If the magnitude of two vectors is 10 and 6 and their dot product is 30, then the angle between the vectors is 60°.
What is a vector?
A vector in mathematics is a quantity that not only expresses magnitude but also motion or position of an object in relation to another point or object. Euclidean vector, geometric vector, and spatial vector are other names for it.
There are two ways to define a dot product: algebraically and geometrically. The sum of the products of the matching entries of the two number sequences is the definition of the dot product in algebra. Geometrically, it is the sum of the cosine of the angle formed by the two vectors and their Euclidean magnitudes.
The magnitude of the vector 1 is, |a| = 10
The magnitude of the vector 2 is, |b| = 6
The dot product of the two vectors is, a·b = 30.
The formula for dot product of vectors is -
a·b = |a| |b| cos θ
Solve the equation to get the angle -
30 = (10 × 6) cos θ
30 = 60 cos θ
cos θ = 30/60
cos θ = 1/2
θ = cos^-1 (1/2)
θ = 60°
Therefore, the angle is obtained as 60°.
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A 6-sided die is rolled 2 times. What is the probability of getting 1 both times? (Give your answer as a fraction in simplest form.
The probability of rolling two ones in a row is equal to P = 1/36
How to find the probability?
We want to find the probability of rolling two ones in a row.
Remember that a dice has 6 sides, so the probability of randomly rolling a 1 is just:
p = 1/6
And if we want to do that two times then we need to have that probability twice:
q = 1/6
And the joint probability (probability of rolling two ones) is equal to the product between the individual ones:
P = p*q = (1/6)*(1/6)
P = 1/36
That is the probability.
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Simplify and evaluate 25 POINTS TO WHO EVER SOLVES IT
Answer: -2 i think
Step-by-step explanation:
(5-4)-3*(5-4)
1-3*1
1-3=-2
Answer:
The value is 0
The simplified expression is
3• (5 - 4) -3 (5 - 4)
Step-by-step explanation:
hope it helps<3Let A1,A2,⋯ be Lebesgue-measurable subsets of [0,1] of measure 1/2, and let A denote the set of points x such that x belongs to infinitely many of the sets An. How we can show that the Lebesgue measure of A is at least 1/2.
Lebesgue outer measure in this instance is a complete extension of Lebesgue measure that meets all other criteria.
What exactly is a Lebesgue measure?The translation invariant is the Lebesgue measure, and the length of the interval I is the same for that measure when it is on the interval I. The Lebesgue measure of E, for instance, is given by λ(E) = l if E is any collection of real numbers (E).
As with a single point or a countable number of points, every set that is a finite collection of points has a Lebesgue measure of zero. The measure of finite and countable unions of disjoint sets has the property of being equal to the total of the measures.
An interval's length is its Lebesgue value. The formal foundation for probability theory is measure theory.
(1) When working with function spaces, the Lebesgue integral is important since it is resistant to a variety of limiting procedures. (2) It easily expands to quite an abstract context and creates a fundamental language of probability theory, as numerous users have noted.To learn more about Lebesgue measure, refer to:
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Amenys earns a#$ 35.00 a month after taxes and his brother Esinam earns three timer as much, how much is their income after five years
determine the number of positive integers less than that contain at least one in their decimal representation.
There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
There are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation. This can be determined by counting the number of possible combinations of digits that can be formed with the numbers 0-9. Since there are five digits in a number less than 100,000, the total number of combinations is 10^5 (10 to the power of 5). Of these combinations, 1/10th will contain at least one "1" as there are 10 possible ways to include a "1" in the five-digit number. Thus, 10^5/10 = 9,999. This means that there are 9,999 positive integers less than 100,000 that contain at least one "1" in their decimal representation.
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the coefficient of static friction between the right bar and the surface at a is. what are the largest angles
The coefficient of static friction is a dimensionless value that represents the ratio of the maximum static friction force to the normal force. It is used to determine the maximum angle at which an object can be inclined on a surface without slipping. The coefficient of static friction between the right bar and the surface at point A is not given in the information provided.
To determine the largest angles at which the right bar can be inclined without slipping on the surface at point A, one would need to know the coefficient of static friction between the bar and the surface, as well as the weight of the bar and the normal force acting on it. The coefficient of static friction multiplied by the normal force must be greater than or equal to the weight of the bar in order for it to remain in static equilibrium.
It is also worth mentioning that the coefficient of static friction varies depending on the materials of the two surfaces in contact and the normal force acting on it. The coefficient of static friction can be measured experimentally and is usually provided in the material properties of the surfaces.
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Each marble bag sold by Dante's Marble Company contains red marbles for every orange marbles. If a bag has orange marbles, how many red marbles does it contain?
If a bag has orange marbles, the number of red marbles it will contain would be also the same as the number of orange marbles.
How to derive the number of marbles?The Dante's Marble Company sells bags of marbles that contains different types of marbles such as both the red and the orange marbles I'm a particular order.
In a bag of marbles, every red marbles = every orange marbles.
Therefore the number of red marbles found in a bag will be the same amount of orange marbles found in the same bag.
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3
Which is different?
O Add-4.5 and 3.5.
O What is -4.5 increased by 3.5?
What is the distance between-4.5 and 3.5?
O Find the sum of -4.5 and 3.5.
Find "both" answers.
Answer for the "different" question:
Answer for the "same" questions:
Answer for the "different" question: The distance between -4.5 and 3.5 is 8.
Answer for the "same" questions:
O Add -4.5 and 3.5: -4.5 + 3.5 = -1
O What is -4.5 increased by 3.5: -4.5 + 3.5 = -1
Find the sum of -4.5 and 3.5: -4.5 + 3.5 = -1
Answer: What is the distance between -4.5 and 3.5?
Step-by-step explanation:
The distance between -4.5 and 3.5 and will be different than all the others because the distance it's asking for the distance between the absolute values, not adding them together.
Find "both" answers.
➜ Answer for the "different" question:
What is the distance between -4.5 and 3.5? = 4.5 + 3.5 = 8
➜ Answer for the "same" questions:
Add -4.5 and 3.5 = -4.5 + 3.5 = -1
Solve for the empty box for question 6
Using the associative property of multiplication the missing value of (x × 8) × 2 = 4 × (2 × 8) is 4.
What is associative property of multiplication?The associative property of multiplication tells us how we group factors that does not alter the result of the multiplication. Therefore, the associative property of multiplication can be represented as follows:
a x (b x c) = (a x b) x c
where
a, b and c are variables representing numbers.Therefore, let's use the associative property of multiplication to solve the following.
(x × 8) × 2 = 4 × (2 × 8)
Hence, using the rule, of associative property of multiplication, a x (b x c) = (a x b) x c, the missing variable is 4.
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The graph shows a hypothetical relationship between tons of fertilizer used and crop yields. Which statement is NOT correct?img
A) The slope of the curve between one and two tons of fertilizer is approximately 2.
B) The relationship between fertilizer usage and yield is nonlinear.
C) Because the relationship is nonlinear, it is difficult to create an economic model describing the relationship between the two variables.
D) Using more than three tons of fertilizer has minimal effect on yield.
The correct answer is C), because it is possible to create an economic model describing the relationship between fertilizer usage and yield.
The economic model would take into account the nonlinear relationship, which is shown in the graph. Specifically, the slope of the curve between one and two tons of fertilizer is approximately 2 (change in yield divided by change in fertilizer usage). This means that for every ton of fertilizer used, the yield increases by two (change in yield / change in fertilizer usage = 2). Although using more than three tons of fertilizer has minimal effect on yield, the economic model would still take this into account and provide a more accurate representation of the relationship between the two variables.
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find the trapezoidal riemann sum approximation of the integral from 1 to 5 of the square root of quantity x squared plus 3 close quantity times dx using four equal partitions.
Answer:
14.115
Step-by-step explanation:
Recall Trapezoidal Rule
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx=\frac{1}{2}\biggr(\frac{b-a}{n}\biggr)\biggr[f(x_0)+2\bigr(f(x_1)+f(x_2)+\text{... }+f(x_{n-1})\bigr)+f(x_n)\biggr][/tex]
Make necessary substitutions and evaluate
[tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx=\frac{1}{2}\biggr(\frac{5-1}{4}\biggr)\biggr[2+2\bigr(\sqrt{7}+\sqrt{12}+\sqrt{19}\bigr)+\sqrt{28}\biggr]\approx14.115[/tex]
Note that the actual value of the integral is [tex]\displaystyle \int\limits^5_1 {\sqrt{x^2+3}} \, dx\approx14.078[/tex], so we can see how accurate the Trapezoidal rule is with just a few equal partions.
Teds farm 4 horses, 12 goats, 2 sheep & 18 cows. Find the angle measure of yhe sextor of a circle graph for each animal animal represents. Fill in the boxes
The angle for each animal is;
Horse - 40 degrees
Goats - 120 degrees
Sheep - 20 degrees
Cows - 180 degrees
What is the measure of the angle in each case?We can see that we want to plot the data that we have on the circle graph and each of the values is going to occupy a given part of the sector and would subtend an angle. We are to obtain the angle that is subtended by each value.
We have;
Total number of farm animals = 4 + 12 + 2 + 18 = 36 animals
Angle for horses = 4/36 * 360 = 40 degrees
Angle for goats = 12/36 * 360 = 120 degrees
Angle for sheep = 2/36 * 360 = 20 degrees
Angle for cows = 18/36 * 360 = 180 degrees
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Missing parts
Ted’s farm has 4 horses, 12 goats, 2 sheep, and 18 cows. Find the angle measure of the sector of a circle graph that represents each animal. Enter the correct answers in the boxes.
the decisions at this level are generally made with the least amount of data and have the longest time horizon
Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large amount investments of resources and have a significant impact on the organization's future.
Decisions at this level are typically strategic in nature and involve long-term planning and goal setting. These decisions may involve large investments of resources and have a significant impact on the organization's future. Examples of decisions at this level include setting the overall strategy, developing new products and services, entering new markets, and deciding on organizational structure. Due to the nature of these decisions, they require extensive data analysis and research. It is important for decision makers at this level to have knowledge about the industry, the marketplace, and the competitive environment in order to make informed decisions. Additionally, since these decisions have a long-term impact, it is important to consider the potential risks and opportunities associated with them. Furthermore, the decisions made at this level must align with the overall mission and vision of the organization. As such, these decisions must be made with careful consideration, as they can have far-reaching implications for the entire organization.
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Write the quadratic equation whose roots are
-1
and
6
, and whose leading coefficient is
4
.
(Use the letter
x
to represent the variable.)
The quadratic equation whose roots are -1 and 6 and the leading coefficient is 4 is written in the form
4x² - 20x - 25How to write the quadratic equationThe roots of a quadratic equation is the value of x when y is zero hence we have the equation
x = -1 and x = 6
(x + 1)(x - 6)
with the leading coefficient of 4
4(x + 1)(x - 6)
expanding will result to
= 4(x² - 6x + x - 6)
= 4(x² - 5x - 6)
= 4x² - 20x - 25
The quadratic equation is 4x² - 20x - 25
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How do you solve a triangle ABC where b=125 c=162 B=40 degrees?
Answer:
Angle A = 83.59° (2 d.p.)
Angle C = 56.41° (2 d.p.)
Side a = 193.25 (2 d.p.)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Sine Rule} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Given:
b = 125c = 162B = 40°Substitute the given values into the Sine Rule formula:
[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]
Solve for angle C:
[tex]\implies \dfrac{\sin 40^{\circ}}{125}=\dfrac{\sin C}{162}[/tex]
[tex]\implies \sin C=\dfrac{162\sin 40^{\circ}}{125}[/tex]
[tex]\implies C=\sin^{-1}\left(\dfrac{162\sin 40^{\circ}}{125}\right)[/tex]
[tex]\implies C=56.4136175...^{\circ}[/tex]
Interior angles of a triangle sum to 180°. Therefore:
[tex]\implies A+B+C = 180^{\circ}[/tex]
[tex]\implies A = 180^{\circ}-B-C[/tex]
[tex]\implies A = 180^{\circ}-40^{\circ}-56.4136175...^{\circ}[/tex]
[tex]\implies A = 83.5863824...^{\circ}[/tex]
Finally, to find a, substitute the found angles and sides into the Sine Rule and solve for a:
[tex]\implies \dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]
[tex]\implies \dfrac{\sin 83.5863824...^{\circ}}{a}=\dfrac{\sin 40^{\circ}}{125}[/tex]
[tex]\implies a=\dfrac{125\sin 83.5863824...^{\circ}}{\sin 40^{\circ}}[/tex]
[tex]\implies a=193.248396...[/tex]
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC=53°, DE=8 and EC=6, Find AC.
AC=?
[tex]\it AC=2\cdot EC=2\cdot6=12[/tex]
prove that the continuous function of order 3 is continuous of order 1 after being differentiated twice.
We use the concepts of continuity and differentiability to prove that a continuous function of order 3 is continuous of order 1 after being differentiated twice.
Let us assume the function x³ as the function of order 3. We know that its 1st derivative will be 3x² and its 2nd derivative will be, 6x. Now, let's check both of their continuities at any point "a" on the function. By putting a limit x tending to a to the function
= lim (x³) = a³
x→a
and putting a directly to the equation i.e, f(a) = a³ therefore, x³ is a continuous function at a. Similarly, by putting a limit x tending to a to the function
= lim (6x) = 6a
x→a
and putting a directly to the equation i.e, f(a) = 6(a) therefore, 6x is also a continuous function at a. Hence we can say that the continuous function of order 3 is continuous of order 1 after being differentiated twice.
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What is the result if the product of 5 and 75 is divided by 3?
Answer: 125
Step-by-step explanation: product of 5 and 75 = 5*75 = 375 divided by 3 which is 375/3 = 125.
Chang has two coupons for. A printer coupon a has 14$ rebate on a 75$ printer
Coupon b has 15%off of a 75 $ printer choose the coupon that gives the lower prize
Answer:
The coupon that gives $14 rebate off $75 gives a lower price
Step-by-step explanation:
Let's figure out what percentage of $75 the $14 rebate coupon is
If this percentage is greater than 15% then the $14 rebate coupon gives a better discount; if not the 15% discount offers a better buy
To find what % $14 is of the $75 cost of printer, divide 14 by 75 and multiply by 100 to convert to %:
[tex]\dfrac{14}{75} \times 100 = 18.67\%\\\\[/tex]
Since 18.67% is greater than 15%, getting $14 off $75 will give a lower price
If the circulation for newspaper 1 is 386 thousand more than the circulation for newspaper 2, and their combined circulation is 2514 thousand, find the circulation for each newspaper.
The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 4.7 per week. Find the probability of the following events.
A. No accidents occur in one week.
Probability =
B. 10 or more accidents occur in a week.
Probability =
C. One accident occurs today.
Probability =
A. No accidents occur in one week. Probability = 0.0113
B. 10 or more accidents occur in a week. Probability = 0.0018
C. One accident occurs today. Probability =0.2122
A. No accidents occur in one week.
Probability = e^(-4.7)
= e^(-4.7)
= 0.0113
B. 10 or more accidents occur in a week.
Probability = 1 - e^(-4.7)(1 + 4.7 + (4.7^2)/2 + (4.7^3)/6 + (4.7^4)/24 + (4.7^5)/120)
= 1 - e^(-4.7)(1 + 4.7 + 22.09 + 100.521 + 470.4724 + 2,054.085)
= 1 - e^(-4.7)(3,648.78)
= 1 - 0.0050
= 0.0018
C. One accident occurs today.
Probability = 4.7e^(-4.7)
= 4.7e^(-4.7)
= 0.2122
The probability of no accidents occurring in one week is 0.0113, the probability of 10 or more accidents occurring in one week is 0.0018, and the probability of one accident occurring today is 0.2122. These probabilities are calculated using the Poisson distribution with a mean of 4.7 accidents per week.
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What is the answer for this equation -9b+2n-4+2b
Answer: Add −9b and 2b. −7b + 2n −4
What common fraction is halfway between 1/8 and 1/10 on a number line?
Answer: 9/80
Step-by-step explanation:
1/8 = 10/80
1/10 = 8/80
9/80 is fraction between 1/8 and 1/10
Have A Good Day :)
Tom wishes to purchase a property that has been valued at $300,000. He has $30,000 available as a deposit, and will require a mortgage for the remaining amount. The bank offers him a 25-year mortgage at 2% interest. Calculate his monthly repayments.
Tom's monthly mortgage repayment will be an amount of $1,144.41.
To calculate Tom's monthly mortgage repayment, we can use the formula:
[tex]M = P [ i(1 + i)^n ] / [ (1 + i)^n -1 ][/tex]
Where:
M = monthly repayment
P = the principal amount (loan amount) = $300,000 - $30,000 = $270,000
i = monthly interest rate = 2%/12 = 0.02/12 = 0.0017
n = number of months = 25 years x 12 months/year = 300 months
Plugging in the values:
M = $270,000 [ 0.0017(1 + 0.0017)³⁰⁰ ] / [ (1 + 0.0017)³⁰⁰ – 1 ]
M = $1,144.41
Thus, his monthly mortgage repayment will be $1,144.41.
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Kayla was asked to rewrite the polynomial expression x2 + 6x + 9 how could she rewrite the polynomial
When Kayla was instructed to rewrite the polynomial expression x2 + 6x + 9, she wrote [tex]x^2+2 x-3+3^2=(x+3)^2[/tex].
What is a polynomial ?Factor [tex]$ x^2+6 x+9: \quad(x+3)^2$[/tex]
[tex]$$x^2+6 x+9$$[/tex]
Rephrase in the manner of [tex]$a^2+2 a b+b^2$[/tex] :
[tex]$9=3^2$[/tex]
[tex]$6 x=2 x \cdot 3$\\$=x^2+2 x \cdot 3+3^2$[/tex]
Using the Perfect Square Formula : [tex]$\quad a^2+2 a b+b^2=(a+b)^2$[/tex]
[tex]$$\begin{aligned}& x^2+2 x-3+3^2=(x+3)^2 \\& =(x+3)^2\end{aligned}$$[/tex]
An expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables is said to be a polynomial. Variables, which are sometimes known as indeterminates, and coefficients make up a polynomial. x2 4x + 7 is an illustration of a polynomial of one uncertain x.
An expression with a single or a number of terms is referred to as a polynomial. The words "polynomial" and "nomial," which are two distinct phrases, are the origins of the term. Nominal is another word for many, while poly is another word for many. An algebraic expression with two or more algebraic terms is referred to as a polynomial.
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Whats the answer please ?
The graph of the quadratic function, y = -x² + 8·x - 15, created with MS Excel is attached.
The roots are; (3, 0) and (5, 0)
The location of the vertex of a parabola is; (4, 1)
What is a parabola?A parabola is a curve formed uy the path of an object that moves such that the distance of the object from a fixed point is the same as the distance of the point from a fixed line.
The specified function is f(x) = -x² + 8·x - 15
The equation is a quadratic equation, and the shape of the graph of the function is a parabola.
The points that can be used to graph tjhe function, obtained using MS Excel are;
x [tex]{}[/tex] f(x)
2 [tex]{}[/tex] -3
3 [tex]{}[/tex] 0
4 [tex]{}[/tex] 1
5 [tex]{}[/tex] 0
6 [tex]{}[/tex] -3
The roots are the x-intercept of the graph, which are the points the graph intersects the x-axis, which are the points where, y = 0.
The roots obtained from the values in the above table are; (3, 0), and (5, 0)
The vertex point is the highest point on the graph. The heighest point or vertex is the point where the y-value is maximum
From the table and the attached graph, the vertex is the point (4, 1)
The vertex of the parabola, obtained using the graph is (4, 1)
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Simplest form 6m-2(-3m+8)
[tex]6m - 2( - 3m + 8)\\ Multiplying :\ each \\ term \\ - 18m + 48m + 6m - 16 \\ - 18m + 54m - 16 \\ 36m - 16 \\ 2(18m - 8)[/tex]
can someone please help me with this question???????? please the deadline is tomorrow
Answer:
D or 12.8
Step-by-step explanation:
Distance (d) = √(-2 - 8)2 + (9 - 1)2
= √(-10)2 + (8)2
= √164
= 2√41
= 12.806248474866
HOPE THIS HELPS AND PLEASE GIVE BRAINLIESTAnswer:
Hello
Hi 2√41 approximately equals to 12.8, good luck and please see the file below for the answer.
It is D.
3) Lina has 20 boxes of markers. Next year, she plans to buy 20% more boxes. How many
boxes will she have in all? I need step by step explanation, thanks.
Answer:
44 boxes
Step-by-step explanation:
You have to find 20% of 20.
20% = 1/5
1/5 of 20 is 4
So next year she will buy 24 boxes
If you add them together, she will have 44 boxes in all
A moving object travels 350 feet in 5 seconds assuming that the object travels at a constant speed , When dropped from a height of 350 feet , It takes exactly 5 seconds for the stone to hit the ground
The speed when the object and dropped from a height of 350 feet and takes exactly 5 seconds is 70 feet per seconds.
How to calculate the speed?Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed. It's a scalar quantity
In this situation, when dropped from a height of 350 feet, it takes exactly 5 seconds for the stone to hit the ground.
The speed will be:
= Distance / Time
= 350 / 5
= 70 feet per seconds
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Complete question
A moving object travels 350 feet in 5 seconds assuming that the object travels at a constant speed , When dropped from a height of 350 feet , It takes exactly 5 seconds for the stone to hit the ground. Calculate the speed.
