Answer:
(3,-2)
Step-by-step explanation:
Given equations of line
3x-2y=13
2y+x+1=0
=> x = -1 -2y
Point of intersection will coordinates where both equation have same value of (x,y)
top get that we have to solve the both equations by using method of substitution of simultaneous equation.
using this value of x in 3x-2y=13, we have
3(-1-2y) -2y = 13
=> -3 -6y-2y = 13
=> -8y = 13+3 = 16
=> y = 16/-8 = -2
x = -1 - 2y = -1 -2(-2) = -1+4= 3
Thus, point of intersection of line is (3,-2)
Matrix A is said to be involutory if A2 = I. Prove that a square matrix A is both orthogonal and involutory if and only if A is symmetric.
Answer:
4 · 1/4 (I-0) = (A-0)∧2
see details in the graph
Step-by-step explanation:
Matrix A is expressed in the form A∧2=I
To proof that Matrix A is both orthogonal and involutory, if and only if A is symmetric is shown by re-expressing that
A∧2=I in the standard form
4 · 1/4 (I-0) = (A-0)∧2
Re-expressing
A∧2 = I as a graphical element plotted on the graph
X∧2=I
The orthogonality is shown in the graphical plot displayed in the picture. Orthogonality expresses the mutually independent form of two vectors expressed in their perpendicularity.
_______% of 44 = 22
Answer:
50%
Step-by-step explanation:
22 is half of 44.
So, this means 50% of 44 is 22.
g If A and B are disjoint events, with P( A) = 0.20 and P( B) = 0.30. Then P( A and B) is: a. .00 b. .10 c. .50 d. 0.06
Answer: A) 0
P(A and B) = 0 when events A and B are disjoint, aka mutually exclusive.
We say that two events are mutually exclusive if they cannot happen at the same time. An example would be flipping a coin to have it land on heads and tails at the same time.
A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)
Answer:
50ft by 120ft
Step-by-step explanation:
Area of a rectangle = L × W
6000ft² = L × W
L = 6000/W
When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.
The formula for a right angle triangle =
a² + b² = c²( c = hypotenuse)
We are told in the question that:
A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel
Let us assume the side that the hypotenuse is longer than = Width
Hence, the Diagonal = (W + 10)²
Therefore
L² + W² = (W + 10)²
Since L = 6000/W
W² + (6000/W)² = (W + 10)²
W² + (6000/W)² = (W + 10) (W + 10)
W² + (6000/W)² = W² + 10W + 10W + 100
W² + (6000/W)² = W² + 20W + 100
W² - W² + (6000/W)² = 20W+ 100
6000²/W² = 20W + 100
6000² = W²( 20W + 100)
6000² = 20W³ + 100W²
20W³ + 100W² - 6000² = 0
20W³ + 100W² - 36000000 = 0
20(W³ + 5W² - 1800000) = 0
Factorising the quadratic equation,
20(W − 120)(W² + 125W + 15000) = 0
W - 120 = 0
W = 120
Therefore,
W(Width) = 120feet
Since the Width = 120 feet
We can find the length
6000ft² = L × W
L = 6000/W
L = 6000/120
L = 50 feet
The dimensions of the land, correct to the nearest foot is 50ft by 120ft
(a) Find the standard error of the mean for each sampling situation (assuming a normal population). (Round your answers to 2 decimal places.) (a) σ = 18, n = 9 (b) σ = 18, n = 36 (c) σ = 18, n = 144
Answer:
a) 6.00
b) 3.00
c) 1.50
Step-by-step explanation:
Sample error of the mean is expressed mathematically using the formula;
SE = σ /√n where;
σ is the standard deviation and n is the sample size.
a) Given σ = 18, n = 9
Standard error of the mean = σ /√n
Standard error of the mean = 18/√9
Standard error of the mean = 18/3
Standard error of the mean = 6.00
b) Given σ = 18, n = 36
Standard error of the mean = σ /√n
Standard error of the mean = 18/√36
Standard error of the mean = 18/6
Standard error of the mean = 3.00
c) Given σ = 18, n = 144
Standard error of the mean = σ /√n
Standard error of the mean = 18/√144
Standard error of the mean = 18/12
Standard error of the mean = 3/2
Standard error of the mean = 1.50
Which is one of the transformations applied to the graph of f(x) = X^2 to change it into the graph of g(x) = -x^2 +16x - 44
Answer: First a horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
Step-by-step explanation:
Let's construct g(x) in baby steps.
Ok, we start with f(x) = x^2
The first thing we have is a horizontal translation of A units (where A is not known)
A vertical translation of N units to the right, is written as:
g(x) = f(x - N)
Then we have:
g(x) = (x - A)^2 = x^2 - 2*A*x + A^2
Now, you can see that actually g(x) has a negative leading coefficient, which means that we also have an inversion over the x-axis.
Remember that if we have a point (x, y), a reflection over the x-axis transforms our point into (x, -y)
Then if we apply also a reflection over the x-axis, we have:
g(x) = -f(x - A) = -x^2 + 2*A*x - A^2 = -x^2 + 16*x - 44
Then:
2*A = 16
A*A = 44.
The first equation says that A = 16/2 = 8
But 8^2 is not equal to 44.
Then we need another constant coefficient, which is related to a vertical translation.
If we have a relation y = f(x), a vertical translation of N units up, will be
y = f(x) + N.
Then:
g(x) = -f(x - A) + B
-x^2 + 2*A*x - A^2 + B = x^2 + 16*x - 44
Now we have:
2*A = 16
-A^2 + B = - 44
From the first equation we have A = 8, now we replace it in the second equation and get:
-8^2 + B = -44
B = -44 + 64 = 20
Then we have:
The transformation is:
First an horizontal shift of 8 units, then a reflection over the x-axis, and then a vertical shift of 20 units.
A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ft/sec, how fast is the height of the top changing (this will be a negative rate) when the lower end is 6 feet from the wall?
Answer:
-4.5ft per sec
Step-by-step explanation:
Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).
This forms a triangle with the ladder as the hypothenus of length 10ft
We have dy/dt = 6ft per sec
According to Pythagoras law the relationship between x and y is
(x^2) + (y^2) = (hypothenus ^2) = 10^2
When we differentiate both sides of the equation
2x(dx/dt) + 2y(dy/dt) = 0
dy/dt = (x/y) * (dx/dt)
y= √(10^2) - (6^2) = 8ft
So dy/dt = (6/8)* (6/1)= -4.5 ft per sec
It is a negative rate
Of 900 people surveyed, 480 were male and 410 had cell phones. Of those with cell phones, 290 were female. What is the probability that a person surveyed was either male or had a cell phone? A. 600/900 = 0.6667 B. 770/900 = 0.8556 C. 360/900 = 0.40 D. 820/900 = 0.9111
Answer:
C. 360/900 = 0.40
Step-by-step explanation:
The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.
The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...
The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]
Given that the odds of the horse winning the race is 7:4
Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:
[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]
From the given question;
The probability of the horse winning the race is:
[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]
[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]
Learn more about probability here:
https://brainly.com/question/11234923?referrer=searchResults
A European study of thousands of men found that the PSA screening for prostate cancer reduced the risk of a man’s dying from prostate cancer from 3.0 percent to 2.4 percent. "But it’s already a small risk. I don’t think a difference of less than 1 percent would be of practical importance," said Ed. Do you agree with Ed’s conclusion?
Answer:
Following are the answer to this question:
Step-by-step explanation:
In the given statement, we don't agree with Ed’s conclusion, because it is not relevant simply since it is not statistically significant. The reduction of prostate cancer is the death risk, which is highly significant even if it decreases significantly. It can also be something statistically important without becoming important.
A survey of the adults in a town shows that 8% have liver problems. Of these, it is also
found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of
those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social
drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability
that this person
i. Has a liver problems? (3 Marks)
ii. Is a heavy drinker (2 Marks)
iii. If a person is found to be a heavy drinker, what is the probability that this person
has liver problem? (2 Marks)
iv. If a person is found to have liver problems, what is the probability that this person
is a heavy drinker? (2 Marks)
v. If a person is found to be a non –drinker, what is the probability that this person has
liver problems. (2 Marks)
(b) The director of admiss
Answer:
The data is:
From the adults in town:
8% have liver problems, of those:
25% heavy drinkers
35% social drinkers
40% non-drinkers.
92% do not have liver problems (100% - 8% = 92%)
5% heavy drinkers
65% social drinkers.
30% non-drinkers
a) An adult is chosen at random, then:
Has a liver problems
We know that 8% of the adults have liver problems, so the probability is 8%, or 8%/100% = 0.08.
Is a heavy drinker
Out of the 8%, 25% are heavy drinkers, and out of the other 92%, 5% are heavy drinkers, so the total percentage of heavy drinkers is:
(i will use decimal math, because you always should work with decimals instead of percentages)
P = 0.08*0.25 + 0.92*0.05 = 0.066
or 6.6% in percentage form
If a person is found to be a heavy drinker, what is the probability that this person
the proability that some one is a heavy drinker was already found, it is p = 0.066.
Now, of those 0.066 we have:
p1 = 0.08*0.25 = 0.02 have liver problems.
So the probability that, given that some one is a heavy drinker, that her/him also have liver problems is:
P = 0.02/0.066 = 0.3 or 30%.
If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
]We already know that out of the 8% with liver problems, a 25% are heavy drinkers, so here the answer is 25% or 0.25.
If a person is found to be a non –drinker, what is the probability that this person has liver problems.
From the 8% with liver problems, we have 40% of non-drinkers,
So the total proportion of non-drinkers with liver problems is:
p1 = 0.8*0.40 = 0.032
From the 92% with no liver problems, we have that 30% of them are non-drinkers, so here we have:
p2 = 0.92*0.30 = 0.276
The total proportion of non drinkers is:
p1 + p2 = 0.032 + 0.276 = 0.308.
Then if we know that some one is non drinker, the proability that the person has liver problems is equal to the quotient between the proportion of non-drinkers with liver problems ( 0.032) and the total proportion of non-drinkers.
p = 0.032/0.308 = 0.104
or 10.4% in percentage form.
A leaf blower was marked up 100% from an original cost of $152. If Eva bought the leaf blower and paid 7% sales tax, how much in total did she pay?
Answer:
$325.28
Step-by-step explanation:
152+152=304
304x1.07=325.28
Answer:
325.28
Step-by-step explanation:
increase the price by 100 %
152* 100%
152
Add this to the original price
152+152 = 304
Now find the sales tax
304 * 7%
304 * .07
21.28
Add this to the amount of the purchase price
304+21.28
325.28
If 2 x 2 + 13 x − 7 = 0 , then x could equal which of the following?
Hi there! :)
Answer:
x = 1/2 or -7.
Step-by-step explanation:
(I'm assuming the expression is 2x² + 13x - 7 = 0)
Factor the equation to solve for the possible values of "x":
2x² + 13x - 7 = 0
When factored, we get:
(2x - 1) ( x + 7) = 0
Use the Zero-Product property to solve for the roots:
2x - 1 = 0
2x = 1
x = 1/2.
-----------
x + 7 = 0
x = -7.
Therefore, possible values of x are x = -1/2, 7.
Answer:
x = 1/2 x=-7
Step-by-step explanation:
2 x^2 + 13 x − 7 = 0
Factor
(2x-1)(x+7)=0
Using the zero product property
2x-1 =0 x+7=0
2x=1 x =-7
x = 1/2 x=-7
Please help!! find the value of the expression
Answer:
7
Step-by-step explanation:
First plug in the variable amounts so the expression now looks like this:
(3 × 4 - 12) + 1/2(4 × 6 - 10)
Now, start by solving the multiplication parts first, so it now looks like this:
(12 - 12) + 1/2(24 - 10)
Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)
Next, solve the multiplication part, so it now looks like this: 0 + 7
Solve that and the answer is 7.
What is the difference in their elevations?
An airplane flies at an altitude of 26,000 feet. A submarine dives to a depth of 700 feet below sea level
Answer:
their difference in elevations are: they both don't fly one fly and one dive if you take the airplane it works quicker but if you take the submarine you won't reach faster
To which number sets of numbers does the number 3.567...belong?
Answer:
It's irrational numberIf the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).
Paula drives 130 miles in 2.5 hours. How far would she drive in 4.5 at the same speed?
*Please answer
I will award the Brainliest answer
Answer:
Paula will travel 234 miles in 4.5 hours
Step-by-step explanation:
Step 1: We first find the speed Paula is going in hours, we divide 130 mile by 2.5 hours to get 52 miles per hour
Step 2: We multiple 52 miles per hour with 4.5 hours to get 234 miles
Therefore Paula will travel 234 miles in 4.5 hours
illustrate the distributive property to solve 144/8
Answer:
8 (19) or 8 (18 +1)
Step-by-step explanation:
Distributive property means to distribute.
HCF of 144 and 8.
=> 8 is the HCF of 144 and 8
8 (18 + 1)
=> 8 (19)
will mark brainliest. PROMISE!! A stick has a length of $5$ units. The stick is then broken at two points, chosen at random. What is the probability that all three resulting pieces are longer than $1$ unit?
Answer:
0.16
Step-by-step explanation:
Length = 5 unitsNumber of broken sticks= 3Equal lengths = 5 units/3See the picture attached for reference.
As you see the best points are the green areas which covers 2 out of 5 zones.
Since it is same for both broken points, the probability of this is:
2/5*2/5 = 4/ 25 = 0.16Answer is 0.16
Musah stands at the center of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°. Sketch musah's movement. How far west is musah's final point from the center?
Answer: 4.17 steps
Step-by-step explanation:
Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°
Use Pythagorean Theorem to find the length of the hypotenuse.
50² + 25² = hypotenuse² --> hypotenuse = 55.9 units
Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.
Create another right triangle using the remaining 5.9 units as the hypotenuse. You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.
see attachment for sketch
An animal population is increasing at a rate of 13 51t13 51t per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years.
Answer:
ΔP = 567
Step-by-step explanation:
The increasing rate of the population is 13,51*t.
That rate by definition is:
dP/dt where P is the population therefore
dP/dt = 13,51*t
dt = 13,51*t*dt
Integrating on both sides of the equation we get:
∫dp = ∫ 13,51*t*dt
P = 13,51*t²/2 + K ( K is population for t = 0 )
Now the population in 10 years P(₁₀)
P(₁₀) = 13,51* (10)² /2 + K
P(₁₀) = 675,5 + K (1)
And P(₄) is
P(₄) = 13,51*(4)²/2 * K
P(₄) = 108,08 + K (2)
Then substracting
P(₁₀) - P(₄) = ( 675,5 + K ) - ( 108,08 + K )
ΔP = 567,42
But we don´t have fraction of animal, then
ΔP = 567
The numbers of words defined on randomly selected pages from a dictionary are shown below. Find the mean, median, mode of the listed numbers. 72 58 62 38 44 66 42 49 76 52 What is the mean? Select the correct choice below and ,if necessary ,fill in the answer box within your choice.(around to one decimal place as needed)
Answer:
72 58 62 38 44 66 42 49 76 52 ( arrange it!)
38 42 44 49 52 58 62 66 72 76 (done!)
Median: Find the number in the middle after we arranged, so the answer is (52+58)/2= 110/2 = 55
Mode : None (there is no number appear more than other number)
Mean = (38+42+44+49+52+58+62+66+72+76)/10
=559/100
=5,5
Hope it helps ^°^
10 easy points!!!! What is the x-intercept of the line?
Answer:
Step-by-step explanation:
As x increases from -74 to -54 (a 'run' of 20), y decreases from 18 to 12 (a 'rise' of -6. Thus, the slope of this line is m = rise/run = -6/20 = -13/10.
From y = mx + b we get 12 = (-13/10)(12) + b, or (after dividing all terms by 12)
1 = -13/10 + b/12, or
60 = -3(6) + 5b, or
42 = - 5b, or b = -42/5
The line is y = (-13/10)x - 42/5.
At the x-intercept, y = 0. Setting y = 0, we get:
(13/10)X = -42/5, or 13x = -84.
Thus, x = -84/13 = -6.46
and so the x-intercept of the line is (-6.46, 0)
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
∠ACB is a circumscribed angle. Solve for x. 1) 46 2) 42 3) 48 4) 44
Answer:
[tex]\Huge \boxed{x=44}[/tex]
Step-by-step explanation:
The circumscribed angle and the central angle are supplementary.
∠ACB and ∠AOB add up to 180 degrees.
Create an equation to solve for x.
[tex]3x+10+38=180[/tex]
Add the numbers on the left side of the equation.
[tex]3x+48=180[/tex]
Subtract 48 from both sides of the equation.
[tex]3x=132[/tex]
Divide both sides of the equation by 3.
[tex]x=44[/tex]
Answer:
4)44
Step-by-step explanation:
From her purchased bags, Rory counted 110 red candies out of 550 total candies. Using a 90% confidence interval for the population proportion, what are the lower and upper limit of the interval? Answer choices are rounded to the thousandths place.
Answer:
The Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Step-by-step explanation:
The formula to be applied or used to solve this question is :
Confidence Interval formula for proportion.
The formula is given as :
p ± z × √[p(1 - p)/n]
n = Total number of red candies = 550 red candles
p = proportion = Number of red candies counted/ Total number of red candies
= 110/550 = 1/5 = 0.2
z = z score for the given confidence interval.
We are given a confidence interval of 90%. Therefore, the z score = 1.6449
Confidence Interval = p ± z × √[p(1 - p)/n]
Confidence Interval = 0.2 ± 1.6449 × √[0.2(1 - 0.2)/550]
= 0.2 ± 1.6449 √0.2 × 0.8/550
= 0.2 ± 1.6449 × 0.0170560573
= 0.2 ± 0.0280555087
Hence, the Confidence Interval = 0.2 ± 0.0280555087
0.2 - 0.0280555087 = 0.1719444913
Approximately = 0.172
0.2 + 0.0280555087 = 0.2280555087
Approximately = 0.228
Therefore, the Confidence Interval = (0.172, 0.228)
Where:
The lower limit = 0.172
The upper limit = 0.228
Answer:
Lower Limit: 0.172
Upper Limit: 0.228
Step-by-step explanation:
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
A plane is flying at the height of 5000 meter above the sea level. at a particular point, it is excatly above a submarine floating 1200 meter below the sea level. what is the vertical distance between them ?
Answer:
3800 meters
Step-by-step explanation:
Vhat is the volume of the right rectangular prism?
Will mark brainliest
Answer:
432 mm³
Step-by-step explanation:
Volume of a Rectangular Prism: V = lwh
Step 1: Define variables
l = 8
w = 6
h = 9
Step 2: Plug into formula
V = 8(6)(9)
Step 3: Evaluate
V = 48(9)
V = 432
And we have our answer!
Find the function h(x) = f(x) - g(x) if f(x) = 3^x and g(x) = 3^2x - 3^x. A.h( x) = 0 B.h( x)=-3^2x C.h( x) = 3^x (2 - 3^x) D.h( x) = 2(3^2x)
Answer:
3^x( 2-3^x)
Step-by-step explanation:
f(x) = 3^x and g(x) = 3^2x - 3^x
h(x) = f(x) - g(x)
3^x - ( 3^2x - 3^x)
Distribute the minus sign
3^x - 3^2x + 3^x
2 * 3^x - 3 ^ 2x
Rewriting
We know that 3^2x = 3^x * 3^x
2 * 3^x - 3^x* 3^x
Factoring out 3^x
3^x( 2-3^x)
