Component form of u is (-18,13) and The magnitude of u is 22.2
What is a vector?A vector is a two-dimensional entity with both magnitude and direction. A vector can be visualized geometrically as a directed line segment.
The component form of a vector is an ordered pair that describes the change in x and y values
This is mathematically expressed as (Δx, Δy) where Δx=x₂-x₁ and Δy=y₂-y₁
Given ;
Initial points of the vector as (14,-6)
The terminal point of the vector is (-4,7)
Here x₁=14,x₂=-4, y₁=-6,y₂=7
The component form of the vector u is (-4-14,7--6) =(-18,13)
Finding the Magnitude of the vector
u=√(x₂-x₁)²+(y₂-y₁)²
u=√-18²+13²
u=√324+169
u=√493
u=22.2
Therefore the Component form of u is (-18,13) and The magnitude of u is 22.2
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The maximum possible correspondence or correlation between two variables is represented by a Pearson product-moment coefficient of:
Correlation analysis is meant to determine the strength of a linear
relationship between variables.
A true statement of correlation analysis is that; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.The complete question is as below:-
Which of the following statements is true of the correlation analysis? The null hypothesis for the Pearson correlation coefficient states that there is always a strong association between two variables. The larger the correlation coefficient, the weaker the association between two variables. The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero. The Pearson correlation coefficient measures the degree of linear association that ranges from 1.0 to 10.0. The Pearson correlation coefficient measures the degree of linear association between three variables.
What is correlation analysis?Correlation analysis is a test to determine the presence and or amount of relationship that exists between variables.
During a hypothesis test aimed at determining the existence of a correlation between variables, the null and alternative hypotheses are as follows;
The null hypothesis, H₀: There are no relationships between the variables
H₀: r = 0
The alternative hypothesis, Hₐ: The variables have an association
Hₐ: r ≠ 0
Therefore, the true statement of the correlation analysis is; The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero.
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Find the slant height x of the pyramid shown, to the nearest tenth.
5 mm
9 mm
9 mm
The slant height of the pyramid can be calculated using Pythagoras theorem. Therefore, the slant height is 6.7 mm
How to find slant height of a pyramid?
The slant height x, can be found using Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenusea and b are other two legs.Therefore,
x² = 4.5² + 5²
x² = 20.25 + 25
x² = 45.25
x = √45.25
x = 6.72681202354
x = 6.7 mm
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please simplify the answer
Answer:
[tex] 56\: in^2[/tex]
Step-by-step explanation:
Surface area of the net = 4* Area of one triangle + Area of square[tex] = 4*\frac{1}{2}*4*5 + (4)^2[/tex][tex] = 40 + 16[/tex][tex] = 56\: in^2[/tex]32, 28, 36, 38, 40, 26, 29, 37 in least to greatest order
Answer:
26, 28, 29, 32, 36, 37, 38, 40
Step-by-step explanation:
Circle O has secant lines AB and BD intersects circle O at points C and D. if AD=40 degrees and BC=120 degrees, find
Answer:
Angle AED: 40
Angle BEC: 105
Explanation:
1) To find Angle AED, you have to do arc BC minus arc AD then divide by 2.
120 - 40 = 80.
80 / 2 = 40
2) To find Angle BEC, you have to do arc BA + CD then divide by 2. But that's only angle CED. You'll have to double the number because BEA is vertical; then minus 360.
62 + 88 = 150
150 / 2 = 75
75 times 2 = 150
360 - 150 = 210
210 / 2 = 105
- You'll divide 210 by 2 because of the vertical angles of AED and BEC.
Shawnee richards and her husband have decided to purchase a cabin in the county. they have applied for a mortgage loan of 80,000 at 6% for a period of 25 years. they will pay it off in equal monthly payments that include interest.
Using it's formula, it is found that their monthly payments for the mortgage loan will be of $515.45.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, we have that the parameters are given as follows:
P = 80000, r = 0.06, n = 25 x 12 = 300.
Hence:
r/12 = 0.06/12 = 0.005.
Then, the monthly payment will be of:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 80000\frac{0.005(1.005)^{300}}{(1.005)^{300} - 1} = 515.45[/tex]
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What is the distance between the following points?
Answer:
if im not mistaken the andswer is D
What is the solution of 4 + StartRoot 5 x + 66 EndRoot = x + 10? x = –10 x = 3 x = –10 or x = 3 no solution
The solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
4 + √(5x + 66) = x + 10
Subtract 4 from both sides
So, we have
√(5x + 66) = x + 6
Take the square of both sides
5x + 66 = x² + 12x + 36
So, we have
x² + 7x - 30 = 0
When expanded, we have
x² + 10x - 3x - 30 = 0
So, we have
(x + 10)(x - 3) = 0
Solve for x
x = -10 and x = 3
Hence, the solution to the equation 4 + √(5x + 66) = x + 10 is x = -10 and x = 3
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Satoranaing
19100
Points C, D, and G lie on plane X. Points E and F lie on
plane Y.
X
B
A
Y
Intro
E
D
G
F
Which statements are true? Select three options.
There are exactly two planes that contain points A,
B, and F.
There is exactly one plane that contains points E, F,
and B.
The line that can be drawn through points C and G
would lie in plane X.
The line that can be drawn through points E and F
would lie in plane Y.
The only points that can lie on plane Y are points E
and F.
Done
The statements that are true about the given points on the line are; Options B, C and D
How to identify points on a Plane?
A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.
Let us check each of the given options;
A) There are exactly two planes that contain points A, B, and F;
If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.
Since we can't make two planes with them, then the statement is false.
B) There is exactly one plane that contains points E, F, and B;
Due to the same reasoning in part A, the statement is true assuming the points are not collinear.
C) The line that can be drawn through points C and G would lie in plane X;
The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.
D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.
E) The only points that can lie on plane Y are points E and F.
This statement is false because infinite points can lie on a plane.
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what is the function
Answer: Exponential
After plotting the points as shown in the image, it is obvious they follow an exponential trend.
10 fish are swimming in the ocean, 6 of them drown, how many are left?
Answer:
10
Step-by-step explanation:
Fish can't drown.
The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t). What does the second coordinate of the vertex of the quadratic function represent?
the minimum height of the baseball
the time at which the baseball hits the ground
the time at which the baseball hits the maximum height
the maximum height of the baseball
The correct answer is option D which is the second coordinate of the vertex of the quadratic function that represents the maximum height of the baseball.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The second coordinate of the vertex of the quadratic function represents the maximum height of the ball.
The height of a baseball hit from a bat is modeled by a quadratic function of time, h(t)
General form of h(t) will be -16x² + v(t) + h
Where v represents initial velocity and h represents the initial height
h(t) represents the height of the baseball
h(t) is negative so the height reaches the maximum
vertex (h,k) represents maximum height (k) when time t=h
So the second coordinate of the vertex of the quadratic function represents the maximum height of the ball.
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Answer: D
Step-by-step explanation
How do I find the vertex function
Answer:
oh ok. So, first, you get the equation in the form y=ax2+bx+c. Next, you calculate -b / 2a. This is the x-coordinate of the vertex. Then finally, you plug in the value of -b / 2a into the equation into the x variable and solve for the y variable. This is the coordinate of the vertex.
Step-by-step explanation:
Hope this helps!
Click on the correct symbol to compare the measurements.
19 in. 2 yd 4 in.
Answer:
I don't see any symbols, so I'll simply compare the two measurements.
Step-by-step explanation:
2 yards and 4 inches
Each yard has 3 feet. Each foot has 12 inches. The total inches in 3 yards is therefore:
(2 yards)*(3 feet/yard)*(12 inches/Foot) = 72 inches [Note how the units cancel to leave only inches]
This means we have a total of 72 + 4 inches = 76 inches total
19 Inches
Compared to 19 inches, 72 inches is almost 3.79 times longer.
what is the value of 50 US dollar in philippine money?
Answer:
Answer is $2,637.38
Step-by-step explanation:
a data set has a mean of 5.3 and a mean absolute deviation of 2. which data points fall within the mean absolute deviation?
select all the correct answers.
2.9
3.1
4.5
6.8
07.3
The data points that fall within the mean absolute deviation are 2.9 and 3.1.
What is the mean absolute deviation?The mean absolute deviation is the mean average distance between every data point and the mean of the data set.
From the information given:
Mean of the data set = 5.3Mean absolute deviation = 2The mean absolute deviation is:
= (|5.3 - 2|)/1
= 3.3
Thus, the data points that fall within the mean absolute deviation are 2.9 and 3.1.
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In August, Sara and Mel decided to spend a week fishing. On the first day, Sara caught 2 fish, and Mel caught 4 fish. The next day, Sara had 4 fish altogether, and Mel had 8 fish. On the third day Sara had 6 fish altogether while Mel had 12 fish altogether.
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
1. If the pattern continues, how many fish will each of them have caught by the end of the week? Fill in the rest of the chart.
Fish caught altogether:
Days
1
2
3
4
5
6
7
Sara
2
4
6
Mel
4
8
12
2. What is the pattern that describes how many fish Sara caught each day? What is the pattern that describes how many fish Sara caught altogether?
3. What is the pattern that describes how many fish Mel caught each day? What is the pattern that describes how many fish Mel caught altogether?
4. What do you notice when you compare Sara’s pattern and Mel’s Pattern?
5. If Sara and Mel continued fishing, how many fish would they have caught by day 10?
this is worth 100 points
Turn into coordinates pair
(2,4)(4,8)(6,12)Slope
m=8-4/4-2=2Equation
y=2x#1
A week is of 7 days
total fishes Sara has=2(7)=14
Total mel will have
y=14(2)=28fishes#2
The each day Sara caught 2fishes
pattern for Sara 's total
2dd is days
#3
Mel also caught 2(2)=4 fishes a day
Mel caught all together is 2(Sara)
#4
They are in proportion to each other
#5
Sara would have 10(2)=20fishes
Mel would have.
20(2)=40fishesAnswer:
Q1)
The number of fish Sara caught increases by 2 each day.
The number of fish Sara caught increases by 4 each day.
[tex]\large \begin{array}{| c | c | c |}\cline{1-3} & \sf SARA& \sf MEL\\\sf Days & \sf fish\:caught & \sf fish\:caught \\& \sf altogether & \sf altogether\\\cline{1-3} 1 & 2 & 4 \\\cline{1-3} 2 & 4 & 8 \\\cline{1-3} 3 & 6 & 12 \\\cline{1-3} 4 & 8 & 16 \\\cline{1-3} 5 & 10 & 20 \\\cline{1-3} 6 & 12 & 24 \\\cline{1-3} 7 & 14 & 28 \\ \cline{1-3}\end{aligned}[/tex]
Q2)
Sara caught 2 fish each day.
The pattern that describes how many fish Sara caught altogether is:
2 times the number of days
Q3)
Mel caught 4 fish each day.
The pattern that describes how many fish Mel caught altogether is:
4 times the number of days
Q4)
The number of fish Mel caught altogether is twice the number of fish Sara caught altogether.
Q5)
The number of fish Sara and Mel would have caught by day 10:
Sara = 10 × 2 = 20 fishMel = 10 × 4 = 40 fishcalculate the angles marked with letters
Answer:
I think m is 70 and n is 40 because I did a bunch of adding and subtracting
will give 25 points for a short answer
No, to be parallel the two given angles would need to be the same(corresponding angles)
The two lines are not parallel.
In circle O, ST is a diameter.
Circle O is shown. Line segment S T is a diameter. Line segments R O and U O are radii. Angles R O U and U O T are congruent. The measure of arc R S is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
What must be the value of x?
22.0
25.0
25.4
37.2
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant. The correct option is B.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
Given the measure of arc, RS is (2 x + 8) degrees, the measure of arc R U is (3 x minus 14) degrees, and the measure of arc U T is (3 x minus 14) degrees.
(3x-14)° + (3x-14)° + (2x+8)° = 180°
8x -20 = 180
8x = 200
x = 25
Hence, the correct option is B.
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find the slope of the line
x-intercept is twice as y-intercept
Answer:
-1/2
Step-by-step explanation:
It mentions that the x-intercept is equal to twice the y-intercept.
=============================================================
Let :
⇒ x-intercept = (2a, 0)
⇒ y-intercept = (0, a)
==============================================================
Slope formula :
m = y₂ - y₁ / x₂ - x₁
=============================================================
Solving :
⇒ m = a - 0 / 0 - 2a
⇒ m = a / -2a
⇒ m = -1/2
[tex]\sf\large\green{\underbrace{\red{Question*}}}:[/tex]
[tex] \mathbb\blue{SOLVE} [/tex]
[tex] \pink{1. \: \: \: \: \: \: (3 - x)(x + 2) = 0}[/tex]
[tex] \pink{2. \: \: \: \: \: {(q + 2)}^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\sf{\color {red}{Solve:}}}}}}[/tex]
[tex] \sf \red{1. \: (3x - x) (x + 2) = 0}[/tex]
[tex] \sf \red{2. \: (q + 2)^{2} - 40}[/tex]
[tex]\large{\underline{\underline{\pmb{\frak {\color {blue}{Answer:}}}}}}[/tex]
2.soln:
(q + 2)² - 40
=> (q)² + 2.q.2 + (2)² - 40
=> q² + 4q + 4 - 40
=>q² + 4q - 36
Here, a = 1, b = 4 and c = - 36
By, using Quadratic formula
See the attachment
MODELING WITH MATHEMATICS Three tennis balls are stored in a cylindrical container with a height of 8 inches and a radius of 1.43 inches. The circumference of a tennis ball is 8 inches. Round your answers to the nearest hundredth.
I just need help with part b
A picture shows three tennis balls placed one above another in a cylindrical container.
a. Find the volume of a tennis ball. Round your answer to the nearest hundredth.
The volume of a tennis ball is about
cubic inches.
Answer is about 8.65
b. Find the amount of space within the cylinder not taken up by the tennis balls. Round your answer to the nearest hundredth.
The volume of the space within the cylinder not taken up by the tennis balls is about
cubic inches.
The volume of a tennis ball is about 8.65 cubic inches
The volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
Calculating volumeFrom the question, we are to determine the volume of a tennis ball
From the given information,
The circumference of a tennis ball is 8 inches
That is,
C = 2πr (C is circumference)
8 = 2πr
∴ r = 8/2π
r = 4/π inches
This the radius of a tennis ball
Now, for the volume of a tennis ball
Using the formula for calculating the volume of a sphere
[tex]V = \frac{4}{3}\pi r^{3}[/tex]
Then, the volume of a tennis is
[tex]V = \frac{4}{3}\pi \times (\frac{4}{\pi})^{3}[/tex]
[tex]V = \frac{4}{3}\pi \times \frac{64}{\pi^{3}}[/tex]
[tex]V = \frac{256}{3\pi^{2}}[/tex]
V = 8.64607 cubic inches
V ≅ 8.65 cubic inches
Hence, the volume of a tennis ball is about 8.65 cubic inches
b. To find the amount of space within the cylinder not taken up by the tennis balls
First, we will calculate the volume of the cylinder
Using the formula for calculating the volume of a cylinder
V = πr²h
Where V is the volume
r is the radius
and h is the height
From the given information,
r = 1.43 inches
h = 8 inches
Putting the parameters into the formula, we get
V = π × 1.43² × 8
V = 16.3592π
V = 51.39 cubic inches
This is the volume of the cylinder
Now, for the amount of space within the cylinder not taken up by the tennis balls
Since there are three tennis balls,
The amount of space not taken up will be
51.39 cubic inches - 3(8.65 cubic inches)
51.39 cubic inches - 25.95 cubic inches
= 25.44 cubic inches
Hence, the volume of the space within the cylinder not taken up by the tennis balls is about 25.44 cubic inches
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PLEASE HELP ME ASAP
Does the series converge or diverge? If it converges, what is the sum? Show your work
The series is a convergence series and the sum of the series is -8/3
The type of the seriesThe series is given as:
[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]
The above series has the following properties:
First term; a = -4Common ratio, r = -1/2Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
The sum of the seriesThis is calculated using:
[tex]S_{\infty} = \frac{a}{1 -r}[/tex]
So, we have:
[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]
Evaluate the sum
[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]
Evaluate the quotient
[tex]S_{\infty} = \frac{-8}{3}[/tex]
Hence, the sum of the series is -8/3
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The inequality described can be written as:
y < 3x + 2.
How to get the inequality?First, we know that we have a dashed line, and the region to the left of that line is shaded, then we will have:
y < line.
The linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we know that the line passes through (-3, -7) and (0, 2), so the slope is:
[tex]a = \frac{2 - (-7)}{0 - (-3)} = 9/3 = 3[/tex]
And because the line passes through (0, 2), the y-intercept is 2, then the inequality is:
y < 3x + 2.
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PLEASE HELP I’LL MAKE YOU THE BRAINIEST Find the area of the parallelogram
Answer:
A=5.4×4.4=23.76 in
because the are of the paralelogram is base ×high
Fill in the missing number in this sequence:
324, 108, 36, 12, { }
Answer:
4
Step-by-step explanation:
Every number is divided by 3
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the missing number in the sequence
[tex]\star~\mathrm{324,108,36,12,(~~)}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Take a look at the common ratio.Since every number here is divided by 3, we divide 12 by the common ratio, 3:
[tex]\mathrm{12\div3}[/tex]
[tex]\star~\star~\mathrm{4}\star~\star[/tex]
Hope it helps you out! :)
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
Persevere with Problems The table shows the highway fuel economy of various popular vehicles.
The mean absolute deviation of highway fuel economy of various popular vehicles is 4.9
How to find mean absolute deviation?Find the mean of the data set
= (38 + 48 + 25 + 35 + 33 + 37 + 32 + 34 + 23 + 30) / 10
= 335 / 10
= 33.5
Mean deviation of each set;
38 - 33.5 = 4.5
48 - 33.5 =14.5
25 - 33.5 = -8.5
35 - 33.5 = 1.5
33 - 33 .5 = -0.5
37 - 33.5 = 3.5
32 - 33.5 = -1.5
34 - 33.5 = 0.5
23 - 33.5 = -10.5
30 - 33.5 = -3.5
Absolute deviation of each value
|4.5| = 4.5
|14.5| = 14.5
|8.5| = 8.5
|1.5| = 1.5
|-0.5| = 0.5
|3.5| = 3.5
|-1.5| = 1.5
|0.5| = 0.5
|-10.5| = 10.5
|-3.5| = 3.5
Total absolute deviation = 4.5 + 14.5 + 8.5 + 1.5 + 0.5 + 3.5 + 1.5 + 0.5 + 10.5 + 3.5
= 49
Mean absolute deviation = Total absolute deviation / mean
= 49/10
= 4.9
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A parade route is 3 4 mile long. there will be a refreshment stand at the beginning and end of the route. there will also be 8 refreshment stands along the route. all the refreshment stands are equally-spaced apart. how far apart are the refreshment stands in feet?
396
440
495
520
The distance between the refreshment stands is 440 feet
Calculating distanceFrom the question, we are to determine how far apart are the refreshment stands in feet
From the given information,
The parade route is 3/4 mile long
and
There are refreshment stands at the beginning and end of the route. And there will also be 8 refreshment stands along the route.
This means there will be 10 refreshment stands in all.
If there are 10 refreshment stands in all, then there will be 9 spaces between the refreshment stands.
∴ The distance between any two refreshment stands will be
3/4 mile ÷ 9 = 3/36 mile = 1/12 mile
Now, we will convert this to feet
NOTE: 1 mile = 5280 feet
∴ 1/12 mile = 1/12 × 5280 feet
= 440 feet
Hence, the distance between the refreshment stands is 440 feet.
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Alice is playing checkers against a computer and has won 8 games out of the 12 she's played so far.
Alice must win the next consecutive games to reach a winning percentage of 80%. After that, losing
consecutive games
will bring her winning percentage down to 50%.
Answer:
Step-by-step explanation:
[tex]\frac{8+x}{12+x} =\frac{80}{100} =\frac{4}{5} \\40+5x=48+4x\\5x-4x=48-40\\x=8[/tex]
so she wins next 8 consecutive games to reach winning percentage of 80%.
let she loses next y games to reach winning percentage of 50 %.
[tex]\frac{16}{12+8+y} =\frac{50}{100} =\frac{1}{2} \\\frac{16}{20+y} =\frac{1}{2} \\32=20+y\\y=32-20=12y=12[/tex]
Hence she loses next 12 games to reach winning percentage of 50 %.