Answer:
The base is 6cm
Step-by-step explanation:
Using [tex]\frac{1}{2}[/tex]bh=area, you just plug in 6 for h and 18 for area and solve. The formula should be 3b=18, which equals 6
The solution is Option D.
The length of the base of the triangle is B = 6 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the area of the triangle be represented as A
Now , the value of A = 18 cm²
Let the base of the triangle be B
Let the height of the triangle be H = 6 cm
Now , area of the triangle = ( 1/2 ) x Length x Base
Substituting the values in the equation , we get
18 = ( 1/2 ) x B x 6
18 = 3B
Divide by 3 on both sides of the equation , we get
B = 6 cm
Hence , the base length of the triangle is B = 6 cm
To learn more about triangles click :
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Want Brainliest? Get this correct , Which of the two functions below has the smallest minimum y-value?
Answer:
B. g(x)
Step-by-step explanation:
g(x) is a function of odd degree, so will tend toward negative infinity as an extreme value.
f(x) is an even-degree function with a positive leading coefficient. Its minimum value is -2.
g(x) has the smallest minimum value
An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the same height. If the target is 60 feet from the archer, how far below the bullseye (in feet) will the arrow hit the target
Answer:
1.84feetStep-by-step explanation:
Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;
Range [tex]R = U\sqrt{\frac{H}{g} }[/tex]
U is the velocity of the arrow
H is the maximum height reached = distance below the bullseye reached by the arrow.
R is the horizontal distance covered i.e the distance of the target from the archer.
g is the acceleration due to gravity.
Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?
On substitution,
[tex]60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}[/tex]
Squaring both sides we have;
[tex](\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet[/tex]
The arrow will hit the target 1.84feet below the bullseye.
Answer:
8.7
Step-by-step explanation:
on edge . You're welcome
Solve x^2 + 5x+6 = 0
Answer:
X=-2or,-3
Step-by-step explanation:
X^2+5x+6=0
or,x^2+(2+3)x+6=0
or,x^2+2x+3x+6=0
or,x(x+2)+3(x+2)=0
or,(x+3) (x+2)=0
Either,
x+3=0 x+2=0
or,x=-3 or,x=-2
Therefore,the value if x is -2 or -3 .
I HOPE IT WILL HELP YOU
About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?
(a) The probability that both will be hopelessly romantic is
0.0361.
(Round to four decimal places as needed.)
(b) The probability that at least one person is hopelessly romantic is
0.3439.
(Round to four decimal places as needed.)
Answer:
a)
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
Step-by-step explanation:
a)
Given data population proportion 'p' = 19% =0.19
q = 1-p = 1- 0.19 =0.81
Given two people are randomly selected
Given n = 2
Let 'X' be the random variable in binomial distribution
[tex]P(X=r) =n_{C_{r} } p^{r} q^{n-r}[/tex]
The probability that both will be hopelessly romantic is
[tex]P(X= 2) =2_{C_{2} } (0.19)^{2} (0.81)^{2-2}[/tex]
P(X = 2) = 1 × 0.0361
The probability that both will be hopelessly romantic is
P(X = 2) = 0.0361
b)
The probability that at least one person is hopelessly romantic is
P( X>1) = 1-P(x<1)
= 1 - ( p(x =0)
= [tex]1- 2_{C_{0} } (0.19)^{0} (0.81)^{2-0}[/tex]
= 1 - (0.81)²
= 1 -0.6561
= 0.3439
The probability that at least one person is hopelessly romantic is
P( X>1) = 0.3439
Circle V is shown. Line segment T V is a radius with length 14 feet. In circle V, r = 14ft. What is the area of circle V? 14Pi feet squared 28Pi feet squared 49Pi feet squared 196Pi feet squared
Answer: The area of circle V is 196π ft² (196Pi feet squared)
Step-by-step explanation:
From the equation for area of a circle,
A = πr²
Where A is the area of the circle
r is the radius of the circle
In Circle V, the radius, r of the circle is 14 feet
That is,
r = 14ft
Hence, Area is
A = π × (14ft)²
A = π × 14ft × 14ft
A = 196π ft²
Hence, the area of circle V is 196π ft² (196Pi feet squared)
Answer:
The answer is D on Edge 2020
Step-by-step explanation:
I did the Quiz
If h = 12 units and r = 4 units, what is the volume of the cone shown above? Use 3.14 for .
Answer:
200.96 units
Step-by-step explanation:
Use the formula for the volume of a cone [tex]V=\pi r^{2} \frac{h}{3}[/tex]
Plug in the values ([tex]\pi[/tex]=3.14) and multiply them all out
Answer:
≈ 201
Step-by-step explanation:
V= πr²h/3
V= 3.14*4²*12/3= 200.96 ≈ 201
what measurement do you use for surface area
Answer:
Step-by-step explanation:
Surface Area is the combined area of all two-dimensional surfaces of a shape. Just like ordinary area, the units are the squares of the units of length (that is, if a shape's sides are measured in meters, then the shape's area is measured in square meters
40 POINTS!!!! Which sequence of transformations will result in an image that maps onto itself?
Answer:
Option C.
Step-by-step explanation:
Let a point (x, y) has a sequence of transformations,
Option A).
Reflects across x-axis then the coordinates will be,
(x, y) → (x, -y)
Then reflects across the y-axis,
(x, -y) → (-x, -y)
Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.
Option B).
(x, y) rotate 90° counter clockwise about the origin.
(x, y) → (-y, x)
Then reflect across x-axis,
(-y, x) → (y, x)
Since coordinates of the image and the actual are not same therefore, image doesn't map itself.
Option C).
(x, y) when reflected across x-axis,
(x, y) → (x, -y)
Then reflected over the x-axis,
(x, -y) → (x, y)
In this option point (x, y) maps onto itself after these transformations.
Option D).
(x, y) rotated 90°counterclockwise about the origin
(x, y) → (-y, x)
Then translated up by 2 units.
(-y, x) → (-y, x+2)
Therefore, (x, y) gets changed after these transformations and doesn't maps itself.
Option (C) will be the answer.
Answer:
you have it correct the answer is option c
Step-by-step explanation:
A triangle has vertices A( -3, 4), B(6, 4) and C(2, -3). The triangle is translated 4 units down and then rotated 90° clockwise. What will be the coordinates of A’’ after both transformations?
Answer:
The coordinates of point A after both transformations becomes (0, 3)
Step-by-step explanation:
Translation 4 units down is equivalent to -4 units in the y direction, therefore, we have;
A(-3, 4), B(6, 4), and C(2, -3) becomes
A(-3, 4 - 4), B(6, 4 - 4), and C(2, -3 - 4) which is A(-3, 0), B(6, 0), and C(2, -7)
Rule on operation on coordinates due to rotation of a triangle 90° clockwise is as follows;
For vertex coordinate, (x, y), we change it to (y, -x)
Therefore, we have the coordinates of the point A(-3, 0) after a rotation of 90° clockwise becomes A(0, 3).
Harper's Index reported that the number of (Orange County, California) convicted drunk drivers whose sentence included a tour of the morgue was 506, of which only 1 became a repeat offender.
a. Suppose that of 1056 newly convicted drunk drivers, all were required to take a tour of the morgue. Let us assume that the probability of a repeat offender is still p= 1/596. Explain why the Poisson approximation to the binomial would be a good choice for r = number of repeat offenders out of 963 convicted drunk drivers who toured the morgue.
The Poisson approximation is good because n is large, p is small, and np < 10.The Poisson approximation is good because n is large, p is small, and np > 10. The Poisson approximation is good because n is large, p is large, and np < 10.The Poisson approximation is good because n is small, p is small, and np < 10. What is λ to the nearest tenth?
b. What is the probability that r = 0? (Use 4 decimal places.)
c. What is the probability that r > 1? (Use 4 decimal places.)
d. What is the probability that r > 2? (Use 4 decimal places.)
e. What is the probability that r > 3? (Use 4 decimal places.)
Answer:
a. The Poisson approximation is good because n is large, p is small, and np < 10.
The parameter of thr Poisson distribution is:
[tex]\lambda =np\approx1.6[/tex]
b. P(r=0)=0.2019
c. P(r>1)=0.4751
d. P(r>2)=0.2167
e. P(r>3)=0.0789
Step-by-step explanation:
a. The Poisson distribution is appropiate to represent binomial events with low probability and many repetitions (small p and large n).
The approximation that the Poisson distribution does to the real model is adequate if the product np is equal or lower than 10.
In this case, n=963 and p=1/596, so we have:
[tex]np=963*(1/596)\approx1.6[/tex]
The Poisson approximation is good because n is large, p is small, and np < 10.
The parameter of thr Poisson distribution is:
[tex]\lambda =np\approx1.6[/tex]
We can calculate the probability for k events as:
[tex]P(r=k)=\dfrac{\lambda^ke^{-\lambda}}{k!}[/tex]
b. P(r=0). We use the formula above with λ=1.6 and r=0.
[tex]P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\[/tex]
c. P(r>1). In this case, is simpler to calculate the complementary probability to P(r<=1), that is the sum of P(r=0) and P(r=1).
[tex]P(r>1)=1-P(r\leq1)=1-[P(r=0)+P(r=1)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\\\P(r>1)=1-(0.2019+0.3230)=1-0.5249=0.4751[/tex]
d. P(r>2)
[tex]P(r>2)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\\\P(r>2)=1-(0.2019+0.3230+0.2584)=1-0.7833=0.2167[/tex]
e. P(r>3)
[tex]P(r>3)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)+P(r=3)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\P(3)=1.6^{3} \cdot e^{-1.6}/3!=4.096*0.2019/6=0.1378\\\\\\P(r>3)=1-(0.2019+0.3230+0.2584+0.1378)=1-0.9211=0.0789[/tex]
Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6.
Write a probability model for this experiment, and use the probability model to predict how many times Stacy would spin a 6 if she spun 50 times. Give the probabilities as decimals, rounded to 2 decimal places.
Spinning 2:
Spinning 3:
Spinning 4:
Spinning 5:
Spinning 6:
Stacy would spin a 6 approximately
times in 50 tries.
Answer:
To compute the probabilities, just divide the number of times a number was landed by the total amount of outcomes.
Spinning 2: 30/120 = 0.25
Spinning 3: 19/120 = 0.16
Spinning 4: 25/120 = 0.21
Spinning 5: 29/120 = 0.24
Spinning 6: 17/120 = 0.14
Stacy would spin a 6 approximately 0.14*50 = 7 times in 50 tries.
Find all solutions of the equation in the interval [0, 2π).
Answer:
x = pi/6
x = 11pi/6
x = 5pi/6
x =7pi/6
Step-by-step explanation:
2 sec^2 (x) + tan ^2 (x) -3 =0
We know tan^2(x) = sec^2 (x) -1
2 sec^2 (x) +sec^2(x) -1 -3 =0
Combine like terms
3 sec^2(x) -4 = 0
Add 4 to each side
3 sec^2 (x) = 4
Divide by 3
sec^2 (x) = 4/3
Take the square root of each side
sqrt(sec^2 (x)) = ±sqrt(4/3)
sec(x) = ±sqrt(4)/sqrt(3)
sec(x) = ±2 /sqrt(3)
Take the inverse sec on each side
sec^-1 sec(x) = sec^-1(±2 /sqrt(3))
x = pi/6 + 2 pi n where n is an integer
x = 11pi/6 + 2 pi n
x = 5pi/6 + 2 pi n
x =7pi/6 + 2 pi n
We only want the solutions between 0 and 2pi
In a data distribution, the first quartile, the median and the means are 30.8, 48.5 and 42.0 respectively. If the coefficient skewness is −0.38
a) What is the approximate value of the third quartile (Q3 ), correct to 2 decimal places.
b)What is the approximate value of the variance, correct to the nearest whole number
Answer:
a) The third quartile Q₃ = 56.45
b) Variance [tex]\mathbf{ \sigma^2 =2633.31}[/tex]
Step-by-step explanation:
Given that :
[tex]Q_1[/tex] = 30.8
Median [tex]Q_2[/tex] = 48.5
Mean = 42
a) The mean is less than median; thus the expression showing the coefficient of skewness is given by the formula :
[tex]SK = \dfrac{Q_3+Q_1-2Q_2}{Q_3-Q_1}[/tex]
[tex]-0.38 = \dfrac{Q_3+30.8-2(48.5)}{Q_3-30.8}[/tex]
[tex]-0.38Q_3 + 11.704 = Q_3 +30.8 - 97[/tex]
[tex]1.38Q_3 = 77.904[/tex]
Divide both sides by 1.38
[tex]Q_3 = 56.45[/tex]
b) The objective here is to determine the approximate value of the variance;
Using the relation
[tex]SK_p = \dfrac{Mean- (3*Median-2 *Mean) }{\sigma}[/tex]
[tex]-0.38= \dfrac{42- (3 *48.5-2*42) }{\sigma}[/tex]
[tex]-0.38= \dfrac{(-19.5) }{\sigma}[/tex]
[tex]-0.38* \sigma = {(-19.5) }{}[/tex]
[tex]\sigma =\dfrac {(-19.5) }{-0.38 }[/tex]
[tex]\sigma =51.32[/tex]
Variance = [tex]\sigma^2 =51.32^2[/tex]
[tex]\mathbf{ \sigma^2 =2633.31}[/tex]
No-Toxic-Toys currently has $400,000 of equity and is planning an $160,000 expansion to meet increasing demand for its product. The company currently earns $140,000 in net income, and the expansion will yield $70,000 in additional income before any interest expense.
The company has three options: (1) do not expand, (2) expand and issue $160,000 in debt that requires payments of 9% annual interest, or (3) expand and raise $160,000 from equity financing. For each option, compute (a) net income and (b) return on equity (Net Income ÷ Equity). Ignore any income tax effects. (Round "Return on equity" to 1 decimal place.)
Answer:
Down below
Step-by-step explanation:
1. It does not expanda. Net income= $100,000 (as given in the question)
b. Return on equity= (net income)/(shareholder’s equity)
Shareholder’s equity= $400,000
Thus return on equity= 100000/400000 = 0.25 or 25%
2. It expands and issue $160,000 in debt
a. Net income= $100000 + 50000 – 12800 (debt interest 8% of $160000)
= $137,200
b. Return on equity= (net income)/(shareholder’s equity)
= 137200/400000
=0.343 or 34.3%
3. It expands and raises equity of $160000
a. Net Income= $100000 + 50000
= $150000
b. Return on equity= (net income)/(shareholder’s equity)
= 150000/(400000 + 160000)
Where ($560,000) 400000 + 160000 is shareholder’s equity
= 0.27 or 27%
Find the missing length, c, in the right triangle below. Round to the nearest tenth, if necessary. a. 76.3 in. b. 5.5 in. c. 3.5 in. d. 8.7 in.
Answer:
i think it's c.)3.5 i may be wrong
Step-by-step explanation:
Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall.What is the unit rate in which Martin paints in walls per gallon
Answer:
32/25 walls per gallon.
Step-by-step explanation:
Martin uses 5/8 Of a gallon of paint to cover 4/5 Of a wall
Hence 1 gallon would be 4/5÷5/8=
4/5 × 8/5= 32/25 walls per gallon.
A tank is filled with 1000 liters of pure water. Brine containing 0.04 kg of salt per liter enters the tank at 9 liters per minute. Another brine solution containing 0.05 kg of salt per liter enters the tank at 7 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 16 liters per minute. A. Determine the differential equation which describes this system. Let S(t)S(t) denote the number of kg of salt in the tank after tt minutes. Then
Answer:
The differential equation which describes the mixing process is [tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex].
Step-by-step explanation:
The mixing process within the tank is modelled after the Principle of Mass Conservation, which states that:
[tex]\dot m_{salt,in} - \dot m_{salt,out} = \frac{dm_{tank}}{dt}[/tex]
Physically speaking, mass flow of salt is equal to the product of volume flow of water and salt concentration. Then:
[tex]\dot V_{water, in, 1}\cdot c_{salt, in,1} + \dot V_{water, in, 2} \cdot c_{salt,in, 2} - \dot V_{water, out}\cdot c_{salt, out} = V_{tank}\cdot \frac{dc_{salt,out}}{dt}[/tex]
Given that [tex]\dot V_{water, in, 1} = 9\,\frac{L}{min}[/tex], [tex]\dot V_{water, in, 2} = 7\,\frac{L}{min}[/tex], [tex]c_{salt,in,1} = 0.04\,\frac{kg}{L}[/tex], [tex]c_{salt, in, 2} = 0.05\,\frac{kg}{L}[/tex], [tex]\dot V_{water, out} = 16\,\frac{L}{min}[/tex] and [tex]V_{tank} = 1000\,L[/tex], the differential equation that describes the system is:
[tex]0.71 - 16\cdot c_{salt,out} = 1000\cdot \frac{dc_{salt,out}}{dt}[/tex]
[tex]1000\cdot \frac{dc_{salt, out}}{dt} + 16\cdot c_{salt, out} = 0.71[/tex]
[tex]\frac{dc_{salt,out}}{dt} + \frac{2}{125}\cdot c_{salt,out} = \frac{71}{100000}[/tex]
(1,6) and (2,3) are on line?
Answer:
y = - 3x + 9 or (y - 6) = - 3(x - 1)
Step-by-step explanation:
I'm assuming you are looking for the equation of the line.
First, let's find the slope of the line, which we use equation (y1-y2) / (x1-x2)
x1: 1 x2: 2
y1: 6 y2: 3
(6-3) / (1-2) = 3 / -1 = -3
The slope of the line is -3.
The equation for slope-intercept form is y = mx + b, where m is slope and b is the y - intercept.
y = -3x+b
Now substitute a set of points in (any coordinates work). I'll use (1, 6)
6 = -3(1)+b
6 = - 3 + b
b = 9
So our equation in slope intercept form is y = - 3x + 9
You can also write this in point slope form, (y-y1) = m (x-x1) m is still slope
(y - 6) = - 3(x - 1)
In November Hillary drove 580 miles in her car the car travelled 33.5 miles for each gallon of petrol used
Petrol cost £1.09 per litre
1 gallon = 4.55 litres
Work out the cost of the petrol the car used in November
Answer:
T = £85.87
the cost of the petrol the car used in November is £85.87
Step-by-step explanation:
Given;
In November Hillary drove 580 miles in her car;
Distance travelled d = 580 miles
the car travelled 33.5 miles for each gallon of petrol used;
Fuel consumption rate r = 33.5 miles per gallon
Number of gallons N consumed by the car is;
N = distance travelled/fuel consumption rate
N = d/r = 580/33.5 = 17.3134 gallons
Given that;
Petrol cost £1.09 per litre
Cost per litre c = £1.09
1 gallon = 4.55 litres
Converting the amount of fuel used to litres;
N = 17.3134 gallons × 4.55 litres per gallon
N = 78.77612 litres
The total cost T = amount of fuel consumption N × fuel cost per litre c
T = N × c
T = 78.77612 litres × £1.09 per litre
T = £85.87
the cost of the petrol the car used in November is £85.87
A single card is drawn at random from a standard 52 card check. Work out in its simplest form
Answer:
1/52
Step-by-step explanation:
The time it takes for a planet to complete its orbit around a particular star is called the? planet's sidereal year. The sidereal year of a planet is related to the distance the planet is from the star. The accompanying data show the distances of the planets from a particular star and their sidereal years. Complete parts? (a) through? (e).
I figured out what
(a) is already.
(b) Determine the correlation between distance and sidereal year.
(c) Compute the? least-squares regression line.
(d) Plot the residuals against the distance from the star.
(e) Do you think the? least-squares regression line is a good? model?
Planet
Distance from the? Star, x?(millions of? miles)
Sidereal? Year, y
Planet 1
36
0.22
Planet 2
67
0.62
Planet 3
93
1.00
Planet 4
142
1.86
Planet 5
483
11.8
Planet 6
887
29.5
Planet 7
? 1,785
84.0
Planet 8
? 2,797
165.0
Planet 9
?3,675
248.0
Answer:
(a) See below
(b) r = 0.9879
(c) y = -12.629 + 0.0654x
(d) See below
(e) No.
Step-by-step explanation:
(a) Plot the data
I used Excel to plot your data and got the graph in Fig 1 below.
(b) Correlation coefficient
One formula for the correlation coefficient is
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}[/tex]
The calculation is not difficult, but it is tedious.
(i) Calculate the intermediate numbers
We can display them in a table.
x y xy x² y²
36 0.22 7.92 1296 0.05
67 0.62 42.21 4489 0.40
93 1.00 93.00 20164 3.46
433 11.8 5699.4 233289 139.24
887 29.3 25989.1 786769 858.49
1785 82.0 146370 3186225 6724
2797 163.0 455911 7823209 26569
3675 248.0 911400 13505625 61504
9965 537.81 1545776.75 25569715 95799.63
(ii) Calculate the correlation coefficient
[tex]r = \dfrac{\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2} -\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{9\times 1545776.75 - 9965\times 537.81}{\sqrt{[9\times 25569715 -9965^{2}][9\times 95799.63 - 537.81^{2}]}} \approx \mathbf{0.9879}[/tex]
(c) Regression line
The equation for the regression line is
y = a + bx where
[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}}\\\\= \dfrac{537.81\times 25569715 - 9965 \times 1545776.75}{9\times 25569715 - 9965^{2}} \approx \mathbf{-12.629}\\\\b = \dfrac{n \sum xy - \sum x \sum y}{n\sum x^{2}- \left (\sum x\right )^{2}} - \dfrac{9\times 1545776.75 - 9965 \times 537.81}{9\times 25569715 - 9965^{2}} \approx\mathbf{0.0654}\\\\\\\text{The equation for the regression line is $\large \boxed{\mathbf{y = -12.629 + 0.0654x}}$}[/tex]
(d) Residuals
Insert the values of x into the regression equation to get the estimated values of y.
Then take the difference between the actual and estimated values to get the residuals.
x y Estimated Residual
36 0.22 -10 10
67 0.62 -8 9
93 1.00 -7 8
142 1.86 -3 5
433 11.8 19 - 7
887 29.3 45 -16
1785 82.0 104 -22
2797 163.0 170 - 7
3675 248.0 228 20
(e) Suitability of regression line
A linear model would have the residuals scattered randomly above and below a horizontal line.
Instead, they appear to lie along a parabola (Fig. 2).
This suggests that linear regression is not a good model for the data.
What is the volume of a cube with a side length of 14 cm.?
Answer:
V =2744 cm^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = 14^3
V =2744 cm^3
Answer: 2,744 cm³
Step-by-step explanation: Since the length, width, and height of a cube are all equal, we can find the volume of a cube by multiplying side × side × side.
So we can find the volume of a cube using the formula s³.
Notice that we have a side length of 14cm.
So plugging into the formula, we have (14 cm)³ or
(14 cm)(14 cm)(14 cm) which is 2,744 cm³.
So the volume of the cube is 2,744 cm³.
Suppose the average driving distance for last year's Player's Champion Golf Tournament in Ponte Vedra, FL, was 292.5 yards with a standard deviation of 14.2 yards. A random sample of 60 drives was selected from a total of 4,244 drives that were hit during this tournament. What is the probability that the sample average was 289 yards or less?
Answer:
The Probability that the sample average was 289 yards or less
P(x⁻≤ 289) = P( Z≤ -1.909) = 0.0287
Step-by-step explanation:
step(i):-
Mean of the Population = 292.5 yards
Standard deviation of the Population = 14.2 yards
sample size 'n' =60 drives
N = 4244 drives
Step(ii):-
Let X⁻ be random sample average
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
Let X⁻ = 289
[tex]Z = \frac{289 -292.5}{\frac{14,2}{\sqrt{60} } }[/tex]
Z = - 1.909
The Probability that the sample average was 289 yards or less
P(x⁻≤ 289) = P( Z≤ -1.909)
= 0.5 -A(1.909)
= 0.5 -0.4713
= 0.0287
Conclusion:-
The Probability that the sample average was 289 yards or less = 0.0287
what is the product a-3/7 ÷ 3-a/21
Answer:
the sum shown is (20/21)a -(1/7)
Step-by-step explanation:
As written, the sum is ...
[tex]a-\dfrac{\frac{3}{7}}{3}-\dfrac{a}{21}=\boxed{\dfrac{20}{21}a-\dfrac{1}{7}}[/tex]
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We wonder if you mean the quotient ...
((a-3)/7)/((3-a)/21)
[tex]\dfrac{\left(\dfrac{a-3}{7}\right)}{\left(\dfrac{3-a}{21}\right)}=\dfrac{a-3}{7}\cdot\dfrac{21}{3-a}=\dfrac{-21(3-a)}{7(3-a)}=\boxed{-3}[/tex]
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Comment on the problem presentation
Parentheses are required when plain text is used to represent fractions. The symbols ÷, /, and "over" all mean the same thing: "divided by." The denominator is the next item in the expression. If arithmetic of any kind is involved in the denominator, parentheses are needed. This is the interpretation required by the Order of Operations.
When the expression is typeset, fraction bars and text formatting (superscript) serve to group items that require parentheses in plain text.
__
Please note that some authors make a distinction between the various forms of division symbol. Some use ÷ to mean ...
(everything to the left)/(everything to the right)
and they reserve / solely for use in fractions. Using this interpretation, your expression would be ...
(a -(3/7))/(3 -(a/21)) = (21a -9)/(63 -a)
That distinction is not supported by the Order of Operations.
Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?
Answer:
8.5
Step-by-step explanation:
For continuous compounding, the account value formula is ...
A = Pe^(rt)
where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...
3550 = 2400e^(.046t)
ln(355/240) = 0.046t
t = ln(355/240)/0.046 ≈ 8.5
It will take 8.5 years for the value to reach $3550.
Between what two integers is square root 54?
Answer:
7 and 8
Step-by-step explanation:
54 is between 7^2 = 49 and 8^2 = 64.
The square roots have the same relationship.
49 < 54 < 64
√49 < √54 < √64
7 < √54 < 8
What is the range of g?
Answer:
{-7, -4, -1, 3, 7}
Step-by-step explanation:
The range is the list of y-coordinates of the points:
range = {-7, -4, -1, 3, 7}
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.(a) What is the velocity of the top of the ladder when the base is given below?7 feet away from the wall ft/sec20 feet away from the wall ft/sec24 feet away from the wall ft/sec(b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 7 feet from the wall. ft2/sec(c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 7 feet from the wall. rad/sec
Answer:
a) The height decreases at a rate of [tex]\frac{7}{12}[/tex] ft/sec.
b) The area increases at a rate of [tex]\frac{527}{24}[/tex] ft^2/sec
c) The angle is increasing at a rate of [tex]\frac{1}{12}[/tex] rad/sec
Step-by-step explanation:
Attached you will find a sketch of the situation. The ladder forms a triangle of base b and height h with the house. The key to any type of problem is to identify the formula we want to differentiate, by having in mind the rules of differentiation.
a) Using pythagorean theorem, we have that [tex] 25^2 = h^2+b^2[/tex]. From here, we have that
[tex]h^2 = 25^2-b^2[/tex]
if we differentiate with respecto to t (t is time), by implicit differentiation we get
[tex]2h \frac{dh}{dt} = -2b\frac{db}{dt}[/tex]
Then,
[tex]\frac{dh}{dt} = -\frac{b}{h}\frac{db}{dt}[/tex].
We are told that the base is increasing at a rate of 2 ft/s (that is the value of db/dt). Using the pythagorean theorem, when b = 7, then h = 24. So,
[tex]\frac{dh}{dt} = -\frac{2\cdot 7}{24}= \frac{-7}{12}[/tex]
b) The area of the triangle is given by
[tex]A = \frac{1}{2}bh[/tex]
By differentiating with respect to t, using the product formula we get
[tex] \frac{dA}{dt} = \frac{1}{2} (\frac{db}{dt}h+b\frac{dh}{dt})[/tex]
when b=7, we know that h=24 and dh/dt = -1/12. Then
[tex]\frac{dA}{dt} = \frac{1}{2}(2\cdot 24- 7\frac{7}{12}) = \frac{527}{24}[/tex]
c) Based on the drawing, we have that
[tex]\sin(\theta)= \frac{b}{25}[/tex]
If we differentiate with respect of t, and recalling that the derivative of sine is cosine, we get
[tex] \cos(\theta)\frac{d\theta}{dt}=\frac{1}{25}\frac{db}{dt}[/tex] or, by replacing the value of db/dt
[tex]\frac{d\theta}{dt}=\frac{2}{25\cos(\theta)}[/tex]
when b = 7, we have that h = 24, then [tex]\cos(\theta) = \frac{24}{25}[/tex], then
[tex]\frac{d\theta}{dt} = \frac{2}{25\frac{24}{25}} = \frac{2}{24} = \frac{1}{12}[/tex]
you decided to save $100 at the end of each month for a year and deposit it in a bank account that earns an annual interest rate of 0.3%, compounded monthly. Use the formula for an annuity, F, to determine how much money will be in the account at the end of the 6th month, rounding your answer to the nearest penny.
Answer:
1.8
Step-by-step explanation:
Robert makes $951 gross income per week and keeps $762 of it after tax withholding. How many allowances has Robert claimed? For weekly income between 950 and 960, the number of withholding allowances claimed are: 0, 259 dollars; 1, 242 dollars; 2, 224 dollars; 3, 207 dollars; 4, 189 dollars; 5, 173 dollars; 6, 162 dollars; 7, 151 dollars; 8, 140 dollars. a. One b. Two c. Three d. Four
Answer:
Option D,four is correct
Step-by-step explanation:
The tax withholding from the gross income of $951 is the gross income itself minus the income after tax withholding i.e $189 ($951-$762)
The percentage of the withholding =189/951=20% approximately
Going by the multiple choices provided,option with 4,189 dollars seems to the correct option as that is the exact of the tax withholding on Robert's gross income and his earnings fall in between $950 and $960
The number of allowances that Robert has claimed is four. Option d is correct.
What is Tax withholding allowance?
A withholding tax is a tax that an employer deducts from an employee's paycheck and delivers it straight to the government (federal income tax).
From the given information:
The gross income per week for Robert = $951 The amount saved after removing tax allowance = $762The tax allowance = Gross income - savings amount
The tax allowance = $951 - $762
The tax allowance = $189
From the weekly income between 950 and 960 data, we can see that the number of allowances claimed related to the withholding allowances are:
0 → $259
1 → $242
2 → $224
3 → $207
4 → $189
5 → $173
6 → $162
7 → $151
8 → $140
Therefore, we can conclude that the number of allowances that Robert has claimed is four.
Learn more about tax withholding here:
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