[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)[/tex]
Let [tex]v=x+y[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}[/tex]:
[tex]\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1[/tex]
Now the ODE is separable, and we have
[tex]\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx[/tex]
Integrating both sides gives
[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx[/tex]
For the integral on the left, rewrite the integrand as
[tex]\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v[/tex]
Then
[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C[/tex]
and so
[tex]\csc v-\cot v=x+C[/tex]
[tex]\csc(x+y)-\cot(x+y)=x+C[/tex]
Given that [tex]y(0)=\dfrac\pi2[/tex], we find
[tex]\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1[/tex]
so that the particular solution to this IVP is
[tex]\csc(x+y)-\cot(x+y)=x+1[/tex]
Solve the equation for x. 4x + 7 = 31
4x + 7 = 31
-7 -7
4x = 24
/4 /4
x = 6 (Answer)
Prove.
4(6) + 7 = 31
24 + 7 = 31
31 = 31
True.
The solution to the given equation 4x + 7 = 31 is x = 6, which is determined by subtraction.
The equation is given as follows:
4x + 7 = 31
To solve the equation 4x + 7 = 31 for x, we want to isolate the variable x on one side of the equation.
First, we can begin by subtracting 7 from both sides of the equation:
4x + 7 - 7 = 31 - 7
Simplifying, we get:
4x = 24
Next, we want to isolate x, so we divide both sides of the equation by 4:
4x/4 = 24/4
This simplifies to:
x = 6
Therefore, the solution to the equation 4x + 7 = 31 is x = 6.
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Please help me out.........
Answer:
This is the answer : (answer given in the picture)
Answer:
vertex = (- 3, 24)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0, then
The x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = - x² - 6x + 15 ← is in standard form
with a = - 1, b = - 6, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-6}{-2}[/tex] = - 3
Substitute x = - 3 into the function for corresponding value of y
y = - (- 3)² - 6(- 3) + 15 = - 9 + 18 + 15 = 24
vertex = (- 3, 24)
What is the answer to life the universe, and ari waters his garden every 3 days and weeds it every Saturday. ari watered and weeded his garden this Saturday. how many days will it be until ari again waters both waters and weeds his garden on the same day?
Ari will water and weed his garden on the same day again in 21 days by finding the Least Common Multiple (LCM) of the watering and weeding cycles, which are 3 and 7 days respectively.
Explanation:The question asks us to find out how many days will pass until Ari once again waters and weeds his garden on the same day. This problem can be solved by finding the Least Common Multiple (LCM) of the watering and weeding cycles. Ari waters his garden every 3 days and weeds it every Saturday, which suggests a 7-day cycle for weeding.
To find the LCM of 3 and 7, we list the multiples of each number:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
The smallest multiple they both share is 21. Therefore, Ari will water and weed his garden on the same day again in 21 days.
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Determine the measure of angle FGC.
A. 22°
B. 70°
C. 11°
D. 120°
Answer:
it look like B but I'm not sure
Find the distance between these points.
C(0, 4), T(-6, -3)
√(37)
√(85)
√(109)
Answer:
√85
Step-by-step explanation:
See image
Distance formula can be used to find the distance between two points.
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Answer: Second option
[tex]d=\sqrt{85}[/tex]
Step-by-step explanation:
The formula to find the distance between two points is:
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
In this problem the points are C(0, 4), T(-6, -3)
This is
[tex]x_1=0\\\\x_2=-6\\\\y_1=4\\\\y_2=-3[/tex]
So the distance is:
[tex]d=\sqrt{((-6)-0)^2 + ((-3)-4)^2}[/tex]
[tex]d=\sqrt{(-6)^2 + (-7)^2}[/tex]
[tex]d=\sqrt{36 + 49}[/tex]
[tex]d=\sqrt{85}[/tex]
Jessica wants to take three books on vacation with her. She has five books to choose from. How many possible combinations of three books could she take on vacation?
It would have to be 3/5
Answer:
We use the combination formula:
combinations = n! / r! * (n-r)!
n = 5 and r =3
combinations = 5! / 3! * 2!
combinations = 5! / 12
combinations = 5 * 4 * 3 * 2 * 1 / 12
combinations = 5 * 2 = 10
Step-by-step explanation:
Let u = <7, -3>, v = <-9, 5>. Find 4u - 3v.
a. <55, -27>
b. <1, 3>
c. <16, 12>
d. <-8, -6>
Answer:
a.<55, -27>
Step-by-step explanation:
The given vectors are u = <7, -3>, v = <-9, 5>.
We want to find 4u - 3v.
We substitute the vectors and multiply by the scalars.
4u - 3v=4<7, -3>-3 <-9, 5>.
4u - 3v=<28, -12>- <-27, 15>.
4u - 3v=<28--27, -12-15>
4u - 3v=<55, -27>
The manager of a company that sells movie tickets online releases a report. The report states that the company's customers do not want the option of reserving a seat when they buy tickets. The report was based on a survey of 200 customers chosen at random from the company's database. Participants were asked the question, "Are you willing to spend the extra time and effort to reserve a seat when you buy tickets?"
Select ALL statements that correctly evaluate the report.
A. The question is biased toward a No response.
B. The question is biased toward a Yes response.
C. The sample is biased because it does not represent the population.
D. The sample is not biased.
E. The question is not biased.
The answer is a okay
Answer:
A and D
Step-by-step explanation:
The customers were chosen at random, so the sample is not biased. However, the question is biased. "Extra time and effort" is phrased to get a No response.
A and D.
What values for theta (0≤theta≤2π) cos theta- tan theta cos theta=0?
ANSWER
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
EXPLANATION
We want to solve the equation;
[tex] \cos( \theta) - \tan( \theta) \cos( \theta) = 0[/tex]
We factor to get:
[tex] \cos\theta(1 - \tan\theta) = 0[/tex]
Either
[tex]\cos\theta = 0[/tex]
Or
[tex]1 - \tan \theta = 0[/tex]
For
[tex]\cos\theta = 0[/tex]
We gave
[tex] \theta = \frac{\pi}{2} ,\frac{3\pi}{2}[/tex]
When
[tex]\tan \theta = 1[/tex]
Then,
[tex] \theta = \frac{\pi}{4} , \frac{5\pi}{4} [/tex]
Therefore the solution on the interval
[tex]0 \leqslant \theta \: \leqslant 2\pi[/tex]
is
[tex]\theta = \frac{\pi}{2} ,\frac{3\pi}{2},\frac{\pi}{4} , \frac{5\pi}{4} [/tex]
Which shows the expressions rewritten with the least common denominator? 5x+3/3x and 7x/2x^2
Answer is B
Answer:
[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].
Step-by-step explanation:
The given expression is:
[tex]\frac{5x+3}{3x}[/tex] and [tex]\frac{7x}{3x^2}[/tex].
The least common denominator is: [tex]6x^2[/tex].
We collect LCM for the denominator to obtain;
[tex]\frac{2x(5x+3)}{6x^2}[/tex] and [tex]\frac{3(7x)}{6x^2}[/tex].
We multiply out the parenthesis to obtain;
[tex]\frac{10x^2+6x}{6x^2}[/tex] and [tex]\frac{21x}{6x^2}[/tex].
Therefore the correct answer is B or the second option.
A 15 ft ladder makes a 52° angle with the ground. How far will the top of the ladder be above the ground.
Answer:
11.820 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...
sin(52°) = height/(15 ft)
Multiplying by the denominator gives you ...
height = (15 ft)·sin(52°) ≈ 11.820 ft
___
You may need to round this number appropriately.
Suppose you are a designer making the traffic sign below.
1. What is the sum of the interior angles of the equilateral triangle?
2. What is the measure of ∠N?
3. What is the measure of ∠M? Explain your reasoning.
4. What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X? Explain your reasoning.
Answer:
Part 1) The sum of the interior angles is equal to 180 degrees
Part 2) The measure of angle N is ∠N=60°
Part 3) The measure of angle M is ∠M=120°
Part 4) The sum of the the exterior angles is 360°
Step-by-step explanation:
Part 1) What is the sum of the interior angles of the equilateral triangle?
we know that
The sum of the interior angles of any triangle must be equal to 180 degrees
Part 2) What is the measure of ∠N?
we know that
An equilateral triangle has three equal sides and three equal internal angles ( each internal angle measure 60 degrees)
so
In this problem
∠N=60°
Part 3) What is the measure of ∠M? Explain your reasoning.
we know that
∠M+∠N=180° -----> by supplementary angles (linear pair)
we have
∠N=60°
substitute
∠M+60°=180°
∠M=180°-60°=120°
Part 4) What is the sum of the exterior angles of the equilateral triangle ∠M + ∠R + ∠X?
we know that
The sum of the the exterior angles of any polygon is equal to 360 degrees
In this problem
we have
∠M=∠R=∠X=120°
so
∠M+∠R+∠X=120°+120°+120°=360°
Answer:
Step-by-step explanation:
The sum of the interior angles is equal to 180 degrees. The measure of angle N is ∠N=60°. The measure of angle M is ∠M=120°. The sum of the the exterior angles is 360°
Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then. Use the formula A = P(1 + r)^t to find the current value of the collection.
Answer:
A = $784.00
Step-by-step explanation:
This is the answer
The current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.
What is simple interest?It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.
We have formula:
A = P(1 + r)^t
Here P = $400
r = 12% = 0.12
t = 8 years
A = 400(1+0.12)^8
A = 400(2.47596)
A = $990.38
Thus, the current value of the coin is $990.38 if the Conner's coin collection, which was worth $400 eight years ago, has been increasing in value by 12% per year since then.
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Which correspondence is equivalent to Δ PQR↔ΔSTU?
A) Δ RQP ↔ ΔUTS?
B) Δ PRQ ↔ ΔTUS?
C) Δ RPQ ↔ ΔSUT?
D) Δ QRP ↔ ΔUST?
Answer:
A) Δ RQP ↔ ΔUTS
Step-by-step explanation:
Answer:
Option A) is correct
Step-by-step explanation:
Given : [tex]\Delta PQR \leftrightarrow \Delta STU[/tex]
We need to find which correspondence is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] .
Solution :
One to one correspondence means measure of each side and each angle of one triangle is equal to the side and angle of the other triangle .
Here, we observe that option A) is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] as explained below :
As per [tex]\Delta PQR \leftrightarrow \Delta STU[/tex] ,
[tex]PQ=ST\,,\,QR=TU\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]
Also, as per [tex]\Delta RQP \leftrightarrow \Delta UTS[/tex] , we have
[tex]PQ=ST\,,\,RQ=UT\,,\,PR=SU\\\angle P=\angle S\,,\,\angle Q=\angle T\,,\,\angle R=\angle U[/tex]
Therefore,
[tex]\Delta RQP \leftrightarrow \Delta UTS[/tex] is equivalent to [tex]\Delta PQR \leftrightarrow \Delta STU[/tex]
So, option A) is correct .
Describe the set of numbers using interval notation.
x > 8 or x ≤ 2
A. [2, 8)
B. (–∞, 2] ∩ (8, ∞)
C.(–∞, 2] ∪ (8, ∞)
D. (–∞, 2) ∪ (8, ∞)
Answer:
Option C.(–∞, 2] ∪ (8, ∞)
Step-by-step explanation:
we know that
The solution of the inequality [tex]x > 8[/tex] Is the interval (8,∞)
The solution of the inequality [tex]x\leq 2[/tex] Is the interval (-∞,2]
therefore
The solution of [tex]x > 8[/tex] or [tex]x\leq 2[/tex] is equal to
(-∞,2] U (8,∞)
Final answer:
The correct interval notation for the inequality x > 8 or x ≤ 2 is (−∞, 2] ∪ (8, ∞), which represents all numbers less than or equal to 2 and all numbers greater than 8.
Explanation:
The question asks to describe the set of numbers using interval notation for the inequality x > 8 or x ≤ 2. Interval notation is a concise way of writing sets of numbers, using brackets to include endpoints and parentheses for exclusive limits. For an inequality like x > 8, we use the notation (8, ∞) to indicate all numbers greater than 8 but not including 8 itself. Likewise, for x ≤ 2, the interval notation is [−∞, 2] which includes all numbers less than or equal to 2. When we combine these with the union because of the 'or' condition, the correct interval notation is (−∞, 2] ∪ (8, ∞). Therefore, the correct answer is C. (8, ∞) indicates all the numbers larger than 8, and (−∞, 2] includes all the numbers up to and including 2.
There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window. The order in which they are chosen does not matter. How many ways are there to choose paintings? A. 7920 B. 330 C.44 D. 121
Answer:
B. 330
Step-by-step explanation:
The question indicates the order doesn't matter, so it's a combination and not a permutation.
The combinations are calculated using this formula:
[tex]C(n,r) = \frac{n!}{r! (n-r)!}[/tex]
In this case we have a population of 11 (n = 11) and a selection of 4 (r=4), so...
[tex]C(11,4) = \frac{11!}{4! (11-4)!} = 330[/tex]
So, there are 330 different combinations that can be made of 4 paintings out of a selection of 11.
Answer:
The correct answer is option B. 330
Step-by-step explanation:
It is given that,There are 11 paintings at an art show. Four of them are chosen randomly to display in the gallery window.
To find the possible ways
There are total 11 paintings.
We have to choose 4 of them
Possible number of ways = 11C₄
= (11 * 10 * 9 )/(1 * 2* 3 * 4)
= 330 ways
Therefore the correct answer is option B. 330
Marti has a jar of 161 coins consisting of pennies and nickels. The total value of the coins is $3.09. How many nickels does Marti have in the jar
Okay, so there are nickels and pennies in this jar.
So, let's call the number of pennies X
Since there are 161 coins altogether, the number of nickels is (161 - X)
So now we solve the equation:
.01X + .05(161 - X) = 3.09
.01X + 8.05 - .05X = 3. 09
4.96 = .04X
124 = X
So, there are 124 pennies
Therefore, there are 161 - 124 = 37 nickels
Let's check our answer:
124 x .01 + 37x .05 = 1.24 + 1.85 = 3.09
It works!
I think it is 18
nickels for $3.09
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
Which equation matches the graph?
Answer: D) -2 |x| - 2
Step-by-step explanation:
A v-shaped graph is an absolute value graph.
The general form of an absolute value equation is: y = a |x - h| + k
where (h, k) represents the vertex and "a" represents the vertical stretch (aka slope).
The vertex of the given graph is (0, 2), however the graph is inverted (upside-down) which is a reflection across the x-axis. Therefore,
a = -2(h, k) = (0, -2) --> y = -2 |x| - 2Please please help me
Answer:
399.6 miles²
Step-by-step explanation:
The area (A) of the major sector is
A = area of circle × fraction of circle
= πr² × [tex]\frac{255}{360}[/tex]
= π × 13.4² × [tex]\frac{255}{360}[/tex]
= [tex]\frac{13.4^2(255)\pi }{360}[/tex] ≈ 399.6 miles²
Kim has $1.65 in nickels, dimes and quarters. She has 10 coins all together and the number of quarters is equal to the number of nickels and dimes combined. Haw many of each coin does she have?
3 nickels, 2 dimes, 5 quarters
3 nickels, 2 dimes, 2 quarters
2 nickels, 3 dimes, 5 quarters
3 nickels, 5 dimes, 2 quarters
Answer:
2 nickels 3 dimes 5 quarters
Step-by-step explanation:
We know it cannot be the second option because there are only 7 coins and Kim has 10. It also cannot be the first option because the coins add up to $1.60, and Kim has $1.65. It could not be the last option either because the coins add up to $1.15, and Kim has $1.65.
Answer: Third option
Why? The third option has a total of $1.65, which is what Kim has. There are 10 coins all together, which is also what Kim has. And the number of nickels and dimes combined (5) is equal to the number of quarters (5).
Jamie evaluated this expression. step 1: step 2: step 3: 26 step 4: 64 Analyze the steps Jamie applied to evaluate the expression. Which rule of exponents was applied in each step? Step 1: Step 2: Step 3:
Answer:
step one: product of powers
step 2:power of powers
step 3: quotient of powers
Step-by-step explanation:
The rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.
What is the definition of arithmetic operation?Arithmetic is a branch of mathematics that studies numbers and the many operations that may be applied to them. The four basic math operations are addition, subtraction, multiplication, and division.
The given expression is;
[tex]\frac{(2)^3(2)^4}{2^{10}}[/tex]
Step 1; Multiplication rule of exponents;
[tex]\frac{(2)^3(2)^4}{2^{10}} \\\\ \frac{2^{3+4}}{2^{10}} \\\\\frac{2^7}{2^{10}}[/tex]
Step 2;Division rule of exponents;
[tex]\frac{2^7}{2{10}} \\\\ (2)^{7-10}\\\\ (2)^{-3}[/tex]
Step 2;Inverse rule of exponents;
[tex](2)^{-3}\\\\ \frac{1}{2^3} \\\\\frac{1}{8}[/tex]
Hence, the rule of exponents was applied in each step will be multiplication rule,division rule and inverse of exponent rule.
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Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
any help is appreciated!
Final answer:
The equation 4x + 3 = 7 is solved algebraically by subtracting 3 from both sides and then dividing by 4 to find x = 1. There is no need for logarithms or the change of base formula to solve this linear equation.
Explanation:
The equation 4x + 3 = 7 is a linear equation and can be solved using simple algebraic manipulations rather than the change of base formula for logarithms. However, to show how logarithms could hypothetically be used (even though it's over-complicating this particular problem), we can take the following steps:
Divide both sides by 4: x = 1.
Therefore, the solution to the equation is x = 1. There is no need to round to the nearest thousandth as the solution is a whole number. The change of base formula, logb y = (log y) / (log b), is not necessary for this equation.
The solution to the equation [tex]\(4x + 3 = 7\) is \(x = 1\),[/tex] obtained by isolating [tex]\(x\)[/tex]
Step-by-Step Solution:
1. Write down the equation:
[tex]\[ 4x + 3 = 7 \][/tex]
2. Isolate the term with the variable [tex]\(x\):[/tex]
- To do this, we need to remove the constant term on the left side by subtracting 3 from both sides of the equation.
[tex]\[ 4x + 3 - 3 = 7 - 3 \][/tex]
- Simplify both sides:
[tex]\[ 4x = 4 \][/tex]
3. Solve for [tex]\(x\):[/tex]
- To isolate [tex]\(x\)[/tex], divide both sides of the equation by 4:
[tex]\[ \frac{4x}{4} = \frac{4}{4} \][/tex]
- Simplify both sides:
[tex]\[ x = 1 \][/tex]
Conclusion:
The solution to the equation [tex]\(4x + 3 = 7\)[/tex] is:
[tex]\[x = 1\][/tex]
Please help me out please
Answer:
262 m³
Step-by-step explanation:
The volume (V) of a cone is calculated as
V = [tex]\frac{1}{3}[/tex] πr²h ( r is the radius of the base and h the height )
here diameter = 10 m, hence radius = 5 m
V = [tex]\frac{1}{3}[/tex]π × 5² × 10
= [tex]\frac{1}{3}[/tex] π × 250 = [tex]\frac{250\pi }{3}[/tex] ≈ 262 m³
The graph shows the system of equations that can be used to solve x3+x2=x-1
Which statement describes the roots of this equation?
1 rational root and 2 complex roots
1 rational root and 2 irrational roots
3 irrational roots
3 rational roots
Answer:
A. 1 rational root and 2 complex roots
Step-by-step explanation:
The equation [tex]x^3+x^2=x-1[/tex] has the expression [tex]x^3+x^2[/tex] in the left side and the expression [tex]x-1[/tex] in the right side.
when ypu plot the graphs of the functions [tex]y=x^3+x^2[/tex] and [tex]y=x-1,[/tex] the number of intersection points shows the number of real solutions. These two graphs intersect only once, so the equation has one real solution. The third power equation should have three solutions, thus, two remaining solutions are complex.
Answer:
The answer is A
Step-by-step explanation:
1. Solve |x| < 13
A) {-13, 13}
B) {x|-13 < x < 13}
C) {x|x < -13 or x > 13}
2. |x| > 4
A) {-4, 4}
B) {x|-4 < x < 4}
C) {x|x < -4 or x > 4}
Answer:
B) {x|-13 < x < 13}
C) {x|x < -4 or x > 4}
Step-by-step explanation:
Given in the question,
1.|x| < 13Remove the absolute value term.
If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:
-(number on other side) < (quantity inside absolute value) < (number on other side)
-13 < x < 13
2.|x| > 4
If your absolute value is greater than a number, then set up an "or" compound inequality that looks like this:
(quantity inside absolute value) < -(number on other side)
OR
(quantity inside absolute value) > (number on other side)
x < - 4 or x > 4
A manufacturer finds that 10% of the flashlights in a sample are defective. Predict how many defective flashlights there will be in a shipment of 4,000 flashlights.
A.
4 flashlights
B.
40 flashlights *
C.
400 flashlights
please help quick
Answer:
400
Step-by-step explanation:
Just take 10% of 4,000 flashlights. 400 flashlights are likely to be defective.
A set of data items is normally distributed with a mean of 500. Find the data item in this distribution that corresponds to the given z-score. z = 2, if the standard deviation is 40.
The data item in this distribution that corresponds to the given z-score of 2 is 580.
Given:
Mean = 500
z score = 2
standard deviation = 40
To find the data item corresponding to a given z-score in a normally distributed data set, use the formula:
[tex]X = \mu + (z * \sigma)[/tex]
where X is the data item, μ is the mean, z is the z-score, and σ is the standard deviation.
Plugging the values into the formula, we have:
[tex]X = 500 + (2 * 40)[/tex]
[tex]X = 500 + 80[/tex]
[tex]X = 580[/tex]
Therefore, the data is 580.
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In a data set with a mean of 500 and standard deviation of 40, the data item that corresponds to the z-score of 2 is 580. This is computed by multiplying the standard deviation by the z-score and adding the product to the mean.
Explanation:This question is dealing with z-scores and the standard normal distribution in statistics. The z-score is a measure of how many standard deviations an element is from the mean. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
When you are given a z-score of 2 for a data set with a mean of 500 and a standard deviation of 40, it means the data item you're looking for is 2 standard deviations above the mean. You compute this by multiplying the z-score by the standard deviation and adding the product to the mean. So in this case, 500 + 2*40 = 580. Therefore, the data item in this distribution that corresponds to the z-score of 2 is 580.
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I cleaned 6/9 of my room, and my friend cleaned 2/9 of my room. How much of my room do we still have to clean?
Answer:
1/9
Step-by-step explanation:
6/9+ 2/9= 8/9
then we subtract 8/9 from 1
1-8/9
then we have to convert 1 into a fraction
9/9-8/9
this leaves 1/9
Answer:
1/9
Step-by-step explanation:
We can make an equation that looks like this:
2/9+6/9+x/9=9/9
Let's cancel out the denominator:
2+6+x=9
Then combine like terms:
8+x=9
Then solve for x:
x=1
Then add in the denominator we canceled out:
x=1/9
Hope I helped, soz if I'm wrong!
~Potato.
Copyright Potato 2019.
P.S. Why would your friend clean your room lel :P
Solve the following equation for x.
225 = 27x -18
Answer:
Step by step explanation
the equation is 225=27x-18
the first step is to add the 18 to the other side to get
243=27x
now divide by 27 on both sides
243/27=27x/27
solve to get
9=x
A diameter of a circle has end points P(-10,-2) And Q(4,6)
A. Find the center of the circle
B. Find the radius.if your answer is not an integer express it in a radical form.
C.write and equation for the circle
GIVING BRAINLIEST
Answer:
Step-by-step explanation:
A]
The center is the average values of the 2 endpoints (which is also the diameter).
x:(-10 + 4)/2 = -6/2 = -3
y:(-2 + 6)/2 = 4/2 = 2
Center(-3,2)
B]
The radius is the distance from the center to one of the end points.
r^2 = (-3 - 4)^2 + (2 - 6)^2
r^2 = (-7)^2 + (-4)^2
r^2 = 49 + 16
r^2 = 65
r = sqrt(65)
C]
(x + 3)^2 + (y - 2)^2 = 65
Graph
The graph has been included so that you can see that the center I have calculated is between (-10,-2) and (4,6)
Further, it shows the the circle goes the two end points of the diameter.