Answer:
x = - 5
Step-by-step explanation:
[tex]Let \ (x _ 1 , y _ 1 ) \ and \ (x _ 2 , y _ 2 ) \ be \ the \ points. \\\\The \ distance \ between \ the \ points \ be ,\ d = \sqrt{(x_2 - x_1)^2 + ( y _ 2 - y_1)^2}[/tex]
Given : d = 10 units
And the points are ( x , - 4) and ( 3 , 2 ).
Find x
[tex]d = \sqrt{( 3 - x)^2 + ( -4 - 2)^2} \\\\10 = \sqrt{( 3 - x)^2 + ( -6)^2} \\\\10^2 = [ \ \sqrt{( 3 - x)^2 + 36} \ ]^2 \ \ \ \ \ \ \ \ \ [ \ squaring \ both \ sides \ ] \\\\100 = ( 3 - x )^2 + 36\\\\100 - 36 = ( 3 - x )^ 2\\\\( 3 - x ) = \sqrt{64}\\\\3 - x = \pm 8\\\\3 - x = 8 \ and \ 3 - x = - 8\\\\-x = 8 - 3 \ and \ -x = - 8 - 3\\\\-x = 5 \ and \ -x = - 11\\\\x = - 5 \ and \ x = 11\\\\[/tex]
Check which value of x satisfies the distance between the points.
x = 11
[tex]d = \sqrt{(3-11)^2 + (-2--4)^2} = \sqrt{(-8)^2 + (-2+4)^2}= \sqrt{64+4} = \sqrt {68} \ units[/tex]
does not satisfy.
x = - 5:
[tex]d = \sqrt{ (3 -- 5)^2 + ( - 4 - 2)^2} = \sqrt{8^2 + 6^2} = \sqrt{100} =10 \ units[/tex]
Therefore , x = - 5
Show all the steps to solve the following
942.6 - 19.734
Answer:
922.868
Step-by-step explanation:
1. Thousandth place of 942.6002. Subtracting[tex]942.600-19.732=922.868[/tex]
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $2000. What is the probability of randomly selecting one employee who earned less than or equal to $45,000
Answer:
The probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621
Step-by-step explanation:
We are given that
Mean,[tex]\mu=50000[/tex]
Standard deviation,[tex]\sigma=2000[/tex]
We have to find the probability of randomly selecting one employee who earned less than or equal to $45,000.
[tex]P(x\leq 45000)=P(\frac{x-\mu}{\sigma}\leq \frac{45000-50000}{2000})[/tex]
[tex]P(x\leq 45000)=P(Z\leq-\frac{5000}{2000})[/tex]
[tex]P(x\leq 45000)=P(Z\leq -2.5)[/tex]
[tex]P(x\leq 45000)=0.00621[/tex]
Hence, the probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621
Martina made$391for17hours of work. At the same rate, how many hours would she have to work to make$253? a 11 hours b 9 hours c 22 hours d 33 hours
Answer:
11 hours is right answer i hope it will help you
Plsss help Get brainiest if right!!
Anita can paint 25 wooden slats in 5.5 hours. If she continues to
work at the same speed without any breaks, how many slats can
she paint in 9.9 hours?
Hello!
25 wooden ..... 5.5 hours
x wooden ..... 9.9 hours
_____________________
25/x = 5.5/9.9
25 × 9.9 = x × 5.5
247.5 = x × 5.5
x × 5.5 = 247.5
x = 247.5 : 5.5
x = 45 wooden
Good luck! :)
Answer:
45
Step-by-step explanation:
In questions such as these it is implied Anita can and does work at a constant rate. Therefore, we can set up the following proportion:
[tex]\frac{25}{5.5}=\frac{x}{9.9}[/tex], where [tex]x[/tex] represents the number of wooden slats she can paint in 9.9 hours.
Multiplying both sides by 9, we get:
[tex]x=\frac{9.9\cdot 25}{5.5},\\x=\boxed{45}[/tex]
Order the following integers from smallest (left side) to biggest (right
side):
20, 0, 22, -35, 100, -59
Need help please
Pls answer? Last one for today!
Step-by-step explanation:
You look for the common factor of both of them which in this case is 5, therefore it's
5(x+7)..just divide 5 in 5x and in 35
A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the other students. Find the probability that, in exactly one of the two classes, all 8 students pass.
Answer:
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability that all students pass in a class:
Class of 8 students, which means that [tex]n = 8[/tex]
Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]
This probability is P(X = 8). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]
Find the probability that, in exactly one of the two classes, all 8 students pass.
Two classes means that [tex]n = 2[/tex]
0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].
This probability is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Find the quotient of the following
Answer:
you simply have to do ide the coefficients and subtract the power
An amusement park offers 2 options on tickets into the park. People can either buy 5 admission tickets for $130 or buy 1 admission ticket for $30. How much money will a group of 5 people save by buying 5 admission tickets for $130?
Answer:
You could save $20
Step-by-step explanation:
For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130
Answer:
20 dollars
Step-by-step explanation:
for the first deal is 5 for $130
and the second is for $30
$30 times 5 (the number of people) = $150
$150-$130= is 20
answer: $20
If I=square root-1 then i^2=
Answer:
i^−3 = i
i^−2 = −1
i^−1 = −i
i^0 = 1
i^1 = i
i^2 = −1
i^3 = −i
i^4 = 1
i^5 = i
i^ 6 = −1
See the pattern
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival rate of 10 requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a service rate of 12 requests per hour. What is the probability that no requests for assistance are in the system
Answer:
0.1667
Step-by-step explanation:
We are given;
Arrival rate, λ = 10 requests per hour
Service rate, μ = 12 requests per hour
From queuing theory, we know that;
ρ = λ/μ
Where ρ is the average proportion of time which the server is occupied.
Thus;
ρ = 10/12
ρ = 0.8333
Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.
This is given by the Formula;
1 - ρ
probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667
Please help me i will give you brainly please
Answer:
19. 3x+5/2x+7 =5
or, 3x+5=5×(2x + 7)
or, 3x + 5 = 10x + 35
or, 5 - 35 = 10x - 3x
or, -30 = 7x
or, -30/7 = x
21. let x be the other number
we know,
or, x × 1/7 =2
or, x/7 =2
or, x = 14
therefore, the other number is 14.
SCALCET8 3.9.013. A plane flying horizontally at an altitude of 2 mi and a speed of 570 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 5 mi away from the station. (Round your answer to the nearest whole number.)
Answer:
DL/dt = 529 miles/h
Step-by-step explanation:
The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t point C) shape a right triangle wich hypothenuse L is:
L² = d² + x²
d is the constant distance between the plane and the ground
Then differentiation with respect to time on both sides of the equation
2*L*dL/dt = 2*d* Dd/dt + 2*x*dx/dt
But Dd/dt = 0
L*dL/dt = x*dx/dt
x = 5 miles dx/dt = 570 m/h L = √ d² + x² L √ (5)² + (2)²
L = √29 L = 5.39 m
5.39 *DL/dt = 5*570 m/h
DL/dt = 5*570/5.39 miles/h
DL/dt = 528.76 miles/h
DL/dt = 529 miles/h
Instructions: Drag and drop the correct name for each angle. Each angle has more than one name so be sure to identity all the correct names
Answer/Step-by-step explanation:
Recall: an angle can be named in three different ways:
i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.
ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2
iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.
✔️Let's name the each angle given according:
1. <G, <3, and <FGH
2. <D, <4, and <CDE
3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)
(2cosA+1) (2cosA-1)=2cos2A+1 prove that
To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1
We try to solve one side of the equation to get the other side of the equation.
In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation (2cosA + 1)(2cosA - 1)
Solving the right hand side: 2cos2A + 1
i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA
Therefore;
cos2A = cos²A - sin²A
ii. We also know that: cos²A + sin²A = 1
Therefore;
sin²A = 1 - cos²A
iii. Now re-write the right hand side by substituting the value of cos2A as follows;
2cos2A + 1 = 2(cos²A - sin²A) + 1
iv. Expand the result in (iii)
2cos2A + 1 = 2cos²A - 2sin²A + 1
v. Now substitute the value of sin²A in (ii) into the result in (iv)
2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1
vi. Solve the result in (v)
2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1
2cos2A + 1 = 4cos²A - 2 + 1
2cos2A + 1 = 4cos²A - 1
2cos2A + 1 = (2cosA)² - 1²
vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e
a² - b² = (a+b)(a-b)
This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;
2cos2A + 1 = (2cosA)² - 1²
2cos2A + 1 = (2cosA + 1)(2cosA - 1)
Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;
(2cosA + 1)(2cosA - 1) = 2cos2A + 1
Answer:
[tex]\boxed{\sf LHS = RHS }[/tex]
Step-by-step explanation:
We need to prove that ,
[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]
We can start by taking RHS and will try to obtain the LHS . The RHS is ,
[tex]\sf\implies RHS= 2cos2A + 1 [/tex]
We know that , cos2A = 2cos²A - 1 ,
[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]
Simplify the bracket ,
[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]
Add the constants ,
[tex]\sf\implies RHS= 4cos^2-1 [/tex]
Write each term in form of square of a number ,
[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]
Using (a+b)(a-b) = a² - b² , we have ,
[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]
This equals to LHS , therefore ,
[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]
Hence Proved !
A, B and C are collinear points. B is between A and C. AB=12 BC=18 AC=3x Find X.
Answer:
[tex]x =10[/tex]
Step-by-step explanation:
Given
[tex]AB = 12[/tex]
[tex]BC = 18[/tex]
[tex]AC = 3x[/tex]
Required
Solve for x
Since B is in between both points, then:
[tex]AC = AB + BC[/tex]
This gives
[tex]3x = 12 + 18[/tex]
[tex]3x = 30[/tex]
Divide by 3
[tex]x =10[/tex]
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8
Answer:
[tex]x = 77[/tex]
Step-by-step explanation:
Given
[tex]First \to Second[/tex]
[tex]35 \to x[/tex]
[tex]20 \to 44[/tex]
[tex]20 \to 44[/tex]
Required
Find x by SSS
Represent the triangle sides as a ratio
[tex]35 : x = 20 : 44[/tex]
Express as fraction
[tex]\frac{x}{35} = \frac{44}{20}[/tex]
Multiply by 35
[tex]x = \frac{44}{20} * 35[/tex]
[tex]x = \frac{44 * 35}{20}[/tex]
[tex]x = \frac{1540}{20}[/tex]
[tex]x = 77[/tex]
Answer:
ccccccccccccccccccccccccccc
Step-by-step explanation:
Help and explain !!!!!!
Answer:
x = -4 or x = 5
Step-by-step explanation:
To solve the absolute value equation
|X| = k
where X is an expression in x, and k is a non-negative number,
solve the compound equation
X = k or X = -k
Here we have |2 - 4x| = 18
In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.
We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.
2 - 4x = 18 or 2 - 4x = -18
-4x = 16 or -4x = -20
x = -4 or x = 5
Answer:
x = -5 . x= 4
Step-by-step explanation:
because |4| = 4 and |-4| = 4
you can see that TWO inputs can get an output of (lets say) 4
The absolute value function can be seen as a function that ignores negative signs
so to get an OUTPUT of "18" using the absolute value function
there are really two ways of getting there
"2-4x = 18" AND "2-4x = -18"
if you solve both of those you will find that -5 and 4 will
produce the 18 and -18
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
Answer:
Independent
Step-by-step explanation:
From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.
were should i go shopping for fidgets
Answer:
Amazon
Step-by-step explanation:
Which operation must you use to find the water temperature after the submarine’s final dive? Which word or words in the problem signify this operation?
Answer:
the temperature drops 2 degrees F
Step-by-step explanation:
Answer:
The problem states that the temperature drops 2 degrees F. The word drops signifies that I should subtract 2 1/5 degrees F from 63 1/4 F.
Step-by-step explanation:
Find the value of x in each case:
Answer:
36
Step-by-step explanation:
2x is an exterior angle
Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).
Put symbolically
<LEG = <EGF + <EFG
<EFG = 180 - 4x In this case you need to find the supplemtnt
<LEG = x + 180 - 4x
2x = 180 - 3x Add 3x to both sides
5x = 180 Divide by 5
x = 36
Know idea how to get an answer to this
Step-by-step explanation:
k=8.6
i think it is the right answer
In the diagram, the measure of angle 3 is 76°. A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8. What is the measure of angle 4?
Answer:
104
Step-by-step explanation:
180-76=104
Answer:
104
Step-by-step explanation:
heres my proof. have a nice day :)
You are hanging a picture on a wall that is 56 1/4 inches long. If the picture frame is 18 2/3 inches long, how much wall space is left? Write your answer as a mixed number.
Answer:
[tex]37 \frac{7}{12}[/tex] inches.
Step-by-step explanation:
Let's start by converting all of these mixed numbers to improper fractions to handle them a little better.
56 × 4 = 224 ⇒ 224 + 1 = [tex]\frac{225}{4}[/tex]
18 × 3 = 54 ⇒ 54 + 2 = [tex]\frac{56}{3}[/tex]
So, we have our improper fractions. Now, we need to convert each to twelfths so we can subtract.
225 × 3 = 675
56 × 4 = 224
[tex]\frac{675}{12} - \frac{224}{12}[/tex] = [tex]\frac{451}{12}[/tex]
[tex]\frac{451}{12} = 37 \frac{7}{12}[/tex]
So, the answer is [tex]37 \frac{7}{12}[/tex] inches.
I need help with these questions
Answer:
1) 6m+8n
4) 21x+14y
7) 14c+16d
10) d+3e
Step-by-step explanation:
3.6 subtract by 1.487 is egual to ______.Pls write in step by step.
Answer:
2.113
Step-by-step explanation:
[tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]
Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.
PLEASE HELP NEED ASAPPPPPP WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRRR
Answer:
The answer is
[tex]y = 3[/tex]
[tex]y = - 4[/tex]
Step-by-step explanation:
We must find a solution where
[tex] \frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Consider the Left Side:
First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get
[tex] \frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1} [/tex]
Which equals
[tex] \frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)} [/tex]
Add the fractions
[tex] \frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]
Simplify the right side by multiplying the fraction
[tex] \frac{6y}{(y + 1)(y + 2)} [/tex]
Set both fractions equal to each other
[tex] \frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)} [/tex]
Since the denomiator are equal, we must set the numerator equal to each other
[tex]6y = {y}^{2} + 7y - 12[/tex]
[tex] = {y}^{2} + y - 12[/tex]
[tex](y + 4)(y - 3)[/tex]
[tex]y = - 4[/tex]
[tex]y = 3[/tex]
Answer:
Step-by-step explanation:
[tex]\frac{6}{y+1}+\frac{y}{y-2}=\frac{6}{y+1} \times \frac{y}{y-2} \\multiply ~by~(y+1)(y-2)\\6(y-2)+y(y+1)=6y\\6y-12+y^2+y=6y\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\\y=-4,3[/tex]
In a particular year, the mean score on the ACT test was 22.5 and the standard deviation was 5.3. The mean score on the SAT mathematics test was 526 and the standard deviation was 101. The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.
Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.
Answer:
- 0.0943
- 0.386
30.185
Step-by-step explanation:
Given :
ACT:
Mean score, m = 22.5
Standard deviation, σ = 5.3
SAT :
Mean score, m = 526
Standard deviation, σ = 101
1.)
Zscore for ACT score of 22:
Since the distribution is normal ; we use the relation ;
Zscore = (score - mean) / standard deviation
Score = 22
Zscore = (22 - 22.5) / 5.3 = - 0.0943
B.)
Zscore for SAT of 487
Zscore = (score - mean) / standard deviation
Score = 487
Zscore = (487 - 526) / 101 = - 0.386
C.)
ACT score, for ACT Zscore of 1.45
Zscore = (score - mean) / standard deviation
ZScore = 1.45
1.45 = (score - 22.5) / 5.3
1.45 * 5.3 = (score - 22.5)
7.685 = score - 22.5
Score = 7.685 + 22.5
Score = 30.185
LOOK AT THE BOTTOM PLEASE MAKE SURE YOU ARE RIGHT
Answer:
reflection
Step-by-step explanation:
B is the mirror image of A across a line between the two images
