Answer:
First Quartile Q1 = 9.9525
Step-by-step explanation:
For a standard normal distribution,
First quartile Q1 = μ - 0.675 σ
From the question mean μ = 10.56
Standard deviation σ = 0.9
Plugging these values into the first quartile equation, we have;
Q1 = 10.56 -0.675(0.9)
Q1 = 10.56 - 0.6075
Q1 = 9.9525
In the figure below, which term best describes point L?
Explanation:
The tickmarks show which pieces are congruent to one another, which in turn show the segments have been bisected (cut in half). The square angle markers show we have perpendicular segments. So we have three perpendicular bisectors. The perpendicular bisectors intersect at the circumcenter. The circumcenter is the center of the circumcircle. This circle goes through all three vertex points of the triangle.
A useful application is let's say you had 2 friends and you three wanted to pick a location to meet for lunch. Each person traveling from their house to the circumcenter's location will have each person travel the same distance. We say the circumcenter is equidistant from each vertex point of the triangle. In terms of the diagram, LH = LJ = LK.
Answer: B.) Circumcenter
Step-by-step explanation:
"A motorist wants to determine her gas mileage. At 23,352 miles (on the odometer) the tank is filled. At 23,695 miles the tank is filled again with 14 gal- lons. How many miles per gallon did the car average between the two fillings?"
Answer:
24.5 mpg
Step-by-step explanation:
(23,695 - 23,252) / 14 = 24.5mpg
Answer:
The car averaged a total of 24.5 miles per gallon between the two fillings
Step-by-step explanation:
Firstly, we calculate the difference between the mileages.
This will give us the total distance traveled.
That would be 23,695 - 23,352 = 343 miles
The tank capacity obviously is 14 gallons
So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon
What is the next term of the geometric sequence? 1, 2, 4, 8, 16,
Answer: 32
Step-by-step explanation:
Help please someone I have solved this multiple times factoring out the quadratic equations and I keep getting m as -1. But the correct answer says m is -5.
Answer: m = -5
Step-by-step explanation:
[tex]\dfrac{m+3}{m^2+4m+3}-\dfrac{3}{m^2+6m+9}=\dfrac{m-3}{m^2+4m+3}\\\\\\\dfrac{m+3}{(m+3)(m+1)}-\dfrac{3}{(m+3)(m+3)}=\dfrac{m-3}{(m+3)(m+1)}\quad \rightarrow m\neq-3, m\neq-1[/tex]
Multiply by the LCD (m+3)(m+3)(m+1) to eliminate the denominator. The result is:
(m + 3)(m + 3) - 3(m + 1) = (m - 3)(m - 3)
Multiply binomials, add like terms, and solve for m:
(m² + 6m + 9) - (3m + 3) = m² - 9
m² + 6m + 9 - 3m - 3 = m² - 9
m² + 3m + 6 = m² - 9
3m + 6 = -9
3m = -15
m = -5
Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.
Answer:
The first statement is incorrect. They have to be complementary.
Step-by-step explanation:
You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.
You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.
The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.
Suppose that you expect SugarCane stock price to decline. So you decide to ask your broker to short sell 2000 shares. The current market price is $40. The proceeds from the short sale $80,000 is credited into your account. However, a few days later the market price of the stock jumps to $80 per share and your broker asks you close out your position immediately. What is your profit or loss from this transaction?
Answer:
Loss = $80000
Step-by-step explanation:
To determine if it's a profit or loss is simple.
He predicted the sugar cane stock to fall so he sold , but few days later the stock grew and went bullish.
He sold at$ 40 for 2000 shares
=$ 80000
But the stock went up to $80 per share that is gaining extra $40
So it was actually a loss.
The loss is =$40 * 2000
The loss = $80000
what is the conjugate √8-√9
Answer:
2√2−3
Step-by-step explanation:
Simplify each term.
Since there are no imaginary terms, the complex conjugate is the same as the simplified expression.
Hope this can help
Please help!!
Find the value of x.
X=
Answer:
Step-by-step explanation:
Hello,
We can write three equations thanks to Pythagoras
[tex]AB^2+AC^2=(7+3)^2\\x^2+7^2=AB^2\\x^2+3^2=BC^2\\[/tex]
So it comes
[tex]x^2+7^2+x^2+3^2=(7+3)^2\\\\2x^2=100-49-9=42\\\\x^2 = 42/2=21\\\\x = \sqrt{\boxed{21}}\\[/tex]
Hope this helps
Answer:
x = [tex]\sqrt{21}[/tex]
Step-by-step explanation:
Δ BCD and Δ ABD are similar thus the ratios of corresponding sides are equal, that is
[tex]\frac{BD}{AD}[/tex] = [tex]\frac{CD}{BD}[/tex] , substitute values
[tex]\frac{x}{7}[/tex] = [tex]\frac{3}{x}[/tex] ( cross- multiply )
x² = 21 ( take the square root of both sides )
x = [tex]\sqrt{21}[/tex]
Two types of survey questions are open questions and closed questions. An open question allows for any kind of response; a closed question allows for only a fixed response. An open question and a closed question with its possible choices are given below. List the advantages and disadvantages of each question.
Open question: What can be done to get students to eat healthier foods?
Closed question: How would you get students to eat healthier foods?
1. Mandatory nutrition course
2. Offer only healthy foods in the cafeteria and remove unhealthy foods
3. Offer more healthy foods in the cafeteria and raise the prices on unhealthy foods
What are the advantag?
A. It is easy to compare the results of surveys with open questions.
B. An open question allows for new solutions to be introduced.
C. It is easy to quantify the responses of open questions.
D. An open question allows the respondent to go in-depth with their answer.
What are the disadvantages of an open question?
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
C. The form of the question may influence the opinion of the respondent.
D. An open question limits the possible responses of the respondent.
Answer and explanation:
Advantages of open questions:
B. An open question allows for new solutions to be introduced.
D. An open question allows the respondent to go in-depth with their answer.
Disadvantages of open questions:
A. It is difficult to compare the results of surveys with open questions.
B. It is difficult to quantify the responses of open questions.
Advantages of closed questions:
- It is easy to compare the results of surveys with closed questions.
- It is easy to quantify the responses of closed questions.
Disadvantages of closed questions:
- A closed question limits the possible responses of the respondent.
-The researcher must spend time to generate a satisfactory list of possible responses from the respondent.
- possible answers may also be insufficient to be useful.
Open questions and closed questions in research questionnaires are two popular methods of getting data from respondents. They both have advantages and disadvantages and can be used interchangeably or together in questionnaires.
Closed Questions have defined answer alternatives or answer categories. Eg: Which is your favourite time of the day? (Morning or Evening etc)
Open Questions have free answers, not clear defined alternatives or categories. Eg : Why do you like morning/ evening time the most ?
Closed Questions give brief concrete answers, Open Questions have more essence of subjective & personal elaboration.
Advantages of Open Questions
Open questions allows for new solutions to be introduced. Open questions allows the respondent to go in-depth with their answer.Disadvantages of Open Questions
It is difficult to compare the results of surveys with open questions.It is difficult to quantify the responses of open questions.Advantages of Closed Questions
It is easy to quantify the responses, with these questions. It is easy to compare the results, with these questionsDisadvantages of Closed Questions
The form of question may influence potential of respondent. It limits the possible responses of respondentTo learn more, refer https://brainly.com/question/2855510?referrer=searchResults
Consider the statemen P. P.X=5 which of the following is an equivalent statement
Answer:
(D)R: x+2=7
Step-by-step explanation:
Given the statement P:x=5
An equivalent statement will be a statement whose result is exactly x=5.
From the given options:
R: x+2=7
R: x=7-2
R: x=5
Therefore, R is an equivalent statement.
The correct option is D.
The altitude of an airplane is decreasing at a rate of 41 feet per second. What is the change in altitude of the airplane over a period of 32 seconds?
Answer:
1312 feet
Step-by-step explanation:
41 ft=1 sec
how about 32 sec
41 x 32=1312/1=1312
A square matrix N is called nilpotent if there exists some positive integer k such that Nk = 0. Prove that if N is a nilpotent matrix, then the system Nx = 0 has nontrivial solutions.
Answer:
Nx = λx
Nx = 0, with x≠0
if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions
Step-by-step explanation:
given that
let N be a square matrix in order of n
note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N
let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ
Nx = λx (x≠0)
N²x = λNx = λ²x
∴[tex]N^{k}x[/tex] = (λ^k)x
[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector
where x = 0, (λ^k) = 0
λ = 0
therefore, Nx = λx
Nx = 0, with x≠0
note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution
the substitution method solve 6x-y=3 4x+3y=1
Answer:
[tex]( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Step-by-step explanation:
6x - y = 3
4x + 3y = 1
Solve the equation for y
y = -3 + 6x
4x + 3y = 1
Substitute the given value of y into the equation
4x + 3y = 1
plug the value
[tex]4x + 3( - 3 + 6x) = 1[/tex]
Distribute 3 through the parentheses
[tex]4x - 9 + 18x = 1[/tex]
Collect like terms
[tex]22x - 9 = 1[/tex]
Move constant to R.H.S and change its sign
[tex]22x = 1 + 9[/tex]
Calculate the sum
[tex]22x = 10[/tex]
Divide both sides of the equation by 22
[tex] \frac{22x}{22} = \frac{10}{22} [/tex]
Calculate
[tex]x = \frac{5}{11} [/tex]
Now, substitute the given value of x into the equation
y = -3 + 6x
[tex]y = - 3 + 6 \times \frac{5}{11} [/tex]
Solve the equation for y
[tex]y = - \frac{3}{11} [/tex]
The possible solution of the system is the ordered pair ( x , y )
[tex](x ,\: y) = ( \frac{5}{11} ,\: - \frac{3}{11} )[/tex]-----------------------------------------------------------
Check if the given ordered pair is the solution of the system of equations
[tex]6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3[/tex]
[tex]4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1[/tex]
Simplify the equalities
[tex] 3 = 3[/tex]
[tex]1 = 1[/tex]
Since all of the equalities are true , the ordered pair is the solution of the system
[tex]( \: x ,\: y \: ) = ( \frac{5}{11} \:, - \frac{3}{11} )[/tex]Hope this helps..
Best regards!!
Can someone solve this for me
Answer:
[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]
Step-by-step explanation:
divide each term by 2y^3
Multiply through by the least common denominator.
tje mean of 12 scores is 8.8 what is the sum of tue 12 scores
Answer:
105.6
Step-by-step explanation:
If the mean is 8.8, than that means that in total the sum must be (8.8 * 12) which equals 105.6.
This is because the sum of all the numbers in a list divided by the amount of numbers in a list equals the mean.
Find the axis of symmetry and vertex for the parabola y=−5x2+30x+7.
Answer:
axis of symmetry x=3
vertex (3, 52)
Step-by-step explanation:
y = -5x² + 30x + 7
x = -b/2a = -30/2(-5) = -30/-10 = 3
y = -5(3)² + 30(3) + 7
y = -45 + 90 + 7
y = 52
Look at this triangle work out length AB
Answer:
2√137
Step-by-step explanation:
To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:
22² + 8² = c²
484 + 64 = c²
548 = c²
c = ± √548 = ± 2√137
c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.
The domain of the function is given. Find the range.
f(x) = 5x - 1
Domain: (-1,0,1,2)
Range:{6, 1, -4,9)
Range: (-6, 1, -4,9)
Range: (-6,-1, 4, 9)
Range:{+6,+1,+4,+9
Answer:
your third answer
Step-by-step explanation:
its easy just plug in each domain into your function and the result will be the range
Solve the equation and give the solution 6x – 3y = 3 –2x + 6y = 14
Answer:
x=3.9 or 39/10 and y=3.13333 or 47/15
Step-by-step explanation:
Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:
6x-3y=14 and 3-2x+6y=14
Simplify the equations
6x-3y=14 and -2x+6y=11
Now, line the equations up and pick a variable (either x or y) to eliminate
6x-3y=14
-2x+6y=11
In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y
Multiply (6x-3y=14) by 2 to get:
12x-6y=28
Line the equations up and add or subtract the terms accordingly
12x-6y=28
-2x+6y=11
This becomes:
10x+0y=39
Isolate for x
x= 39/10 or x= 3.9
Now substitute the x value into either of the original equations
6x-3y=14
6(3.9)- 3y=14
Isolate for y
23.4-14=3y
3y= 9.4
y= 3.1333 (repeating) or y= 47/15
Answer: x = 39/10, y = 94/30
Step-by-step explanation:
6x - 3y = 3 - 2x + 6y,
Now solving this becomes
6x + 2x -3y - 6y = 3
8x - 9y = 3 ------------------- 1
3 - 2x + 6y. = 14
-2x + 6y = 14 - 3
-2x. + 6y = 11
Now multiply both side by -1
2x. - 6y = -11 ----------------- 2
Solve equations 1 & 2 together
8x - 9y. = 3
2x - 6y = -11
Using elimination method
Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8
16x - 18y = 6
-16x - 48y = -88 ------------------------- n, now subtract
30y = 94
Therefore. y = 94/30.
Now substitute for y in equation 2
2x - 6y = -11
2x - 6(94/30) = -11
2x - 94/5 = -11
Now multiply through by 5
10x - 94 = -55
10x = -55 + 94
10x = 39
x = 39/10
need help with these 3 questions (giving brainiest if you can answer with equations)
Problem 10
Answer: approximately 57.39159 kmExplanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.
=====================================
Problem 11
Answer: approximately 10.46162 metersExplanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162
=====================================
Problem 12
Answer: approximately 16.05724 cmExplanation: Now we use the tangent rule to connect the opposite and adjacent sides.
tan(37) = 12.1/x
x*tan(37) = 12.1
x = 12.1/tan(37)
x = 16.05724 approximately
A sample of 150 CBC students was taken, and each student filled out a
survey. The survey asked students about different aspects of their college
and personal lives. The experimenter taking the survey defined the
following events:
A=The student has children
B = The student is enrolled in at least 12 credits
C = The student works at least 10 hours per week
The student found that 44 students in the sample had children, 73 were
enrolled in at least 12 credits, and 105 were working at least 10 hours per
week. The student also noted that 35 students had children and were
working at least 10 hours per week.
Calculate the probability of the event BC for students in this sample. Round
your answer to four decimal places as necessary.
Answer:
The probability of the event BC
= the probability of B * C = 48.6667% * 70%
= 34.0667%
Step-by-step explanation:
Probability of A, students with children = 44/150 = 29.3333%
Probability of B, students enrolled in at least 12 credits = 73/150 = 48.6667%
Probability of C, students working at least 10 hours per week = 105/150 = 70%
Therefore, the Probability of BC, students enrolled in 12 credits and working 10 hours per week
= 48.6667% * 70%
= 34.0667%
What is the vertex of the graph of g(x) = |x – 8| + 6?
Answer:
(8,6)Step-by-step explanation:
g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:
8 unit right
6 units up
a parent absolute value function has a vertex at (0,0)
if the function is moved so is the vertex:
(0+8,0+6)
(8,6)
So, the vertex of this function is at (8,6)
Answer: vertex = (8, 6)
Step-by-step explanation:
The Vertex form of an absolute value function is: y = a|x - h| + k where
a is the vertical stretch(h, k) is the vertexg(x) = |x - 8| + 6 is already in vertex form where
h = 8 and k = 6
so the vertex (h, k) = (8, 6)
Which statement must be true if ?
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
D because they are congruent try measuring it.
Answer:
[tex]\boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
The triangles are congruent.
The angles that are corresponding on both triangles must be congruent.
Angle Q in triangle PQR must be congruent to angle T in triangle STU.
Variables A and B have a covariance of 45, and variables C and D have a covariance of 627. How does the A and B relationship compare to the C and D relationship?
Answer:
variable A and Variable B are more negatively related than variable C and variable D.
Step-by-step explanation:
Variables A and B have a covariance = 45
Variables C and D have a covariance = 627
Comparing the relationship between variable A AND B with the relationship between variable C and D
variable A and Variable B are more negatively related than variable C and variable D. this is because the covariance between variable A and Variable B are less positive
plz help.... 2|x-3|-5=7
Answer:
x = -3 and x = 9.
Step-by-step explanation:
2|x - 3| - 5 = 7
2|x - 3| = 12
|x - 3| = 6
x - 3 = 6
x = 9
-(x - 3) = 6
-x + 3 = 6
-x = 3
x = -3
Hope this helps!
Answer:
x=9 x=-3
Step-by-step explanation:
2|x-3|-5=7
Add 5 to each side
2|x-3|-5+5=7+5
2|x-3|=12
Divide by 2
2/2|x-3|=12/2
|x-3|=6
There are two solutions to an absolute value equation, one positive and one negative
x-3 =6 x-3 = -6
Add 3 to each side
x-3+3 = 6+3 x-3+3 = -6+3
x=9 x = -3
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30
6th grade math help me, please :D
Answer:
option: D
51200
Step-by-step explanation:
64000 x 80/100 = 51200
Answer:
Hi there!!!
your required answer is option D.
explanation see in picture.
I hope it will help you...
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answer:
Step-by-step explanation:
Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B
differentiate with respect to X
[tex] \sqrt{ \frac{cos2x}{1 +sin2x } } [/tex]
Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):
[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]
Simplify the leading term as
[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]
Quotient rule:
[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]
Chain rule:
[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]
[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]
Put everything together and simplify:
[tex]\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]
[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]
[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]