2(EF) [triangle midsegment theorem]
Substitute
x - 3 = 1/2(28)
2(x - 3) = 28
2x - 6 = 28
2x = 28 + 6
2x = 34
2x/2 = 34/2
x = 17
HF = x - 7
Plug in the value of x
HF = 17 - 7
HF = 10
HF = DH = 10
y + 8 = DH
y + 8 = 10
y = 10 - 8
y = 2
b. Length of DF = HF + DH
Length of DF = 10 + 10 = 20 units.
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Does the equation y+x=45 2y+2x=6 have No solutions or infinite solutions
The equation, y + x = 45 and 2y + 2x = 6 has No Solution .
In the question ,
it is given that ,
the equations are y + x = 45 and 2y + 2x = 6 .
y = 45 - x
Substituting the value of y = 45 - x in the equation 2y + 2x = 6
we get ,
2(45 - x) + 2x = 6 ...by using associative property
Simplifying further ,
we get
90 - 2x + 2x = 6
90 = 6 .....because -2x+2x = 0
we know that 90 ≠ 6 ,
hence , the equations have No Solution .
Therefore , The equation, y + x = 45 and 2y + 2x = 6 has No Solution .
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in september 2011, gallup surveyed 1,004 american adults and asked them whether they blamed barack obama a great deal, a moderate amount, not much, or not at all for u.s. economic problems. the results showed that 53% of respondents blamed barack obama a great deal or a moderate amount. using these data, we calculated a 99% confidence interval of (0.489, 0.571) for the proportion of all american adults who blame barack obama a great deal or a moderate amount. does the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems?
The 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).
In the given question we have to find the confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems.
Gallup surveyed 1,004 american adults.
So n=1004
The results showed that 53% of respondents blamed barack obama a great deal or a moderate amount.
So p=53% = 0.53
The 99% confidence interval for the proportion of all american adults who blame barack obama a great deal or a moderate amount for u.s. economic problems is
CI=p±z× √{p(1−p)}/n
Now finding the value of z for 99% confidence interval.
The z critical value at 99% confidence interval is 2.575.
Now putting the value
CI=0.53±2.575× √{0.53(1−0.53)}/1004
CI=0.53±2.575× √(0.53*0.47)/1004
CI=0.53±2.575× √0.2491/1004
CI=0.53±2.575× √0.00025
CI=0.53±2.575× 0.0158
CI=0.53±0.0407
CI=(0.53+0.0407, 0.53−0.0407)
CI=(0.571, 0.489)
Hence, the 99% confidence interval indicate that a majority of all american adults blame barack obama a great deal or a moderate amount for u.s. economic problems is (0.571, 0.489).
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complete the recursive formula of the arithmetic sequence calculator -5,-25,-45,-65
The recursive formula of the arithmetic sequence calculator -5, -25, -45, and -65 is an = -20n + 15
The arithmetic sequence is
-5,-25,-45,-65
The initial term = -5
The common difference = The second term - The first term
= -25 - (-5)
= -25 + 5
= -20
The nth term of the arithmetic sequence is
an = a+(n- 1)d
When an is the nth term
a is the initial term
d is the common difference
Substitute the values in the equation
an = -5 +(n-1)( -20)
Apply the distributive property
an = -5 -20n + 20
an = -20n + 15
Hence, the recursive formula of the arithmetic sequence calculator -5,-25,-45,-65 is an = -20n + 15
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I need help ASAP!!!!!!!
Step-by-step explanation:
in that setup they will both explode after traveling the same distance.
A is just going faster and has to launch therefore a little bit later.
so, we need to make an equation based on distance traveled and find in that process the number of seconds needed to travel that distance.
speed is distance/time, so we need to multiply speed by time to get distance.
x = seconds for B
x - 0.25 = seconds for A
A is launched after B but explodes at the same time.
so, A's trip is of shorter time than B's trip.
(x - 0.25)×360 = x×320
360x - 90 = 320x
40x - 90 = 0
40x = 90
4x = 9
x = 9/4 = 2.25 seconds
both fireworks will explode 2.25 seconds after B launches (and 2.25 - 0.25 = 2 seconds after A launches).
the explosion will be at
320×2.25 = 360×2 = 720 feet height.
Need help!! Hurry!!!!!
what’s the question mark?
Answer:
? ≈ 5.01
Step-by-step explanation:
using the sine ratio in the right triangle
sin24.3° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2.06}{?}[/tex] ( multiply both sides by ? )
? × sin24.3° = 2.06 ( divide both sides by 24.3° )
? = [tex]\frac{2.06}{sin24.3}[/tex] ≈ 5.01 ( to 3 significant figures )
emma estimated the
first digit in the quotient of 2,183 ÷ 42 as 4. She adjusted the quotient to 3. What did she do wrong? Explain how Emma can avoid her mistake.
Quotient is 51.97 by dividing 2,183 by 42. A quotient is the amount that results from dividing two numbers.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.
Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.
The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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The mistake she done is that the acutal quotient is 51.97.
How to divide a number ?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The additional operations are multiplication, addition, and subtraction.Multiply the first fraction by the reciprocal of the second to divide rational expressions. We factor everything and search for common factors after rewriting the division as multiplication of the first statement by the reciprocal of the second. Separate logical expressions.The number 2183 is called the numerator or dividend, and the number 42 is called the denominator or divisor.
The quotient of 2183 and 42, the ratio of 2183 and 42, as well as the fraction of 2183 and 42 all mean (almost) the same:
2183 divided by 42, often written as 2183/42.
2183/42 = 51.97
The answer that is quotient is 51.97
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What is the equation of the line that passes through the point (-1,5) and has a slope of -3
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-1)}) \implies y -5= -3 (x +1) \\\\\\ y-5=-3x-3\implies {\Large \begin{array}{llll} y=-3x+2 \end{array}}[/tex]
i need help with b helpppppppppppppppp plssssssssssssssssssssssssssssssss
The order of in which the operation in the expression 9 + 3·2² - 1·4, indicates;
3. (a) The value of the expression, 9 + 3·2² - 1·4 is 17
(b) The left and right side of the grouping symbol (the left side) should be placed between the number 3 and 2 and then (the right side should be placed between 1 and 4, so that we get;
9 + 3 × (2² - 1) × 4 = 45
What is the order of operations in mathematics?The order of operations is a rule or guide, that states the sequence in which the operations in an expression are to be performed.
3. The specified expression is; 9 + 3·2² - 1·4
(a) The value of the expression 9 + 3·2² - 1·4 can be found using the order of operation of PEMDAS, which stands for; operations from left to right, items in Parenthesis, then Exponents, followed by Multiplication, and Division first then Addition and Subtraction of the terms from left to right as follows;
Therefore;
9 + 3·2² - 1·4 = 9 + 3 × 4 - 1 × 4 = 9 + 12 - 4 = 17
The value of the expression, 9 + 3·2² - 1·4, is 17(b) A grouping symbol is the parenthesis.
The location of the parenthesis in the specified expression so that the value is 45 can be found as follows;
Placing the grouping symbol between 3 and 2 and the right parenthesis between 1 and 4, we get;
9 + 3·2² - 1·4 = 9 + 3·(2² - 1)·4 = 9 + 3 × (2² - 1) × 4
9 + 3 × (2² - 1) × 4 = 9 + 3 × (3) × 4 = 9 + 36 = 45
The location to place the grouping symbol so that the value of the expression is 45 is between 3 and 2 and between 1 and 4.
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1. A revenue of $2000 is obtained from the sales of item A at $40 each and item B at $35 each. Write an
equation that shows the relationship between the numbers of items sold.
2. A revenue of $3000 is obtained from the sales of item A at $50 each and item B at $80 each. Write an equation that shows the relationship between the numbers of items sold.
Answer:
Step-by-step explanation:
Hi vengefull, :0 like that show on Netflix about revenge, huh :0 anyway, back to math.
the equation 1):
40*A+ 35*B=2000
the equation 2):
50*A + 80*B=3000
These tables represent a quadratic function with a vertex at (0, -1). What is
the average rate of change for the interval from x = 8 to x = 9?
OA. -82
OB. -17
C. -65
D. -2
x y
0
1
23456
125
-10
-17
-26
-37
Interval
0 to 1
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
Average rate
of change
-1
-3
-5
-7
-9
-11
3-2
1-2
3-2
1-2
3-2
Answer:
B
Step-by-step explanation:
We can notice that based on the given pattern, the average rate of change from [tex]x=n[/tex] to [tex]x=n+1[/tex], where [tex]n \in \mathbb{Z}[/tex], is [tex]-2n-1[/tex].
So, the average rate of change from [tex]x=8[/tex] to [tex]x=9[/tex] is [tex]-2(8)-1=-17[/tex].
The rate of change for the interval from x = 8 to x = 9 is -17.
What is Rate of change?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The relationship defining how one quantity changes in relation to the change in another quantity is given by the rate of change formula.
We know the standard form of quadratic function
y = a (x - b)² + c with vertex (b, c)
Since the vertex is (0, -1) then b= 0, c= -1.
Then, the quadratic equation is:
y= ax² - 1 passes through (1, 2), (2, -5),.....
So, the rate of change in interval (8, 9) is
= y(9)- y(8)/ (9-8)
= -9² -1 - 8² - 1/ 1
= -17.
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what is the slope of this line a) 1/4 b) 4 c) -1/4 the 1 is not negitive the / is negitive d) -4
to get the slope of any straight line, we simply need two points off of it, so let's use those two in the picture below.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-8}{1 +1} \implies \cfrac{ -8 }{ 2 } \implies - 4[/tex]
Points located on a function include: (3, 6), (-5, 7), (13, 1), and (7, 14). Which point cannot be included in the function?
A (14, 5)
B (5, 6)
C (7, 2)
D (8, 0)
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
The given coordinate points are (3, 6), (-5, 7), (13, 1), and (7, 14).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
A) (14, 5)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (14, 5) is included in the function.
It is a function as every input has a unique output.
B) (5, 6)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (5, 6) is included in the function.
It is a function as every input has a unique output.
C) (7, 2)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (7, 2) is not included in the function.
Since the element 7 corresponds to two different images i.e., 14 and 2.
D) (8, 0)
Along with the given points (3, 6), (-5, 7), (13, 1), and (7, 14), the point (8, 0) is included in the function.
It is a function as every input has a unique output.
The point cannot be included in the function is (7, 2). Therefore, option C is the correct answer.
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A model train goes 8 inches in 2 seconds.
1. Calculate two unit rates for the model train and enter them in the table.
2. Explain the meaning of each of the numbers you found.
Answer:
16
Step-by-step explanation:
8 x 2 = 16 16 - 8 =2
Answer:
16......................
can anyone please help me? (pic attached)
Answer:
No, Eduardo made a mistake from Step 1 to Step 2. Eduardo should have subtracted 4 from 6 instead of evaluating the exponent. The order of operations says to perform all operations inside parentheses first.
Noah is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Noah made a total of 11 shots altogether and scored a total of 29 points. Write a system of equations that could be used to determine the number of two point shots noah made and the number of three point shots he made. Define the variables that you use to write the system.
The system of equations is x + y = 11 and 2x + 3y = 29 and variables are x and y.
Let us assume the number of two point shots be x and the number of three point shots be y. Forming the equation now -
x + y = 11 : Equation 1
2x + 3y = 29 : Equation 2
Rewriting the equation 1 as per x.
x = 11 - y : Equation 3
Keep the value of x form equation 3 in equation 2
2(11 - y) + 3y = 29
Performing multiplication on Left Hand Side of the equation
22 - 2y + 3y = 29
y = 29 - 22
y = 7
Keep the value of y in equation 3.
x = 11 - 7
x = 4
So, the two point shots are 4 and three points shots are 7. The variables are x and y and system of equations are equation 1 and equation 2.
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7.34 the gpas of all students enrolled at a large university have an approximate normal distribution with a mean of 3.02 and a standard deviation of .29. find the probability that the mean gpa of a random sample of 20 students selected from this university is
The probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher is 10.93%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:Problems of normally distributed samples are solved using the z-score methods.
We know that, in a set with mean and standard deviation , the z-score of a measure X is given by:
Z = X - μ/σ
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem:The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .
For a Skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
μ = 3.02 , σ = 0.29 , n = 20 and s = 0.29/√ 20 = 0.0648
Find the probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
This is 1 subtracted by the p- value of Z when X = 3.10. So
By the Central Limit Theorem:
Z = X - μ / s
⇒ Z = 3.1 - 3.02/ 0.0648
⇒ Z = 1.23
The Z = 1.23 has a P- value of 0.8907
∴ 1 - 0.8907 = 0.1093
Now, for getting the percentage,
0.1093 × 100% = 10.93%
10.93% probability that the mean GPA of a random sample of 20 students selected from this university is 3.10 or higher.
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Can anybody solve this for me?
Answer:
y = x + 6
Step-by-step explanation:
y = mx + c
2 = -4m + c
-2 = -8m + c
2 + 4m = c
-2 = -8m + 2 + 4m
-2 - 2 = -4m
-4 = -4m
-4/-4 = m
m = 1
2 + 4(1) = c
c = 6
y = x + 6
Steven's birthday party will cost $168 if he invites 14 guests. If there are 59 guests, how much will Steven's birthday party cost? Solve using unit rates.
Calculated using unit rates, Steven's birthday party will cost him $ 708 if he were to invite 59 guests.
If the party will cost him $168 for him to invite 14 guests, then we will need to calculate the cost for each guest using unit rates.
if 14 guests = $168,
1 guest = 168/14 = $12
so it will cost him $12 per guest he invites
Knowing that each guest will cost him $12, then if Steven wants to invite 59 guests to his birthday party, he will be spending:
59 × $12 = $708
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Give the name (monomial,
binomial, trinomial etc.) and
degree of the polynomial.
15x2
The given polynomial is a binomial and the degree is 2.
What are the various degrees of polynomial ?In a given expression if we have to know the degree of the polynomial we must look at the HIGHEST degree of the polynomial. This along with the table given below will help us identify the degree of the polynomial.
Degree 0 Constant Polynomial
Degree 1 Linear Polynomial
Degree 2 Quadratic Polynomial
Degree 3 Cubic Polynomial
Degree 4 Quartic Polynomial
The above mentions the various degrees of the polynomial , you may refer to it for future references .
The given expression is [tex]15x^2[/tex]
since the degree of the given polynomial is 2
the given is a binomial polynomial .
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