(a) i. See comment...
(a) ii. We have
[tex]\vec p = 6\,\vec\imath - 3\,\vec\jmath + 9\,\vec k[/tex]
and
[tex]\vec q = 3\,\vec\imath - 6\,\vec\jmath - 3\,\vec k[/tex]
(b) We can parameterize the line segment from P to Q by the vector function
[tex]\vec r(t) = (1-t) \vec p + t \vec q = (6-3t) \, \vec\imath + (-3-3t) \,\vec\jmath + (9-6t) \,\vec k[/tex]
with [tex]0\le t\le1[/tex]. The point R is located 1/3 of the way along this line segment, i.e. at [tex]t=\frac13[/tex], so its position vector is
[tex]\vec r\left(\dfrac13\right) = 5\,\vec\imath -4\,\vec\jmath + 7\,\vec k[/tex]
and hence its coordinates are [tex]\boxed{(5,-4,7)}[/tex].
In which year did Eugene, Oregon have the greatest difference between high and low temperatures in November?
A)November 2009
B)November 2010
C)November 2011
D)November 2008
NEED HELP ASAP!!!!!!!!
PLEASE
For which set of data are the median and mode the same number?
(A) 4, 5, 7, 8, 9, 9
(B) 4, 5, 7, 7, 8, 10
(C) 3, 5, 6, 8, 8, 9
(D) 5, 5, 6, 8, 9, 10
Answer:
b
Step-by-step explanation:
I need help with this math question
Answer:
D = 12
Step-by-step explanation:
Side ST is corresponding to side QT. 9" / 3" = 3
3 is the proportion between the two triangles.
Side PT is the corresponding side to side RT.
PT = 4" x 3 = 12"
A measure of the strength of the relationship between two variables is referred to as the.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient.
To gauge how strongly two variables are related to one another, correlation coefficients are used.
A statistical indicator of the strength of the association between the relative movements of two variables is the correlation coefficient. The values are in the -1.0 to 1.0 range. There was a measurement error in the correlation if the estimated value was larger than 1.0 or lower than -1.0. Perfect negative correlation is shown by a correlation of -1.0, and perfect positive correlation is shown by a correlation of 1.0. A correlation of 0.0 indicates that there is no linear link between the two variables' movements. Finance and investing can benefit from the usage of correlation statistics.
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A pen and a ruler cost $2.10. 2 such pens and 3 such rulers cost $4.90. Find the cost of one ruler.
The cost of one ruler is $0.70
Applications of simultaneous equationsFrom the question, we are to determine the cost of one ruler
Let x represent the cost of a ruler
and
y represent the cost of a pen
From the given information, we can write that
y + x = $2.10 ----------- (1)
2y + 3x = $4.90 ----- (2)
From equation (1),
y + x = $2.10
Then,
y = $2.10 - x
Substitute this into equation (2)
2y + 3x = $4.90
2($2.10 - x) + 3x = $4.90
$4.20 - 2x + 3x = $4.90
$4.20 +x = $4.90
x = $4.90 - $4.20
x = $0.70
Hence, the cost of one ruler is $0.70
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In a large population, 76% of the households have cable tv. A simple random sample of 225 households is to be contacted and the sample proportion computed. What is the mean and standard deviation of the sampling distribution of the sample proportions
0.017559
It is given that:
Probability of Households Having cable TV, p₀ = 76% = 0.76
Therefore,
The probability that the Households not having cable TV = 1 - 0.76 = 0.24
Sample size, n = 225 households
sample proportions is less than 82% i.e p = 0.82
Now,
The standard error, SE = [tex]\sqrt{} \frac{0.76(1-0.76)}{225}[/tex]
= 0.02847
Z = [tex]\frac{0.82-0.76}{0.02847}[/tex]
Z = 2.107
therefore, P(sample porportions < 0.82) = P(Z < 2.107)
now from the p value from the Z table we get P(sample porportions < 0.82) = 0.017559
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5 quick algebra 1 questions for 50 points!
Only answer if you know the answer, shout-out to subtomex0, tysm for the help!
[tex]x {}^{2} - 8x - 9 = 0 \\ x + y = 8 \\ xy = - 9[/tex]
Two numbers who sum up to 8 and multiply to -9 are: 9 and -1Q 4 - d -[tex]g(x) = x {}^{2} - 7x + 12 \\ g(6) = 36 - 42 + 12 = 6 \\ g( - 7) = 49 + 49 + 12 = 110 \\ g( - 3) = 9 + 21 + 12 = 42 \\ g(4) = 16 - 28 + 12 = 0[/tex]
x=4 is a rootThese problems can be approached in many ways: completing the square/factoring/using the quadratic formula...Q 1 - c -h(x)= -2x+10h(0)=10 ( 0 , 10 )h(x)=0x=5 ( 5 , 0 )Q 5 - True -f(x) = 2x²+3x-2f(x)=02x²+3x+2=0x=-2 x=1/2Q 4 - 3 is the zero -b
Answer:
Question 1:The correct answer is C. -1 and 9
Question 2: The correct answer is D.4
Question 3: The correct answer is C. The x-intercept of (5,0) and y-intercept of (0,10)
Question 4: The correct answer is B. True
Question 5: The correct answer is b.
Classify the polynomial by its degree and number of terms. Select all choices that apply for each polynomial.
(which is correct ??)
Step-by-step explanation:
The polynomial highest degree is 2 so the degree is 2.
The binomial have three terms so it is a trinomial.
The______is the set of inputs For a fraction
The set of all input values of a function is the domain of the function
What is a function?A function relates an input to an output.
A function defines a relationship between one variable (the independent variable) and another variable.
The set of all input values of a function is the domain of the function.
The domain of a function are also called independent variables.
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2 dogs, 4 horses 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
8+16+2= 24 legs on ground
Step-by-step explanation:
Pauley graphs the change in temperature of a glass of hot tea over time. he sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. which best describes this function?
Non-linear graph best describes this function.
Why nonlinear?
As described in the question, Pauley graphs the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes. It is linear because the graph decreases over time. It is linear because there is both an independent and a dependent variable but it doesn't satisfies one condition of being linear. Thus, It's Nonlinear because linear functions are increasing functions. It is nonlinear because linear functions increase or decrease at the same rate.
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Answer:
B
Step-by-step explanation:
Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2
2
1
2, start fraction, 1, divided by, 2, end fraction meters. Then he climbed straight up 6\dfrac{3}{4}6
4
3
6, start fraction, 3, divided by, 4, end fraction meters. Eric was wondering what his change in elevation was after these two moves.
Which of the following equations matches the situation above?
The equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
We know that in mathematics, subtraction means removing something from a group or a number of things. What is left in the group gets smaller when we subtract. The minuend is the first element we use. The subtrahend is the part that is being removed. The difference is the portion that remains after subtraction.
Assume that "negative" means climbing down and "positive" means climbing up. We must locate the elevation change in this area.
Given that Eric climbed straight down [tex]2\frac{1}{2}[/tex] meters. So we can write [tex]-2\frac{1}{2}[/tex].
Again Eric climbed straight up [tex]6\frac{3}{4}[/tex] meters. So, we can write [tex]6\frac{3}{4}[/tex].
Then the change = [tex]-2\frac{1}{2}+6\frac{3}{4}[/tex]
=[tex]-\frac{(2*2+1)}{2}+\frac{6*4+3}{4}[/tex]
=[tex]-\frac{5}{2} +\frac{27}{4}[/tex]
=[tex]\frac{-(5*2)+27}{4}[/tex]
=[tex]\frac{-10+27}{4}[/tex]
=[tex]\frac{17}{4}[/tex]
=[tex]\frac{4*4+1}{4}[/tex]
=[tex]4\frac{1}{4}[/tex]
Therefore, the equation that matches the given situation is [tex]-2\frac{1}{2}+6\frac{3}{4}=?[/tex] . So, after two moves, Eric's elevation changed [tex]4\frac{1}{4}[/tex] meters above.
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change the unit of weight 1,000 lb =___ t ?
Answer:
0.5 t
Step-by-step explanation:
Since we know that 2,000lbs=1 t
1,000lbs is half a ton, which makes it 0.5 tons
The question is already stated on the picture.
The central angle is 77 degrees mate.
Give the outcomes for each of the following events.
Find the length of the midsegment .
A.15
B.44
C.22
D.13
Answer: 22
Step-by-step explanation:
Using the triangle midsegment theorem,
[tex]2(5x+2)=3x+32\\\\10x+4=3x+32\\\\7x+4=32\\\\7x=28\\\\x=4[/tex]
So, the length of the midsegment is 5(4) + 2 = 22
Which could be used to evaluate the expression negative 6 (4 and two-thirds)? (negative 6) (4) (negative 6) (two-thirds) (negative 6) (4) times (negative 6) (two-thirds) (negative 6 4) (negative 6 two-thirds) (negative 6 4) times (negative 6 two-thirds)
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?LHS,
(-6)([tex]\frac{14}{3}[/tex]) = -28
RHS,
(-6)()[tex]4+\frac{2}{3}[/tex]) = -28
LHS=RHS
Hence, the required expression is (Negative 6) (4) + (negative 6) (two-thirds).
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For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions.
35. f(x) = 3x + 2, g(x) = 5 − 6x
Answer:
The value of [tex]$(f \circ g)(x)$[/tex] is 17-18x and [tex]$(g \circ f)(x)$[/tex] is -7-18x.
Step-by-step explanation:
It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.
It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].
To find [tex]$(f \circ g)(x)$[/tex], substitute g(x) for x in f(x) and simplify the expression.
To find [tex]$(g \circ f)(x)$[/tex], substitute f(x) for x in g(x) and simplify the expression.
Step 1 of 2
Substitute g(x) for x in f(x) and simplify the expression.
[tex]$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$[/tex]
Step 2 of 2
Substitute f(x) for x in g(x) and simplify the expression.
[tex]$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$[/tex]
Try it
Which graph represents the function h(x) = 5.5|x]?
LIV
-2
2 4
-4-2
Intro
2
-4-2
O
2 4
-4-2
2
[tex]take \: some \: values \\ h(1) = 5.5 \times |1| = 5.5 \times 1 = 5.5 \\h(2) = 5.5 \times |2| = 5.5 \times 2 = 11 \\ h(4) = 5.5 \times |4| = 5.5 \times 4= 22[/tex]
It's clearly the second option since the other ones aren't steep enough.Question is on the picture:)
Answer:
Z = 90 degrees
Step-by-step explanation:
Reason is a diameter subtends angle of 90 degrees on the circumference
Given the following linear function sketch the graph of the function and find the domain and range. f( x ) = 2/7 x− 2
Answer:
Domain: All Real Numbers Range: All Real Numbers
Step-by-step explanation:
The domain and range is going to be infinite. The linear function will be using the x and y- axis in order to continue being a function. The y-intercept will be -2 on the y-axis. I recommend using the rise-over-run method for your slope value. from the point (0, -2) on the y-axis. Go up two on the y-axis, and right 7 on the x-axis.
Sorry, it may be difficult to explain through words.
The steps to derive the quadratic formula are shown below:
Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared
Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared
Step 6
Provide the next step to derive the quadratic formula. (1 point)
x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared
x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a
Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Step-by-step explanation:
We can rewrite the left hand side as a perfect square, more specifically
[tex]\left(x+\frac{b}{2a} \right)^2[/tex]
So, taking the square root of both sides,
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]
Pina has two equations that she found to be valuable models for her research. She thinks that if she can find the solution of the two graphs, she will be able to identify a key point to her studies. What can Pina expect in terms of solutions of these two graphs?
-3x + y = 10
y = 3x − 6
parallel lines
infinite solutions
both parallel lines and no solution
no solution
Which statements about the local maximums and minimums for the given function are true? Choose three options.
Over the interval [1, 3], the local minimum is 0
Over the interval [2, 4], the local minimum is –8.
Over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0.
Over the interval [3, 5], the local maximum is 0.
The statements about the local maximums and minimums for the given function which are true include:
Over the interval [2, 4], the local minimum is –8.Over the interval [3, 5], the local minimum is –8.Over the interval [1, 4], the local maximum is 0.What is Function?This is defined as the mathematical entities which assign unique outputs to given inputs and defines a relationship between the two variables.
According the the graph: over the interval [2, 4], the local minimum is –8 because the given minimum point is (3.4, -8) and over the interval [3, 5], the local minimum is –8.
Over the interval [1, 4], the local maximum is 0 and over the interval [3, 5], there is no maximum point hence why it is false.
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Joe ordered a large cake for his brothers. He gave 1 out of 12 of the cake to David, 5 out of 12 of the cake to John, and 2 out of 12 of the cake to Ali. He ate the remaining cake himself. What fraction of the whole cake did Joe eat?
Answer: 4/12 or 1/3
Step-by-step explanation:
A whole cake is 12/12.
He gave away 1/12, 5/12, and 2/12s of the cake
1+5+2 = 8
So he gave out 8/12s of the cake, which means he has 4/12 left, or 1/3 if you want simplest form.
Hope this helps.
Calculate the area of triangle OPQ.
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
Is this triangle solvable?
In this question we must analyze if the area of the triangle OPQ can be found by all information given. By the law of the cosines we understand that lengths of two sides and the measure of an angle should be known to construct a triangle and by the law of the sines we understand that either two angles and a side or two sides and an angle must be known.
Thus, we need information about the sides OQ and PQ to solve the triangle and find the area. The information given is not enough to determine the area of the triangle.
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In the falcon's nest ice cream cost 20 cents. if the school pays 15 cents, what percent mark-up is it?
Answer: 25% off
Step-by-step explanation:
1= 0.25 + 0.75
25% is off is the equivalency of multiplying the value of the original cost with 0.75.
20*0.75=15
I need answer fast!!
3. Write the rule that describes the second transformation. (5 points)
The rule that describes the second transformation is; Rotated at 90° clockwise
How to Interpret Transformations?From the given diagram we can see that;
The transformation from Rectangle ABCD to A'B'C'D' follows the transformation sequence of;
Shift 1 unit downwards then translate 5 units to the right.
However, for the transformation of A'B'C'D' to A"B"C"D", we see that the transformation is; Rotated at 90° clockwise
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Evaluate 43 – 3m for m = 6.
Answer:
= 43 - 3×6= 43 - 18Therefore , 25 ans.
Compared to continental crust, oceanic crust is:
A. mostly granite
B. more dense
C. All of these
D. thicker
Answer:
B. more dense