The distance from the ground to where the ladder is touching the wall is 7
feet. The distance from the wall to the base of the ladder is 4 feet. What is
the length of the ladder?
wall
ladder
Answer:
L=8.062 feet
Step-by-step explanation:
wall=7
distance=4
Pythagorean theorem
7^2+4^2=L^2
49+16=L^2
65=L^2
L=8.062 feet
The required length of the ladder is given as 8.06 feet.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.
here,
As mentioned in the question,
perpendicular length = 7, base length = 4 feet,
Let the length of the ladder be x,
Following the Pythagoras theorem,
x² = 7 ² + 4²
x ² = 49 + 16
x² = 65
x = √65
x = 8.06
Thus, the required length of the ladder is given as 8.06 feet.
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Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)
Answer:
[tex]P(X > 11) = 0.368[/tex]
[tex]P(X > 22) = 0.135[/tex]
[tex]P(X > 33) = 0.050[/tex]
[tex]x = 33[/tex]
Step-by-step explanation:
Given
[tex]E(x) = 11[/tex] --- Mean
Required (Missing from the question)
[tex](a)\ P(X>11)[/tex]
[tex](b)\ P(X>22)[/tex]
[tex](c)\ P(X>33)[/tex]
(d) x such that [tex]P(X <x)=0.95[/tex]
In an exponential distribution:
[tex]f(x) = \lambda e^{-\lambda x}, x \ge 0[/tex] --- the pdf
[tex]F(x) = 1 - e^{-\lambda x}, x \ge 0[/tex] --- the cdf
[tex]P(X > x) = 1 - F(x)[/tex]
In the above equations:
[tex]\lambda = \frac{1}{E(x)}[/tex]
Substitute 11 for E(x)
[tex]\lambda = \frac{1}{11}[/tex]
Now, we solve (a) to (d) as follows:
Solving (a): P(X>11)
[tex]P(X > 11) = 1 - F(11)[/tex]
Substitute 11 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{1}{11}* 11})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-\frac{11}{11}})[/tex]
[tex]P(X > 11) = 1 - (1 - e^{-1})[/tex]
Remove bracket
[tex]P(X > 11) = 1 - 1 + e^{-1}[/tex]
[tex]P(X > 11) = e^{-1}[/tex]
[tex]P(X > 11) = 0.368[/tex]
Solving (b): P(X>22)
[tex]P(X > 22) = 1 - F(22)[/tex]
Substitute 22 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{1}{11}* 22})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-\frac{22}{11}})[/tex]
[tex]P(X > 22) = 1 - (1 - e^{-2})[/tex]
Remove bracket
[tex]P(X > 22) = 1 - 1 + e^{-2}[/tex]
[tex]P(X > 22) = e^{-2}[/tex]
[tex]P(X > 22) = 0.135[/tex]
Solving (c): P(X>33)
[tex]P(X > 33) = 1 - F(33)[/tex]
Substitute 33 for x in [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{1}{11}* 33})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-\frac{33}{11}})[/tex]
[tex]P(X > 33) = 1 - (1 - e^{-3})[/tex]
Remove bracket
[tex]P(X > 33) = 1 - 1 + e^{-3}[/tex]
[tex]P(X > 33) = e^{-3}[/tex]
[tex]P(X > 33) = 0.050[/tex]
Solving (d): x when [tex]P(X <x)=0.95[/tex]
Here, we make use of:
[tex]P(X<x) = F(x)[/tex]
Substitute [tex]F(x) = 1 - e^{-\lambda x}[/tex]
[tex]P(X<x) = 1 - e^{-\lambda x}[/tex]
So, we have:
[tex]0.95 = 1 - e^{-\lambda x}[/tex]
Subtract 1 from both sides
[tex]0.95 -1= 1-1 - e^{-\lambda x}[/tex]
[tex]-0.05=- e^{-\lambda x}[/tex]
Reorder the equation
[tex]e^{-\lambda x} = 0.05[/tex]
Substitute 1/11 for [tex]\lambda[/tex]
[tex]e^{-\frac{1}{11} x} = 0.05[/tex]
Solve for x:
[tex]x = -\frac{1}{1/11}\ ln(0.05)[/tex]
[tex]x = -11\ ln(0.05)[/tex]
[tex]x = 32.9530550091[/tex]
[tex]x = 33[/tex] --- approximated
Steph had 24 cards . He gave 4 cars to his brother. Then he passed the rest of the cars out equally among 4 of his friends. Which operation would you use to represent he first part of this situation
Answer:
16 is the answer
I hope this answer help you
Answer:
Subtract 4 1st
Step-by-step explanation:
Subtract 4 of the cars since he gave them to his brother then divide between 4
Martha will build a pool in her backyard. She wants the pool to have a rectangular shape
and to be five meters long and three meters wide. What would the area in Martha's backyard that will be lost due to the construction of the pool? There are 3.28084 feet in
one meter.
A 15 square feet
B 80.729 square feet
C 161.459 square feet
D 322.918 square feet
9514 1404 393
Answer:
C. 161.459 square feet
Step-by-step explanation:
In feet, the dimensions of the pool are ...
(5 m)(3.28084 ft/m) = 16.4042 ft
(3 m)(3.28084 ft/m) = 9.84252 ft
Then the area of the pool is ...
(16.4042 ft)(9.84252 ft) = 161.458666584 square feet
about 161.459 square feet
_____
Additional comment
If you consider that a square meter is slightly less than 11 square feet, the pool area can be estimated to be (5 m)(3 m)(11 ft²/m²) = 165 ft². This is close enough to point you to the correct answer choice.
How are these three numbers related. 50 1/2, 1/4, 202
Answer: If you divide 202/4=50.5 or 50 1/2
Step-by-step explanation:
The lifetimes of a certain brand of light bulbs are known to be normally dsitributed with a mean of 1700 hours and standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. The probability is 0.20 that the sample mean lifetime is more than how many hours?
A. 1652.
B. 1725.
C. 1752.
D. 1670.
Answer:
1742 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Single light:
Mean of 1700 hours and standard deviation of 400 hours, which means that [tex]\mu = 1700, \sigma = 400[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{400}{\sqrt{64}} = 50[/tex]
The probability is 0.20 that the sample mean lifetime is more than how many hours?
This is the 100 - 20 = 80th percentile, which is X when Z has a pvalue of 0.8. So X when Z = 0.84
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]0.84 = \frac{X - 1700}{50}[/tex]
[tex]X - 1700 = 50*0.84[/tex]
[tex]X = 1700 + 50*0.84[/tex]
[tex]X = 1742[/tex]
Please help me!!!!!!!!!!
Which graph represents the parametric equations x = 1 – t2 and y = 2t, where 0 ≤ t ≤ 5?
ANSWER: A
After plotting the above equation on the coordinate plane, we can see the graph of the function.
What are parametric equations?A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.
We have two parametric equations:
x = 1 – t² and
y = 2t
t = y/2 and
0 ≤ t² ≤ 5
1 ≤ 1 - t²≤ 4
1 ≤ x≤ 4
Plug the above value in x = 1 – t²
x = 1- (y/2)²
x = 1 - y²/4
4x = 4 - y²
y² = 4(1 - x)
Thus, after plotting the above equation on the coordinate plane, we can see the graph of the function.
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What is the discriminate of y=x^2-8x+2
Answer:
56
Step-by-step explanation: Use the values of a, b, and c to find the discriminant.
Answer:
[tex]\Delta =56[/tex]
Step-by-step explanation:
We are given:
[tex]y = x^2 - 8x + 2[/tex][tex]y=x^2-8x+2[/tex]
So, a = 1, b = -8, and c = 2.
The discriminant (symbolized by Δ) is given by:
[tex]\Delta =b^2-4ac[/tex]
So, our discriminant in this case will be:
[tex]\Delta=(-8)^2-4(1)(2)=64-8=56[/tex]
Since our discriminant is a positive value, our equation has two real roots.
3/4 divided by 1/5 PLEASE ANSWER
Answer:
3.75
Step-by-step explanation:
To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.
Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:
To make the answer to 3/4 divided by 1/5 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
15/4 = 3.75
The answer is rounded to the nearest four decimal points if necessary.
15/4 is an improper fraction and should be written as 3 3/4.
Answer:
3.75
Step-by-step explanation:
4/5 ÷ 1/5 = ?????????
Answer:
4
Step-by-step explanation:keep change flip 4/5 x 5/1 = 20/5= 4
This probability distribution shows the typical grade distribution for a Geometry course with 35 students. HELLLPPP PLSSS
Answer:
P(A, B or C) = 6/7 or 0.8571
Step-by-step explanation:
From the image, we have the frequency for each grade as;
Grade A = 5
Grade B = 10
Grade C = 15
Grade D = 3
Grade F = 2
We want to find the probability that a student earns a grade of A, B or C.
Total frequency for A, B & C = 5 + 10 + 15 = 30
There are a total of 35 students overall for the geometry course.
Thus;
P(A, B or C) = 30/35
P(A, B or C) = 6/7 or 0.8571
Answer:
0.86Step-by-step explanation:
Total frequency for A, B & C = 5 + 10 + 15 = 30
There are a total of 35 students overall for the geometry course.
P(A, B or C) = 30/35
P(A, B or C) = 6/7 or 0.8571
now we round to the hundredths place
0.8571 ⇒ 0.86
The graph show how the amount of fuel in the gas tank changes over time. Choose the graph that correctly combines the graphs of Car A and Car B to show when Car B has more fuel in its tank than Car A.
Answer:
its b
Step-by-step explanation:
I need the answers ASAP
Answer:
Image attached
Step-by-step explanation:
Just wandering, no hate, you can post answers on brainly but can't read an analog clock.
BTW I've got one in my house
I need question 4 and 5
Answer:
4) x=14
Step-by-step explanation:
multiply the area by 2 to get 140then devide by 10 to find x
Complete the statement to illustrate the commutative property. (PLEASE ANSWER FAST FOR BRAINLIEST!!!)
10 + (9 + 11) = 10 + (11 + ___ )
a. 11
b. 20
c. 9
d. 10
Answer:
9
Step-by-step explanation:
help me do this please!!!
Answer:
Step-by-step explanation:
ok soo....
the area of the one like higher up would be 42
and then the area of the one like landscape would be 48
and then the area of like the box they make in the middle is 30
so ya i hope this helped
12+22+32+...+102 =?
Answer:
750 is the answer. Hope it helps!
Find two numbers whose sum is 8 and whose product is 17
Answer:
Step-by-step explanation:
x+y = 8
y = 8-x
xy = 17
x(8-x) = 17
8x - x² = 17
x² - 8x + 17 = 0
Quadratic formula
x = [8 ± √(8² – 4·1·17)] / [2·1]
= [8 ± √(-4)] / 2
= [8 ± 2i] /2
= 4±i
x = 4+i
y = 4-i
A quadratic equation is written in the form of ax²+bx+c. The two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers. It is written in the form of ax²+bx+c.
Let the first number be 'a' and the second number be 'b'. Therefore, the sum of the two numbers is,
a+b=8
The product of the two numbers is,
ab=17
b=17/a
now, the equation can be written as,
a+b=8
a+(17/a)=8
a² + 17 = 8a
a²-8a+17=0
a = 4±i
Hence, the two numbers whose sum is 8 and whose product is 17 are (4+i) and (4-i).
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Let f(x) = 4x - 1, h(x) = - X-3.
Find (f o h)(-5).
Answer:
(f o h)(-5)=-33
Step-by-step explanation:
Let f(x) = 4x - 1, h(x) = - X-3.
(f o h)=4(-x-3)-1
(f o h)=-4x-12-1
(f o h)=-4x-13
(f o h)(-5)=-4(-(-5))-13
(f o h)(-5)=-20-13
(f o h)(-5)=-33
What is the difference between the greatest and the smallest rational numbers
given below?
7/15,11/20,2/5,12/25
Answer:
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given that the rational numbers
[tex]\frac{7}{15} , \frac{11}{20} ,\frac{2}{5} ,\frac{12}{25}[/tex]
we have to find that the difference between the greatest and the smallest rational numbers
solution:-
The greatest rational number = [tex]\frac{11}{20}[/tex]
Convert into decimal = 0.55
The smallest rational number = [tex]\frac{2}{5}[/tex]
Convert into decimal = 0.4
The difference between the greatest and smallest rational number
[tex]= \frac{11}{20} - \frac{2}{5}[/tex]
= [tex]\frac{11-8}{20}[/tex]
[tex]=\frac{3}{20}[/tex]
Final answer:-
The difference between the greatest and smallest rational number [tex]=\frac{3}{20}[/tex]
-2 - 5r = 18
help mee
Answer:
r = -4
Step-by-step explanation:
-2 - 5r = 18
+2 +2
––––––––
-5r = 20
/5 /5
––––––
-r = 4
/-1 /-1
–––––
r = -4
Elena is designing a paint can with thickness ttt millimeters and height hhh centimeters. She calculates that the thickness of the can in milimeters must be at least 0.1, point, 1 times the height of the can in centimeters in order to withstand pressure. Due to cost constraints, the cost of material used, (0.2 + t+ 0.5h)cents, must be at most 12.2, point, 2 cents. Which system of inequalities best models the relationship between height and thickness?
Answer:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Step-by-step explanation:
Given
[tex]t= thickness[/tex]
[tex]h =height[/tex]
From the first statement, we have that:
[tex]t\ mm \ge 0.1 * h\ cm[/tex]
Convert mm to cm
[tex]t\ * 0.1*cm \ge 0.1 * h\ cm[/tex]
[tex]t\ *0.1 \ge 0.1 * h[/tex]
Divide both sides by 0.1
[tex]t \ge h[/tex]
From the second statement, we have that:
[tex]Cost \le 12.2[/tex]
Substitute 0.2 + t + 0.5h for Cost
[tex]0.2 + t + 0.5h \le 12.2[/tex]
Collect Like Terms:
[tex]t + 0.5h \le 12.2-0.2[/tex]
[tex]t + 0.5h \le 12.0[/tex]
So, the inequalities are:
[tex]t \ge h[/tex] and [tex]t + 0.5h \le 12.0[/tex]
Answer: it's a, the answer
Step-by-step explanation:
What is the factors for x squared plus 5x - 6
Answer:
=[tex](x-1)(x+6)[/tex]
Step-by-step explanation:
Answer:
[tex]x^{2} +5x-6=(x-1)(x+6)[/tex]
Step-by-step explanation:
A statistics student wants to determine if there is a relationship between a student's number of absences, x, and
their grade point average (GPA), y. The given data lists the number of absences and GPAs for 15 randomly selected
students
15
1
0
6
9
12
3
3
1
2
7
0
4
Number of
Absences
GPA
2.1
4.3 4.5
3.2
4.0
1.7
3.8
2.9
3.6
3
3.4
2
2.6
3.1
2.8
Using technology, what is the equation for the least-squares regression line?
O ý= 3.79 -0.10x
O ý= 0.10 + 3.79x
O ý= 16.15 – 3.28x
O ý= -3.28 + 16 15x
Answer: A. ÿ=3.79-0.10x
Step-by-step explanation:I’m a genius
ILL GIVE BRAINLEST !!!!
Enter an equation for the function that includes the points. Give your answer in the form a(b*). In the
event that a = 1, give your answer in the form b*.
(1, 12) and (2, 144)
The equation is f(x)=
The medical practice you are working at has seen an average of 22.4 patients a day for the past 3 months. 3/4ths of those patients have insurance in one form or another.
Complete each equation so that it is true for no values of x.
x - 2 = -(__- x)
nswer:
(x +5)^2 = -2
Step-by-step explanation: w t f
We can subtract the constant to get ...
x^2 +10x = -27
Then add the square of half the x-coefficient:
x^2 +10x +5^2 = -27 +5^2
(x +5)^2 = -2 . . . . . . write as a square
Find the difference.
4-(-8)=
Answer:
4
Step-by-step explanation:
subtract negative 4 by negative 8
What is the fraction shown above?