If h > 42 and h < 60, where h is in inches, then we can say 42 < h < 60.
This translates to "the person's height must be between 42 inches and 60 inches, excluding both endpoints".
So for example, if someone is h = 50 inches, then they can go on the ride. This is because 42 < 50 < 60 is true. I've simply replaced h with 50.
On the other hand, something like 42 < 70 < 60 is false, meaning that h = 70 isn't allowed as they are too tall.
The person cannot have a height of h = 42, and they can't have a height of h = 60 either since we're leaving the endpoints out.
As a final example, if the person is h = 40 inches, then they can't ride either because 42 < 40 < 60 is false. They are too short in this case.
-------------------
Side notes:
12 inches = 1 foot42 inches = 3 feet, 6 inches60 inches = 5 feet50 inches = 4 feet, 2 inches70 inches = 5 feet, 10 inches40 inches = 3 feet, 4 inchesGJ is a midsegment of △HIK. If HI=s–59 and GJ=s–65, what is the value of s?
Answer:
s = 71
Step-by-step explanation:
Given that GJ is a midsegment of the triangle then it is half the length of the third side, that is
GJ = [tex]\frac{1}{2}[/tex] HI , so
s - 65 = [tex]\frac{1}{2}[/tex] (s - 59) ← multiply both sides by 2 to clear the fraction
2s - 130 = s - 59 ( subtract s from both sides )
s - 130 = - 59 ( add 130 to both sides )
s = 71
The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent by a random variable x where repair time follow a normal distribution with mean 5 hour and standard deviation 1 hour , if 5 electrical breakdown ore randomly chosen , Find the probability that ( a all repaired time below 6 hours ( b ) exactly 3 of them repaired below 6 hours
Answer:
a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.
b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours
Step-by-step explanation:
To solve this question, we need to understand the normal and the binomial probability distributions.
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.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Proportion repaired below 6 hours:
Mean 5 hours and standard deviation 1 hour, which means that [tex]\mu = 5, \sigma = 1[/tex]
This proportion is the p-value of Z when X = 6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6 - 5}{1}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
0.8413 repaired below 6 hours.
For the binomial distribution, this means that [tex]p = 0.8413[/tex]
5 are chosen:
This means that [tex]n = 5[/tex]
a) Probability that all are repaired in less than 6 hours
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.8413)^{5}.(0.1587)^{0} = 0.4215[/tex]
0.4215 = 42.15% probability that all are repaired in less than 6 hours.
b) Probability that exactly 3 of them repaired below 6 hours
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{5,3}.(0.8413)^{3}.(0.1587)^{2} = 0.15[/tex]
0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours
simplify
3a + 2b - 8a + b
Answer:
-5a+3b
Step-by-step explanation:
just adding and subtracting like terms
Answer:
3b-5a
Step-by-step explanation:
hope this helps:)
Harry just transferred $6 out of his bank account. As a result, the account now has $488 left in it. How much money was in the account before the transfer?
Answer:
$494
Step-by-step explanation:
Given data
Amount transfer= $6
Balance after transfer= $488
Let the total amount in the account before the transfer be x
Hence
x-6= 488
x= 488+6
x=$494
Hence the amount in the account before the transfer is $494
Help? Luis has saved $15. He doubles the amount he saves each week. Does this represent an exponential function? Choose the correct word in each drop-down menu.
This___ represent an exponential function, because his savings increase by a constant___
1st blank (does not, does)
2nd blank (ratio, difference)
Answer:
1). Does Not
2). Ratio
Step-by-step explanation:
According to the Question,
Given that, Luis has saved $15. He doubles the amount he saves each week.
This DOES NOT represent an exponential function, because his savings increase by a constant RATIO.PLEASE HELP! NO SPAMMING! SHOW WORK!
The ratio of the dimensions of the model to the dimensions of the Great Pyramid is about 1 to 38. The surface area of the real pyramid is about how many times the surface area of the model.
Dimensions: a pyramid with a square base.
base sides: 6m
height: 4m
========================================================
Explanation:
Consider a square on paper that is 3 inches by 3 inches. It's area would be 3*3 = 9 square inches.
The ratio 1 to 38 means that 1 inch on paper corresponds to 38 inches in real life (assuming the "1 to 38" doesn't have any verbal units attached to it; if so, then refer to the note below). So a 3 by 3 square corresponds to a 114 by 114 square because 3*38 = 114.
The area of the second larger square is 114*114 = 12,996 square inches.
Now divide the two areas: (12,996)/(9) = 1444
It's probably not entirely obvious, but through a bit of playing around with various numbers, you should find that 38^2 = 1444. It's not a coincidence that this happens. The linear scale factor is 38 which means the area scale factor is 38^2 = 1444.
In short, the larger square in real life has area that is 1444 times that of its scaled down counterpart.
Or put another way:
large area = 1444*(small area)
------------------
Side note: This all assumes that the numbers in "1 to 38" are both the same unit. If we had a mixed ratio of units like "1 inch to 38 feet", then the answer would be different. You would need to convert from feet to inches, and then follow the steps above to get a different answer.
Question 19:
1 point
In the diagram below of circle O, chords JT and ER intersect at M.
E
М.
M
ºo
R
If EM = 8 and RM = 15, the lengths of JM and TM could be
(1) 12 and 9.5
(3) 16 and 7.5
(2) 14 and 8.5
(4) 18 and 6.5
Applying the intersecting chords theorem, the possible lengths of JM and TM could be: 16 and 7.5.
What is the Intersecting Chords Theorem?The intersecting chords theorem states that product of the divided segments of each intersectint chords are equal to each other.
Based on the intersecting chords theorem, we would have:
(EM)(RM) = (JM)(TM)
If JM and TM are 16 and 7.5 respectively, we would have:
(8)(15) = (16)(7.5)
120 = 120
The lengths of JM and TM could therefore be: 16 and 7.5.
Learn more about the intersecting chords theorem on:
https://brainly.com/question/13950364
#SPJ2
Answer:
16 and 7.5
Step-by-step explanation:
Use the Substitution method to solve the system of equations
3x+4y=10
y=x-1
Answer: 2
Step-by-step explanation:
3x+4y=10
3x+4(x-1)=10
3x+4x-4=10
7x-4=10
Add 4 to both sides
7x=14
x=2
Answer:(2,1)
Step-by-step explanation:ap3x beans
I need help with number 1 and 2
Answer:
1. 452.39
2. 615.75
Step-by-step explanation:
area of a circle = A=πr2
Tell whether the triangle with the given side lengths is a right triangle.
60, 63, 88
The answer is
yes or
no
Answer:
no
Step-by-step explanation:
so in order for it to be a right triangle this would have to be true:
a^2 + b^2 = c^2
since c represents the hypoteneuse, it will be the longest side. so:
60^2 + 63^2 = 88^2
3600 + 3969 = 7744
7569 = 7744
since that statement is not true, the answer is no.
it is not a right triangle
the square root of 7569 is 87, so the triple would have to be : {60,63,87}
helpppppppppp plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Step-by-step explanation:
The left side represent the tens place of the number, and the right side represent the one sides of the number. So the numbers are
12,12,13,14,18,19,19, 20,23,26,27,31,31,31,32,34,41,44,45,48.
a. There are 20 terms so this equation 20/2=10 means the 10th term will be the median. make sure to also include the number 11th term becuase the number of terms is even. The 10th and 11th term are 26,27 so the median is the midpoint.
[tex] \frac{26 + 27}{2} = 26.5[/tex]
The median is 26.5
b. The range is maximum value minus minimum value.
[tex]48 - 12 = 36[/tex]
c. The mode is the number that appear the most
That number is 31.
d. 20 students took apart of this survey.
How much money does an employee
working for a salary of $48,000 per
year get paid each month?
A. $48,000 per month
B. $1,846 per month
C. $923 per month
D. $4,000 per month
Answer:
D. 4000 per month
Step-by-step explanation:
If they make 48000 per year, to find how mmuch s/he makes in a month, we have to divide it by 12 because there are 12 months in a year.
$48,000/12= $4000 per month
Use and method to find the total number of outcomes in each situation.
choosing one math class from Algebra and Geometry and one foreign language
class from French, Spanish, or Latin
===========================================================
Explanation:
Think of a table that has 2 rows and 3 columns.
Each row represents a different math class (either Algebra or Geometry).
Each column represents a different foreign language class (French, Spanish or Latin).
This table has 2*3 = 6 cells inside. Each cell represents a different combination of classes possible.
In short, all we have to do is multiply the number of classes for each subject.
Answer:
Explanation:
Think of a table that has 2 rows and 3 columns.
Each row represents a different math class (either Algebra or Geometry).
Each column represents a different foreign language class (French, Spanish or Latin).
This table has 2*3 = 6 cells inside. Each cell represents a different combination of classes possible.
In short, all we have to do is multiply the number of classes for each subject.
Step-by-step explanation:
What is the recursive rule for the sequence?
−2.7, −8.3, −13.9, −19.5, −25.1
an=an+1+5.6, where a1=−2.7
an=an+1−5.6, where a1=−2.7
an=an−1+5.6, where a1=−2.7
an=an−1−5.6, where a1=−2.7
Answer:
[tex]a_{n} =a_{n-1} -5.6[/tex] where [tex]a_{1} =-2.7[/tex]
Step-by-step explanation:
This is an arithmetic sequence with the first term is [tex]a_{1}[/tex] = -2.7 and has a common difference of [tex]d=-5.6[/tex].
Arithmetic Sequence: [tex]a_{n} =a_{n-1} +d[/tex]
[tex]a_{n}[/tex] is the nth term and [tex]d[/tex] is the common difference.
The common difference: -2.7, -8.3, -13.9...
Subtract: -2.7- (-8.3) = -5.6, -13.9 - (-8.3) = -5.6
Common difference: [tex]d = -5.6[/tex]
Recursive rule: [tex]a_{n} = a_{n-1} -5.6[/tex]
Can someone please help me?
create your own scale, it could be 2cm=40mm, so 3cm=60mm and 2.5cm=50mm.
then draw your trapezium in the given space using your scale
which word describes the slope of the line?
a) positive
b) negative
c) zero
d) undefined
Answer: To me it (Zero) or (Undefined)
jalil asked for two triple-dip ice-cream cones.if each single -dip cone costs $1.69 and each extra scoop of ice cream is 00. 85 how much will he have to pay
Solve for X enter your answer in the box
Answer:
x = 6
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
GIVEN :-
AD ║ BCAE = 16 unitsAB = 5x + 2 unitsDE = 12 unitsDC = 24 unitsTO FIND :-
Value of xGENERAL CONCEPT TO BE USED IN THIS QUESTION :-
Basic Proportionality Theorem -
If a line drawn parallel to one side of a triangle and intersects the other two sides at distinct points , it divides the other two sides in equal proportion.
SOLUTION :-
AD is the line drawn parallel to BC and intersects EB & EC at A & D respectively. By using Basic Proportionality Theorem , it can be stated that -
[tex]\frac{AE}{AB} = \frac{DE}{DC}[/tex]
[tex]=> \frac{16}{5x + 2} = \frac{12}{24}[/tex]
[tex]=> \frac{16}{5x + 2} = \frac{1}{2}[/tex]
[tex]=> 5x + 2 = 16 \times 2 = 32[/tex]
[tex]=> 5x = 32 - 2 = 30[/tex]
[tex]=> x = \frac{30}{5} = 6[/tex]
Can someone really help
Me !
(b) Simplify 4q2 – 3q2
Hellllllppppppppppp
Plsssss
Answer:
q^2
Step-by-step explanation:
Answer:
q^2
Step-by-step explanation:
4q^2 – 3q^2
Factor out the q^2
q^2 ( 4-3)
q^2(1)
1q^2
q^2
HI I NEED HELP ASAP I GIVE BRAINLEST IF YOU GET IT RIGHT
Cho tập số tự nhiên từ 1 đến 20, lấy ngẫu nhiên ba số. Xác suất để ba số lấy được lập thành cấp số cộng là
I will mark you brainliest if you solve this
show your working as well
4) (4x2– x – 7) + (2x3+ 6x2– 11)
5)(2x3– x + 4) + (5x2– 6x – 5)
6)(3x2+ 2x + 1) – (x2– 3x + 4)
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Answer:
4) 2x3 + 10x2−x−18
5) 2x3+5x2−7x−1
6) 2x2+5x−3
7) −3x2−6x+1
Step-by-step explanation:
4) (4x2 - x - 7) + (2x3+ 6x2– 11)
Combine Like Terms:
=4x2+−x+−7+2x3+6x2+−11
=(2x3)+(4x2+6x2)+(−x)+(−7+−11)
=2x3+10x2+−x+−18
5) (2x3– x + 4) + (5x2– 6x – 5)
Combine Like Terms:
=2x3+−x+4+5x2+−6x+−5
=(2x3)+(5x2)+(−x+−6x)+(4+−5)
=2x3+5x2+−7x+−1
6) (3x2+ 2x + 1) – (x2– 3x + 4)
Distribute the Negative Sign:
=3x2+2x+1+−1(x2−3x+4)
=3x2+2x+1+−1x2+−1(−3x)+(−1)(4)
=3x2+2x+1+−x2+3x+−4
Combine Like Terms:
=3x2+2x+1+−x2+3x+−4
=(3x2+−x2)+(2x+3x)+(1+−4)
=2x2+5x+−3
7)(2x2– 3x + 7) – (5x2+ 3x + 6)
Combine Like Terms:
= (2x2 −5x2 )+(−3x−3x)+(7−6)
Solve for r.
Enter the solutions from least to greatest.
-2x2 – 9 = -107
lesser I =
greater x =
Step-by-step explanation:
[tex] - 2 {x}^{2} - 9 = - 107 \\ - {2x}^{2} = - 98 \\ {x}^{2} = 49 \\ x = \sqrt{49} \\ x = 7 \\ { \boxed{lesser : \: - 7}} \\ { \boxed{greater : \: + 7}}[/tex]
How many three digit numbers greater than 540 can be formed using the digits
0,2,4,5,6,8 ?
Answer:
Step-by-step explanation:
Determine the equation of the circle in standard form:
x^2+y^2+4x+6y-36=0
Answer:
2. (x+2)²+(y+3)²=49
Step-by-step explanation:
it is possible to re-write the given equation:
x²+4x+4+y²+6y+9-49=0;
(x+2)²+(y+3)²-49=0;
(x+2)²+(y+3)²=7².
Write an equation of the line that passes through the point (4,5) and has a slope of -2.
Answer:
y = - 2x + 13
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 2 , then
y = - 2x + c ← is the partial equation
To find c substitute (4, 5) into the partial equation
5 = - 8 + c ⇒ c = 5 + 8 = 13
y = - 2x + 13 ← equation of line
Answer:
Step-by-step explanation:
slope=-2
now using slope intercet formof equation of straight line,we get
y=mx+b
or, y=-2x + b
y + 2x =b
2x + y=b ...................... eq(i)
since the line passes through the point (4,5) it satisfies the equation (i)
y=5 and x=4 so,
equation is 2x +y =b
2*4 + 5=b
8+5=b
13=b
substituting the value of b in eq(i)
2x + y=b
2x + y=13
2x + y-13=0 is the required equation of the line.
Evaluate the exponential expression.
3•42
Answer:
48
Step-by-step explanation:
Trust me
Find the following
[tex]2x + 3y = 13[/tex]
[tex]xy = 6[/tex]
find
[tex]8 {x}^{3} + 27 {y}^{3} [/tex]
Answer:
793
Step-by-step explanation:
x=2, y =3
8x³+27y³ = 64 + 729 = 793
The figure below is a square. Find the length of side x in simplest radical form with a
rational denominator.
VT
Answer:
x = [tex]\sqrt{14}[/tex]
Step-by-step explanation:
[tex]\sqrt{7}[/tex] / sin(45) = x / sin(90) (Cause its a square, the edges are 90 degrees)
[tex]\sqrt{14}[/tex] = x / 1
x = [tex]\sqrt{14}[/tex]