Answer: When the addition of two or more equations leads to the elimination of one of the variables.
Step-by-step explanation:
When we have a system of equations, the addition method seems to be useful only when adding the equations will lead to the elimination of one of the variables:
An example of this can be, for the variables x and y:
3*x + x*y - 2*y = 3
x^2 + x*y - 2y = 42
now we can "add" (actually subtract) the equations and get (eq2 minus eq1)
(x^2 + x*y - 2y) - (3*x + x*y - 2*y ) = 42 - 3
x^2 - 3*x = 39
x^2 - 3*x - 39 = 0
And now we can solve it for x, and then find the value of y.
Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50 Steps On A Bearing Of 3150 Sketch Musah's Movement Mark 41 Ii. How Far West Is Musah's Final Point From The Centre? [Mark 41 Iv. How Far North Is Musah's Final Point From The Centre? Mark 41 Describe How You Would Guide A JHS Student
Answer:
60.36 steps West from centre
85.36 steps North from centre
Step-by-step explanation:
Refer to attached
Musah start point and movement is captured in the picture.
1. He moves 50 steps to North, 2. Then 25 steps to West, 3. Then 50 steps on a bearing of 315°. We now North is measured 0°or 360°, so bearing of 315° is same as North-West 45°.
Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.
How far West Is Musah's final point from the centre?
25 + 50/√2 ≈ 60.36 stepsHow far North Is Musah's final point from the centre?
50 + 50/√2 ≈ 85.36 stepsMatch the example on the left with the corresponding property on the right.
1. 3(x + 3) = 3x + 9
2. 2 + 3 + 4 = 4 + 3 +2.
3. 4(2 x 3) = (4 x 2)3
4. 6 + (7 + x) = (6 + 7) + x
A. Commutative Property
B. Associative Property
C. Distributive Property
Answer:
1 = C
2 = A
3= B
4 = B
Step-by-step explanation:
What is the measure of x?
Answer:
22
Step-by-step explanation:
This is a right angle so the sum of those would be equal to 90 degrees
x + 7 + 3x - 5 = 90 add like terms
4x + 2 = 90 subtract 2 from both sides
4x = 88 divide both sides by 4
x = 22
Find xAssume that segments that appear tangent are tangent
Step-by-step explanation:
I assume the length that got cut off is 18.
Use Pythagorean theorem:
x² + 36² = (x + 18)²
x² + 1296 = x² + 36x + 324
972 = 36x
x = 27
Write the equation of the line that passes through the points (- 5, 1) and (2, 0) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Answer:
y=-1/7x + 12/7
Step-by-step explanation:
Start by finding the slope
m=(1-0)/(-5-2)
m=-1/7
next plug the slope and the point (-5,1) into point slope formula
y-y1=m(x-x1)
y1=1
x1= -5
m=-1/7
y- 1 = -1/7(x - -5)
y-1=-1/7(x+5)
Distribute -1/7 first
y- 1=-1/7x + 5/7
Add 1 on both sides, but since its a fraction add 7/7
y=-1/7x + (5/7+7/7)
y=-1/7x+12/7
In four years,George saved $540. His twin sister, Georgette, saved 10 times as much. How much did Georgette saved?
5400 dollars
540x10= 5400
Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a
continuous rate of 25% every day (that's why they're magic). How many grams of
crystals will you have after one week (7 days)?!
ANSWER IS BRAINLEIST
Answer:
After 7 days the crystals will be 57.57 grams.
Step-by-step explanation:
In this the continuous exponential growth formula will be used.
y = A e ^rt
Where A = original amount = 10 grams
y is the growth after 7 days
e is Euler's number= 2.719
t is the time in hours , weeks, years etc.= 7 days
r is the rate in decimals = 25% = 0.25
Putting the values in the formula:
y = A e ^rt
y = 10 e ^0.25 (7)
Calculating with the calculator
y = 10* 2.719^1.75
y= 57.57 grams.
After 7 days the crystals will be 57.57 grams.
Answer:
57.55g
Step-by-step explanation:
Use the formula f(t) = aert, where a = 10, r = 0.25, and t = 7. This gives f(7) = 10e(0.25)(7) = 10e1.75 ≈ 10(5.755) ≈ 57.55.
5/root 7 - root 3 +1/root 7+ root 3
[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]
I need help on the decimal estimate can you tell me step by step please
* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.
Answer:
The probability that the diagnosis is correct is 0.95249.
Step-by-step explanation:
We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.
Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.
Let the probability that people in the United States have diabetes = P(D) = 0.083.
So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917
Also, let A = event that the diagnostic test is accurate
So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98
And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95
Now, the probability that the diagnosis is correct is given by;
Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')
= (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)
= 0.08134 + 0.87115
= 0.95249
Hence, the probability that the diagnosis is correct is 0.95249.
According to the Empirical Rule, 99.7% of scores in a normal distribution fall within 2 standard deviations of the mean.
a. True
b. False
Answer:
False
Step-by-step explanation:
Here, we want to check the validity of the given statement. The statement is false.
Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.
Please check attachment for diagrammatic representation of the empirical rule.
What's the exact value of tan 15°?
Answer:
The answer is 0.267949192
Step-by-step explanation:
I hope that is enough numbers.
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
Answer:
hiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two. What is the probability of no defects in 10 feet of steel
Answer:
the probability of no defects in 10 feet of steel = 0.1353
Step-by-step explanation:
GIven that:
A roll of steel is manufactured on a processing line. The anticipated number of defects in a 10-foot segment of this roll is two.
Let consider β to be the average value for defecting
So;
β = 2
Assuming Y to be the random variable which signifies the anticipated number of defects in a 10-foot segment of this roll.
Thus, y follows a poisson distribution as number of defect is infinite with the average value of β = 2
i.e
[tex]Y \sim P( \beta = 2)[/tex]
the probability mass function can be represented as follows:
[tex]\mathtt{P(y) = \dfrac{e^{- \beta} \ \beta^ \ y}{y!}}[/tex]
where;
y = 0,1,2,3 ...
Hence, the probability of no defects in 10 feet of steel
y = 0
[tex]\mathtt{P(y =0) = \dfrac{e^{- 2} \ 2^ \ 0}{0!}}[/tex]
[tex]\mathtt{P(y =0) = \dfrac{0.1353 \times 1}{1}}[/tex]
P(y =0) = 0.1353
Please help! Anyways how was your day? lol
Answer:
>
Step-by-step explanation:
the less negative the greater the number
on a 25 square grid how many squares need to be shaded to make 60% shaded
Answer:
15 squares
Step-by-step explanation:
60/100 * 25 = 15
The area of a rectangle is 44 m^2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
length :
width :
Answer:
Length:8
Width:5.5
Step-by-step explanation:
We're given area = 44m^2, and the formula for the area of a rectangle is the length multiplied by the width. So,
A = L * w = 44
We're given that the length is 3m shorter than 2 times the width, which is 2w - 3. "2w" is the same as "2 times the width", and the 3 is subtracted because it says 3m shorter than 2 times the width. So L = 2w - 3, and we can substitute that into our equation above.
(2w - 3)(w) = 44
2w^2 - 3w - 44 = 0
Use the quadratic formula here.
x = {3 ± √(-3)^2 - 4(-44)(2)}/2(2)
= {3 ± √9 + 352}/4
= (3 ± 19)/4
You'll get two answers, but remember, we're measuring the length of the sides of shapes, so it has to be positive. It's impossible to have negative lengths, so we're going to stick with the (3 + 19)/4 answer, which is 22/4, which is 5.5. However, we are not finished yet. This is just the width. Now we need to plug it into the equation for length, which was 2w - 3
2(5.5) - 3 = 11 - 3 = 8
The length is 8m and the width is 5.5m.
A mutual fund owns 20,000 shares in Company Y. Company Y has 2 million shares issued. In one particular year, Company Y announces annual profits of $6 million, and decides to pay dividends to its shareholders at a rate of 15% of its annual profits. How much will the mutual fund receive in the form of dividends from Company Y? Round your answer to the nearest dollar.
Answer: $9,000
Step-by-step explanation:
Step 1
Calculate the amount of dividends the company will pay to all its shareholders.
= 15% of profits
= 15% * 6,000,000
= $900,000
Step 2
Calculate how much dividends each share will get;
$900,000 to 2 million shares of Company Y.
= 900,000/2,000,000
= $0.45
Step 3
Calculate how much the Mutual fund will get for its 20,000 shares
= 20,000 * 0.45
= $9,000
Find the sum of the first 12 terms of the sequence 512, 256, 128, … This is infinite series notation, the answer is NOT 896...
Answer:
1023.75
Step-by-step explanation:
The sum of a geometric sequence is
sum = a( 1 - r^n) / (1-r)
where a is the first term r is the common ratio and r^n is the nth term
We need to find the common ratio
r = 256/512 = 1/2
sum = 512 ( 1 - 1/2^12) / ( 1-1/2)
=512( 1-.000244141) / (.5)
=512(.999755859) /.5
=1023.75
Answer:
1023.75
Step-by-step explanation:
sum = a( 1 - r^n) / (1-r)
a1 = 512
n = 12
r = 256 / 512 = 1/2
512 (1 - 1/2¹²)
therefore.. sum = ------------------ = 1023.75
1 - 1/2
sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim
Answer:
The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.
Step-by-step explanation:
The company's promotional literature claimed that 28% do not fail in the first 1000 hours of their use.
At the null hypothesis, we test that at least 28% do not fail, that is:
[tex]H_0: p \geq 0.28[/tex]
At the alternative hypothesis, we test if the proportion is of less than 28%, that is:
[tex]H_1: p < 0.28[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.28 is tested at the null hypothesis:
This means that [tex]\mu = 0.28, \sigma = \sqrt{0.28*0.72}[/tex]
Sample of 1800 computer chips revealed that 25% of the chips do not fail in the first 1000 hours of their use.
This means that [tex]n = 1800, X = 0.25[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.25 - 0.28}{\frac{\sqrt{0.28*0.72}}{\sqrt{1800}}}[/tex]
[tex]z = -2.83[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion below 0.25, which is the p-value of Z = -2.83.
Looking at the z-table, z = -2.83 has a p-value of 0.0023.
The p-value of the test is 0.0023 < 0.02, which means that there is sufficient evidence at the 0.02 level to dispute the company's claim.
what should be added to 4x get 9X please help me in this pic also all
Answer:
[tex]thank \: you[/tex]
18. Solve the equation for X.
Answer:
Option a is the correct answer
Use the dot product to determine whether v and w are orthogonal.
v=-i-j, w=-i+j
Select the correct choice below and fill in the answer box to complete your choice.
O A. The vectors v and w are not orthogonal because their dot product is ___
O B. The vectors v and w are orthogonal because their dot product is ___
Answer:
B. The vectors v and w are orthogonal because their dot product is 0
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is 0
Problem is attached in a photo
Answer:
y<(x-2)^2
Step-by-step explanation:
To graph this inequality, we first identify the function.
This is a quadratic function y=x^2
The function is translated horizontally to the right two. (x-2)^2
It is also a dotted line, <.
Help due today
No links
Answer:
-6
Step-by-step explanation:
Answer:
[tex]24 + x = 13 \\ x = 13 - 24 \\ x = - 11 \\ thank \: you[/tex]
If a triangular pyramid has a base area of 10ft and a height of 6ft, what is the volume?
. 20ft^3
. 40ft^3
.60ft^3
.80ft^3
.120ft^3
Answer: 20 ft³
Step-by-step explanation:
volume of triangular pyramid = [tex]\frac{1}{3} bh[/tex]
b = base area = 10 fth = height = 6 ftTherefore, the volume is:
[tex]\frac{1}{3} *10*6=\frac{1}{3}*60=\frac{60}{3}=20[/tex]
Simplify to create an equivalent expression.
\qquad{7n-(4n-3)}7n−(4n−3)
Answer:
[tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Step-by-step explanation:
Given
[tex]7n - (4n - 3)[/tex]
Required
Simplify
To simplify the given expression, you start by opening the bracket
[tex]7n - (4n - 3)[/tex]
[tex]7n - 4n + 3[/tex]
Next, you perform arithmetic operations on like terms
[tex]3n + 3[/tex]
The answer can be further simplified;
Factorize [tex]3n + 3[/tex]
[tex]3(n+1)[/tex]
Hence;
[tex]7n - (4n - 3)[/tex] when simplified is equivalent to [tex]3n + 3[/tex] or [tex]3(n+1)[/tex]
Answer:
3n+n
Step-by-step explanation:
Find the general solution of the following differential equation. Primes denote derivatives with respect to x.(x+2y)y'=2x-yleft parenthesis x plus 2 y right parenthesis y prime equals 2 x minus y
Answer:
[tex]-[ln(x^2-yx-y^2)] = K\\[/tex]
Step-by-step explanation:
Given the differential equation [tex](x+2y)y'=2x-y[/tex], this can also be written as;
[tex](x+2y)\frac{dy}{dx} =2x-y[/tex]
On simplification
[tex](x+2y)\frac{dy}{dx} =2x-y\\\\\frac{dy}{dx} = \frac{2x-y}{x+2y} \\\\let \ y = vx\\\frac{dy}{dx} = v+x\frac{dv}{dx}[/tex]
The differential equation becomes;
[tex]v+x\frac{dv}{dx} =\frac{ 2x-vx}{x+2vx}\\\\v+x\frac{dv}{dx} = \frac{ x(2-v)}{x(1+2v)}\\\\v+x\frac{dv}{dx} = \frac{2-v}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v}{1+2v} - v\\\\x\frac{dv}{dx} = \frac{(2-v)-v(1+2v)}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-v-v-2v^2}{1+2v}\\\\x\frac{dv}{dx} = \frac{2-2v-2v^2}{1+2v}[/tex]
[tex]\frac{dx}{x} = \frac{1+2v}{2-2v-2v^2}dv\\\\integrating\ both \ sides\\\\[/tex]
[tex]\int\limits \frac{dx}{x} = \int\limits \frac{1+2v}{2-2v-2v^2}dv\\\\lnx = \frac{1}{2} \int\limits \frac{1+2v}{1-v-v^2}dv\\\\lnx + C = -\frac{1}{2}ln(1-v-v^2)[/tex]
[tex]C = -\frac{1}{2}ln(1-v-v^2) - lnx \\\\ -ln(1-v-v^2) - 2lnx = 2C\\\\-[ln(1-v-v^2) + lnx^2] = 2C\\\\-[ln(1-v-v^2)x^2] = 2C\\since\ v = y/x\\\\- [ln(1-y/x-y^2/x^2)x^2] = K\\\\-[ln(x^2-yx-y^2)] = K\\[/tex]
Hence the solution to the differential equation is [tex]-[ln(x^2-yx-y^2)] = K\\[/tex]
The one-sample z test is: a. a hypothesis test b. used to test hypotheses c. concerning a single population with a known variance d. concerning at least one population e. concerning the variance in a population d. all of the above
Answer:
d. all of the above
Step-by-step explanation:
A one sample z test measures whether the mean of a population is greater, less or equal to a specific value. It is called one sampl z test since the standard normal distribution is used in calculation of critical values. It makes use of the null hypothesis and alternative hypothesis in determining if the mean is greater than or equal or less than the reference value. Variance and standard deviation is assumed to be known and at least one population is used
is [tex]\sqrt[4]{5x^{5} }[/tex] equal [tex](\sqrt[4]{5x} )^{5}[/tex] ?