if two nonzero vectors point in the same direction, their dot product must be zero. T/F
False. If two nonzero vectors point in the same direction, their dot product will not be zero.
The dot product of two vectors is a mathematical operation that measures the degree of similarity or alignment between the vectors. It is calculated by multiplying the corresponding components of the vectors and summing the results.
When two vectors point in the same direction, their dot product will be positive, indicating that they are aligned or have a certain degree of similarity. The dot product will be equal to the product of the magnitudes of the vectors multiplied by the cosine of the angle between them.
If two nonzero vectors are parallel and point in the same direction, the angle between them is 0 degrees, and the cosine of 0 degrees is 1. Therefore, the dot product of two nonzero vectors pointing in the same direction will be equal to the product of their magnitudes.
In other words, if the vectors are represented as A and B, and they point in the same direction, the dot product (A · B) will be equal to ||A|| * ||B||, where ||A|| and ||B|| represent the magnitudes of the vectors A and B, respectively.
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Use the drawing tools to form the correct answer on the provided graph.
Graph the line that represents the equation y=-2/3x+1
Answer:start on (0,1) and go up two and left three. keep going until you run out of room. then, draw a line through the points.
Step-by-step explanation:
gg
The complete question is,
Use the drawing tool(s) to form the correct answers on the provided graph.
Graph the system of equations given below on the provided graph.
2x– 3y = –18
3x + y = -5
A graph can be described as a pictorial representation or a diagram that methodically describes data or values.
What is Graph?In math, a graph can be described as a pictorial representation or a diagram that methodically describes data or values. The points on the graph often characterize the connection between two or more things.
2x– 3y = –18
3x + y = -5
Transforming the equation in slope-intercept form
2x-3y= -18
-3y= -2x-18
-3y= -(2x+18)
3y=2x+18
y=(2x+18)/3
And for equation 2
y= -5-3x
For plotting the graph, the online graphing calculator can be utilized.
The points can be estimated by putting negative and positive values of x in both equations.
The graph exists attached as a picture.
As we can see from the graph that two lines intersect at (-3,4) so it stands for the solution of the provided system of linear equations.
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identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 64
just look at the picture i’m confused, whoever gets it right gets a thanks and brainliest whatever that is lol
Answer:
The three points lie on a straight line
A line through the points passes through the origin
The graph shows a proportional relationship
Step-by-step explanation:
Given statements:
a) The three points do not lie on a straight line.
b) The three points lie on a straight line.
c) A line through the points passes through the origin.
d) A line through the points does not pass through the origin.
e) The graph shows a proportional relationship.
f) The graph does not show a proportional relationship.
For the first and second statements, we can see that the points are able to be connected with a straight, diagonal line (see attached graph). This makes statement a false, and statement b true.
a = false
b = true
For the third and fourth statements, we can see that on the attached (revised) graph on my answer, that the line can continue and pass through the origin, or (0,0). This means that statement c is true, and statement d is false.
c = true
d = false
For the fifth and sixth statements, we know that a relationship is proportional if it is a straight line and passes through the origin when graphed. We have already concluded above that both of these are true, so this means that the graph does represent a proportional relationship. This means that statement e is true, and statement f is false.
e = true
f = false
From the above work, we can conclude that the following statements are true:
b (The three points lie on a straight line)
c (A line through the points passes through the origin)
e (The graph shows a proportional relationship)
Hope this helps :)
Hiya! I need help please! Thanks I really appreciate it!
(2 screenshots included)
Answer:
8. the line the vertical
9. y=3/4x-10
Step-by-step explanation:
For number nine, you must find b with the information given if you were to use slope intercept form.
4= 3/4(-8)+b
4= -6+b
-10=6
Now, just plug this number back into the equation.
y= 3/4x-10
the weights of bags of cement are normally distributed with a mean of 53 and a standard deviation of 2 a. what is the likelihood that a randomly selected individual bag has a weight greater than 50
The likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%
When dealing with normally distributed data, we use the mean and standard deviation to determine the likelihood of certain events occurring. In this case, the mean weight of bags of cement is 53 with a standard deviation of 2.
To find the likelihood that a randomly selected bag has a weight greater than 50, we need to calculate the z-score for 50. The z-score tells us how many standard deviations away a particular value is from the mean.
z = (X - μ) / σ
where X is the value we're interested in (50), μ is the mean (53), and σ is the standard deviation (2).
z = (50 - 53) / 2 = -1.5
A z-score of -1.5 means that a weight of 50 is 1.5 standard deviations below the mean. To find the likelihood of a bag weighing more than 50, we can use a z-table or a calculator to find the area to the right of this z-score.
Looking up a z-score of -1.5, we find that the area to the left is approximately 0.0668, which means the area to the right (the likelihood of a bag weighing more than 50) is:
1 - 0.0668 = 0.9332
Thus, the likelihood that a randomly selected bag of cement weighs more than 50 is approximately 93.32%.
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at is the equation in slope-intercept form for a line that goes through the points (- 2, 16) and (2, - 8)
Answer:
y=-6x+4
Step-by-step explanation:
Giving brainliest!!!! Plzz put the correct answers.
2^(10)= 2x...x2 how many times
15^(57)= 15x...x15 how many times
(-4)x...x(-4) 7 times =
(1.5)x...x(1.5) 12 times =
If you give me the answer after like an hour i willl report you!!
Answer:
See below
Step-by-step explanation:
aⁿ = a×a×a×....×a (power n of the number a = number a multiplied by itself n times)2^(10)= 2x...x2 how many times = 10 times 2
15^(57)= 15x...x15 how many times = 57 times 15
(-4)x...x(-4) 7 times = (-4)^(7)
(1.5)x...x(1.5) 12 times = (1.5)^(12)
Solve each equation for x 3х- 12у= 27
Where are the zeros for f(x) = cos x/4 on the interval [0, 2n]?
A. X = 2 pi, 6 pi
B.X = 0,2 pi
C. none
D. x = 2 pi
The zeros of a function are the values of x that make the function equal to zero. To find the zeros of f(x) = cos x/4 on the interval [0, 2π], we need to solve the equation cos x/4 = 0. Since cosine is equal to zero at odd multiples of π/2, we have:
cos x/4 = 0
x/4 = (2n + 1)π/2, where n is an integer
x = (2n + 1)π/2 * 4, where n is an integer
Now we need to find the values of n that make x lie in the interval [0, 2π]. We have:
0 ≤ x ≤ 2π
0 ≤ (2n + 1)π/2 * 4 ≤ 2π
0 ≤ (2n + 1)π ≤ π/2
0 ≤ 2n + 1 ≤ 1/2
-1/4 ≤ n ≤ -1/2
Since there are no integers n that satisfy this inequality, there are no zeros of f(x) = cos x/4 on the interval [0, 2π]. Therefore, the answer is C. none.
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Question 1 of 10
Rewrite the following linear equation in slope-intercept form. Write your
answer with no spaces.
v-5= 3(x+1)
Answer here
SUBMIT
Answer:
v-5=3(x+1)
1. v-5= 3x+3
2. v= 3x+3+5
3. v= 3x+8
Step-by-step explanation:
1. distribute the 3
2. add the 5 to both sides
3. simplify
Answer:
v=3x+8
Step-by-step explanation:
you would have to use the formula y= mx + b if you want an easier way look up math way
if h(x)=x2-x find h(3)
Answer:
h(3) = 1
Step-by-step explanation:
\(h\left(3\right)=\left(3\right)\cdot \:2-3\\h\left(3\right)=3\cdot \:2-3\\h\left(3\right)=6-3\\h\left(3\right)=3\)
Divide
\(\frac{h\cdot \:3}{3}=\frac{3}{3}\\h=1\)
what is 4.4.4 as an exponent
Answer:
4*4*4=4^3
Step-by-step explanation:
4 is multiplied by itself 3 times so it's to the third power which equals \(4^{3}\)
Solve the following equation:
a/3.5 - 4.8 = 6.3
a= ______
Answer:
a= 38.85
Step-by-step explanation:
Answer:
\(\boxed {a = 38.85}\)
Step-by-step explanation:
Solve for the value of \(a\):
\(\frac{a}{3.5} - 4.8 = 6.3\)
-Add both sides by \(4.8\):
\(\frac{a}{3.5} - 4.8 + 4.8 = 6.3 + 4.8\)
\(\frac{a}{3.5} = 11.1\)
-Multiply both sides by \(3.5\):
\(a = 11.1 \times 3.5\)
\(\boxed {a = 38.85}\)
Therefore, the value of \(a\) is \(38.85\).
James takes out a loan of 9000 euros which keeps on charging simple interest at a rate of 3% of the original amount per annum until it is cleared. James pays of 770 euros each year to reduce the loan. After how many years will James have fully cleared the loan?
James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.
To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.
The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.
In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.
In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.
This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.
Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.
Combining like terms, we have 9000 + 270 = 1.04x.
Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.
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exercise: total expectation calculation 0.0/2.0 points (graded) we have two coins, a and b. for each toss of coin a, we obtain heads with probability ; for each toss of coin b, we obtain heads with probability . all tosses of the same coin are independent. we select a coin at random, where the probabilty of selecting coin a is , and then toss it until heads is obtained for the first time. the expected number of tosses until the first heads is:
Let's denote the probability of obtaining heads on a toss of coin A as pA and the probability of obtaining heads on a toss of coin B as pB. The probability of selecting coin A is denoted as p(select A).
To calculate the expected number of tosses until the first heads, we can use the concept of conditional expectation. Let E be the expected number of tosses until the first heads. If we select coin A, the expected number of tosses until the first heads is 1/pA, as the probability of obtaining heads on each toss is pA. If we select coin B, the expected number of tosses until the first heads is 1/pB, as the probability of obtaining heads on each toss is pB. Using the law of total expectation, we can calculate the overall expected number of tosses: E = p(select A) * (1/pA) + p(select B) * (1/pB) Simplifying further, we have: E = (p(select A)/pA) + (p(select B)/pB) Therefore, to find the expected number of tosses until the first heads, we need to know the probabilities pA, pB, and p(select A). Without these specific values, we cannot provide an exact numerical answer.
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The difference of twice a number and 9
Answer:
2x - 9
Step-by-step explanation:
2 times x minus 9
Find the area for this problem
Answer:
63 for the whole figure, for the different shaded regions it goes as follows, 17.5 for the white area and 45.5 for the grey area
Step-by-step explanation:
What is the slope of the line
Given \(log_{b}(R)=5.4\), \(log_{b}(Q)=1.2\), and \(log_{b}(T)=-1.4\)
Evaluate \(log_{b}(\sqrt{\frac{RQ}{T} } )\)
\(\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\[-0.35em] \rule{34em}{0.25pt}\)
\(\log_b(R)=5.4\hspace{5em}\log_b(Q)=1.2\hspace{5em}\log_b(T)=-1.4 \\\\[-0.35em] ~\dotfill\\\\ \log_b\left(\sqrt{\cfrac{RQ}{T}} \right)\implies \log_b\left( ~~ \left( \cfrac{RQ}{T} \right)^{\frac{1}{2}} ~~ \right)\implies \cfrac{1}{2}\log_b\left( \cfrac{RQ}{T} \right) \\\\\\ \cfrac{1}{2}[\log_b(RQ)~~ - ~~\log_b(T)]\implies \cfrac{1}{2}[\log_b(R)+\log_b(Q)~~ - ~~\log_b(T)] \\\\\\ \cfrac{1}{2}[5.4+1.2 - (-1.4)]\implies \cfrac{1}{2}[5.4+1.2 +1.4] \implies \cfrac{1}{2}[8]\implies \text{\LARGE 4}\)
Which function is most likely graphed on the coordinate plane below?
a) f(x) = 3x – 11
b) f(x) = –4x + 12
c) f(x) = 4x + 13
d) f(x) = –5x – 19
Based on the characteristics of the given graph, the function that is most likely graphed is f(x) = -4x + 12. This function has a slope of -4, indicating a decreasing line, and a y-intercept of 12, matching the starting point of the graph.The correct answer is option B.
To determine which function is most likely graphed, we can compare the slope and y-intercept of each function with the given graph.
The slope of a linear function represents the rate of change of the function. It determines whether the graph is increasing or decreasing. In this case, the slope is the coefficient of x in each function.
The y-intercept of a linear function is the value of y when x is equal to 0. It determines where the graph intersects the y-axis.
Looking at the given graph, we can observe that it starts at the point (0, 12) and decreases as x increases.
Let's analyze each option to see if it matches the characteristics of the given graph:
a) f(x) = 3x - 11:
- Slope: 3
- Y-intercept: -11
b) f(x) = -4x + 12:
- Slope: -4
- Y-intercept: 12
c) f(x) = 4x + 13:
- Slope: 4
- Y-intercept: 13
d) f(x) = -5x - 19:
- Slope: -5
- Y-intercept: -19
Comparing the slope and y-intercept of each function with the characteristics of the given graph, we can see that option b) f(x) = -4x + 12 matches the graph. The slope of -4 indicates a decreasing line, and the y-intercept of 12 matches the starting point of the graph.
Therefore, the function most likely graphed on the coordinate plane is f(x) = -4x + 12.
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Answer:
It's D.
Step-by-step explanation:
Edge 2020;)
Which of the following equation has one solution?
Responses
4x + 2x = 6x - 4
3 (2x + 4) = 2 (2x - 4)
5(x - 3) = 5x - 3
2x = 2x + 4
a) 4x + 2x = 6x - 4
= 6x = 6x - 4
cannot be solved further.
b) 3(2x + 4) = 2(2x - 4)
= 6x + 12 = 4x - 4
(bring the numbers and variables on one side)
= 6x + 4x = 12 - 4
10x = 8
x = 8/10 = 4/5
can be solved.
c) 5(x - 3) = 5x - 3
= 5x - 15 = 5x - 3
= (bring the variables and numbers on one side)
5x + 5x = -15 - 3
= 10x = -18
x = -18/10 = 9/5
can be solved
d) 2x = 2x + 4
= 2x + 2x = 4
= 4x = 4
x = 4/4 OR 1.
THUS, (B, (C AND (D CAN BE SOLVED WITH ONE SOLUTION.a restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts. how many possible 3-course meals are there?
Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
Given,
In the question:
A restaurant offers a choice of 4 salads, 5 main courses, and 3 desserts.
To find the how many possible 3-course meals are there?
Now, According to the question:
Let's know:
What is the Fundamental Counting Theorem?
It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
\(N=n_1\) × \(n_2\) × \(n_3\)... ×\(n_n\)
In this problem, considering the number of salads, main courses and desserts, we have that:
\(n_1=4 , n_2=5,n_3=3\)
The total number of options is given by:
N = 4 × 5 × 3
N = 60
Hence, Using the Fundamental Counting Theorem, it is found that there are 60 possible 3-course meals.
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PLEASE ANSWER ITS IMPORTANT
what is linear graph
Answer:
A linear graph is nothing but a straight line or straight graph which is drawn on a plane connecting the points on x and y coordinates.
Answer: is a diagram which shows a connection or relation between two or more quantity.
Step-by-step explanation:
A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 50 and 20 , respectively. The standard error of the mean is a. 2. b. 5.
c. 10 . d. 0.5
The standard error of the mean would be 0.63.
What is the standard error of the mean?
A statistic's standard error is the standard deviation of its sampling distribution or an estimate of that standard deviation. The standard error of the mean is used when the statistic is the sample mean.
Given data:
Standard mean(m) = 50.
Standard deviation = 20.
N = 100.
\(C_v=\frac{\sigma}{x}*100\\\\C_v=\frac{20}{50}*100\\\\C_v=40\%\)
Now,
\(N=(\frac{C_v}{\epsilon})^2\\\\100=(\frac{40}{\epsilon})^2\\\\\epsilon^2=\frac{1600}{100}\\\\\epsilon = 1.26\)
Now calculate the standard error of the mean, we get
Standard error of mean = mean * percentage of absolute mean error
= 50 * (1.26/100)
= 0.63
Hence, the standard error of the mean would be 0.63.
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PLEASE BRO DUE TODAY!!!! PLS HELP DUE TODAY
Enter your answer and show all the steps that you use to solve this problem in the space provided.
The table shows how the number of sit-ups Marla does each day has changed over time. At this rate, how many sit-ups will she do on Day 12? Explain your steps in solving this problem.
The difference in the number of sit-ups between each day is constant. Therefore, we can use arithmetic sequence to solve that problem.
What we'll be looking for is \(a_{12}\).
\(a_n=a_1+(n-1)\cdot d\)
\(a_1=17\)
\(d=4\)
Therefore
\(a_{12}=17+(12-1)\cdot 4=17+11\cdot4=17+44=61\)
How to solve 1000/11 via long divison… pls help with full working out
tuition at FSU used to cost $85/credit hour. Four years later it is $147/credit hour. What is the percent change?
The percent change in tuition at FSU from $85/credit hour to $147/credit hour is approximately 72.94%.
To calculate the percent change, you can use the formula:
Percent Change = [(New Value - Old Value) / Old Value] × 100
In this case, the old value is $85/credit hour and the new value is $147/credit hour.
Percent Change = [($147 - $85) / $85] × 100 = ($62 / $85) × 100 ≈ 72.94%
The tuition at FSU has increased by approximately 72.94% over the four-year period.
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Kaitlin drove 567 miles in 9 hours. At the same rate, how long would it take her to drive 819 miles? hours
Answer:
13 hours
Step-by-step explanation:
to drive 567 miles in 9 hours you would be going 63mph and it would take 13 hours at 63 mph to travel 819 miles.