Answers
9514 1404 393
Answer:
k = 2
Step-by-step explanation:
The geometric mean theorem for the altitude tells you ...
ON = √(OL·OM)
ON² = OL·OM . . . . . square both sides
4² = 8·k . . . . . . . . substitute values
k = 16/8 = 2 . . . . divide by the coefficient of k
_____
Additional comment
The geometric mean theorem for the legs tells you ...
MN = √(MO·ML) ⇒ l = 2√5
LN = √(LO·LM) ⇒ m = 4√5
These relations come from the fact that corresponding sides of the right triangles are proportional. (All of the triangles are similar.)
Related Questions
I need help ASAP anyone?
Answers
Explanation:
Each vertical asymptote is due to a division by zero error.
For instance, the vertical asymptote x = 3 is from the factor (x-3) in the denominator. If we plugged x = 3 into (x-3), then it turns into 0 and we cannot have 0 in the denominator.
Similarly, the factor (x+3) leads to x = -3
So overall, we have (x-3)(x+3) in the denominator.
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.)
2 sec^2(t)/tan^2(t) + 14 tan(t) + 48 dt
Answers
Complete the square in the denominator to get
tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1
… = (tan(t ) + 7)² - 1
Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}[/tex]
Separate the integrand into partial fractions:
[tex]\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)[/tex]
Then we get
[tex]\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}[/tex]
356 miles in 5 days
is a:
Unit Rate
Unit Price
Ratio
Rate
Answers
9514 1404 393
Answer:
Rate
Step-by-step explanation:
Since there are no currency units involved, it is not a price or unit price.
Since the denominator (days) is not 1, it is not a unit rate.
The usual wording for a ratio is "to" rather than "in", so we probably would not say this is a ratio. Though, the usual reason for expressing the numbers this way is to indicate we might be interested in their ratio.
There is time involved, so it is reasonable to call this a "rate," which is usually the ratio of some quantity to the time associated with that quantity.
If x+y=8 and xy =15 find the value of x³+y³.
Answers
Answer:
152Step-by-step explanation:
let x= 5 and y= 3x + y = 85 + 3 = 8xy = 155 × 3 = 15x³ + y³ = ?5³ + 3³ = ?125 + 27 = 152[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Of all the people applying for a certain job 75% are qualified and 25% are not. The personnel manager claims that she approves qualified people 80% of the time, she approves unqualified people 30% of the time. Find the probability that a person is qualified if he or she was approved by the manager The probability is:_______.
Type an integer or decimal rounded to four decimal places as needed)
Answers
Answer:
The probability is: 0.8889.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Approved
Event B: Qualified
Probability of a person being approved:
80% of 75%(qualified)
30% of 25%(not qualified). So
[tex]P(A) = 0.8*0.75 + 0.3*0.25 = 0.675[/tex]
Probability of a person being approved and being qualified:
80% of 75%, so:
[tex]P(A \cap B) = 0.8*0.75[/tex]
Find the probability that a person is qualified if he or she was approved by the manager.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.8*0.75}{0.675} = 0.8889[/tex]
The probability is: 0.8889.
i would like some help please i am stuck
Answers
Answer: -2(d) is the answer.
Step-by-step explanation:
x1 = 3
y1 = -5
x2 = -2
y2 = 5
slope (m) = rise/run = (y2 - y1)/(x2-x1)
=(5-(-5))/(-2-3)
= 10/-5
= -2
The length of a rectangle is five times the width if the area of the rectangle is 180 in.² then find the length and the width
Answers
Let breadth be x
Length=5x
ATQ
[tex]\\ \sf \longmapsto Area=Length\times breadth[/tex]
[tex]\\ \sf \longmapsto 5x(x)=180[/tex]
[tex]\\ \sf \longmapsto 5x^2=180[/tex]
[tex]\\ \sf \longmapsto x^2=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x^2=36[/tex]
[tex]\\ \sf \longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf \longmapsto x=6in[/tex]
Width=6inLength=6×5=30inA 5 ounce bottle of juice cost $1.35 and an 8 ounce bottle of juice cost $2.16 a what is the unit cost per ounce of juice and b what is the better buy
Answers
Answers:
First bottle's unit cost = 27 cents per oz
Second bottle's unit cost = 27 cents per oz
Both have the same unit cost.
----------------------------------------
Work Shown:
unit cost = price/(number of ounces)
1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz
2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz
Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.
About 10% of 8900 commuters carpool to work. Find the number of commuters who carpool.
How many commuters carpool?
Answers
Answer: 890 commuters carpool
Step-by-step explanation:
10% of 8900 = 890
8900/10= 890
Note: 10% to decimal form is 10
Answer:
10% of 8900
10/100×8900
=890
hope this is helpful
Which numbers are 9 units from −5 on this number line?
Drag and drop all of the numbers that are 9 units from −5 to their correct position on the number line.
-14,-5 -4 4 5 9
Answers
Answer:
-14 and 4
Step-by-step explanation:
To find the values subtract 9 from -5, as well as add 9 to -5
-5-9= -14
-5+9= 4
A zookeeper published the following stem-and-leaf plot showing the number of lizards at each major zoo in the country:
∣
0
1
2
3
4
5
6
∣
0
6
8
8
8
0
2
6
6
7
8
1
2
6
6
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
00
10
20
30
40
50
60
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
∣
0
0
0
0
1
0
0
6
2
2
8
6
6
8
6
6
8
7
0
0
8
0
Key:
2
∣
0
=
20
2∣0=202, vertical bar, 0, equals, 20 lizards
How many zoos have more than 26 lizards
Answers
The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a standard deviation of 0.08 ounce. Every car that has more than 12.20 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that need to be cleaned because of spillage to 3%
Answers
Answer:
x = 12.15 oz
Step-by-step explanation:
z = 1.8808
1.8808 = (x - 12)/.08
7,25 x (y+5,6)=58 vậy y =
Answers
Answer:
y=2,4
Step-by-step explanation:
7,25x( y+5,6)=58
7,25y+ 40,6=58
7,25y=58-40,6
y=17,4:7,25
y=2,4
x
2/8
QUESTION 8.1 POINT
If $20,000 is invested at 8.3% compounded continuously, how long, to the nearest tenth of a year will it take before the
investment doubles?
Answers
9514 1404 393
Answer:
8.4 years
Step-by-step explanation:
The value of P compounded continuously at rate r for t years is ...
A = Pe^(rt)
Solving for t, we find ...
t = ln(A/P)/r = ln(2)/0.083 ≈ 8.35117
It will take about 8.4 years for the investment to double.
Given that ƒ(x) = 3^x, identify the function g(x) shown in the figure. A) g(x) = −3^-x
B) g(x) = −(1∕3)^x
C) g(x) = 3^−x
D) g(x) = −3^x
Answers
Answer:
Option (D)
Step-by-step explanation:
From the graph attached,
Function 'f' is the reflected across x-axis to get the graph function 'g'.
Therefore, by definition of reflection across x-axis,
g(x) = -f(x)
g(x) = [tex]-3^x[/tex]
Option (D) will be the answer.
PLEASEEEE HELP
In the diagram, AABC-ADEC What is the value of x?
Answers
Similar triangles are proportional, meaning one will be a factor larger or smaller than the other. This factor will be the same for all of the sides. So, we can say that one corresponding pair of sides is equal to another corresponding pair of sides.
BA / ED = AC / CD
42 / 6 = (64 - x) / (x)
6(64 - x) = 42(x)
384 - 6x = 42x
384 = 48x
x = 8
Hope this helps!
Write each decimal as a fraction or mixed number in simplest form.
1 3/8
Answers
3/2
Step One: 1 3/8, transform the number into a improper fraction:
To have a mixed number in to a improper fraction, you need to use addition and multiplication. For 1 3/8, We first multiply the denominator (8, also know to be the bottom number of the fraction) to the whole number (1). 8x1= 8NOTE: The original denominator (8) will be use for are improper, again playing as the denominator, we only multiply the denominator for the numerator (which is the top number of a fraction).After multiplying, we'll add are product with the numerator (3) for the process. 8+3= 12 Now we have both numerator and denominator for 1 3/8, we can create the improper fraction. 12 as the numerator and 8 as the denominator. 12/8We still need to simplify the number. To that, we need the biggest whole number, or rather I call it the lowest number, that can be divide both in 12 and 8. 4 can be divide by both number so: 12/4= 3 and 8/4=2Now 3 is are simplify numerator and 2 is are simplify denominator.The surface area of a cylinder?
Answers
Answer:
18. 84 ft² or 18.85 ft² when rounded to the nearest tenth
Step-by-step explanation:
2πrh+2πr²
2× 3.14 × 1 × 2= 12.56
2 × 3.14 × 1² = 6.28
12.56 + 6.28 = 18.84
Have a great day :)
Answer:
18.85 [tex]ft^2\\[/tex]
*You should run the numbers yourself as well. Sometimes different calculators will get marginally different numbers or use a different rounding for [tex]\pi[/tex] that gives a slightly different answer*
Step-by-step explanation:
Surface area of a cylinder: [tex]2\pi rh+2\pi r^2[/tex]
Where h is the height and r is the radius. Remember that the radius is half the diameter, and the diameter is a straight line that passes through a circle.
I could be wrong, but I think you had the correct equation but used the diameter in stead of the radius to get 50.36.
Radius: 1 Height: 2
Plug numbers into equation:
[tex]A=2\pi (1)(2)+2\pi (1)^2= 18.8495. . .[/tex]
I hope that helps!
Express the decimal 0.7 as a percentage.
Answers
Answer:
70% IS THE ANSWER
Step-by-step explanation:
Hope I helped.
Answer:
70%
Step-by-step explanation
0.7×100=70
what is the square root of 24
Answers
Answer:
the square root of 24 is 4.89897948557
Answer:
4.89
Step-by-step explanation:
2root 6........***
Ilang litro ng tubig ang kailangang isalin sa timba na naglalaman ng 10 000 mililitro
Answers
Answer
nghiệmTrảingu từng bước:
D. Rom has just given an insurance company $35,000. In return, he will receive an annuity of $3,700 for 20 years. At what
rate of return must the insurance company invest this $35,000 in order to make the annual payments?
Answers
Answer:
0.53%
Step-by-step explanation:
hope it is well understood
Suppose that the probability that a person will develop hypertension over a life time is 60%. Of 13 graduating students from the same college are selected at random. find the mean number of the students who develop hypertension over a life time
Answers
Answer:
The mean number of the students who develop hypertension over a life time is 7.8.
Step-by-step explanation:
For each person, there are only two possible outcomes, either they will develop hypertension, or they will not. The probability of a person developing hypertension is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
Suppose that the probability that a person will develop hypertension over a life time is 60%.
This means that [tex]p = 0.6[/tex]
13 graduating students from the same college are selected at random.
This means that [tex]n = 13[/tex]
Find the mean number of the students who develop hypertension over a life time
[tex]E(X) = np = 13*0.6 = 7.8[/tex]
The mean number of the students who develop hypertension over a life time is 7.8.
Find the area of the parallelogram. Show all your work.
Answers
Answer:
30m^2
Step-by-step explanation:
area of parallelogram is b×h
Answer:
The area of the parallelogram is 30 square meters.
Step-by-step explanation:
The area of a parallelogram is given by the formula:
A = bh
Where b is base and h is height
The base of the parallelogram is:
6 + 4 = 10 m
The height perpendicular to the base is 3 m
Use the formula A = bh:
A = (10)(3)
= 30
So the area of the paralleogram is 30 m^2
Hope this helps!
A physical education class is running a mile. The teacher has set a goal of 12 minutes to complete the mile. Students
receive a score to show how close they are to the target of 12 minutes. For example, if students run the mile in 8
minutes, their scores will be 4. Complete the statements about the students' scores.
Anja ran the mile in Her score is -2.
Issac ran the mile in 13 minutes. His score is
Simon ran the mile in 12 minutes. His score is
Answers
Answer:
Isaac is 26
Simon is 24
if 8 is 4 I.e 8 divide by 4 is 2
therefore 1 minute is 2 scores
Isaac :13 x 2=26
(do the same to Simon to get his score)
does x represents Mount Everest height ?
Answers
Answer:
Bro what do you mean to represent Mount Everest height by x but if you want to sove a maths sum than you can take any alphabet
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
The temperature in Kansas City varies greatly some days. One day in January, the temperature was 16 degrees but then the temperature decreased by 23 degrees by midnight. What was the temperature at midnight?
Answers
Answer:
-7 degrees
Step-by-step explanation:
the temperature was 16 degrees then was the decrease by 23 degrees so subtract 23 from 16 and the answer is -7
what is the answer of
445+584-85
Answers
Answer:
944 is the correct answer
Answer:
the answer it's 944
445+558=1,029
1,029-85=. [944]✓
If (x^2−1)/(x+1) = 3x + 5, then x + 3 =
(A) -3
(B) -2
(C) 0
(D) 2
(E) 4
Answers
Explanation yep
Find the greatest common factor of the
following monomials:
39c^2
9c^3'
Answers
Answer:
3c^2
Step-by-step explanation:
