Answer:
D
Step-by-step explanation:
In a 30-60-90 triangle, the longer leg is [tex]\sqrt{3}[/tex] times larger than the smaller leg. The length of the shorter leg is therefore:
[tex]\dfrac{18}{\sqrt{3}}= \\\\\\\dfrac{18\sqrt{3}}{3}= \\\\\\6\sqrt{3}[/tex]
Hope this helps!
Find the linearization L(x,y,z) at P_0. Then find the upper bound for the magnitude of the error E in the approximation f(x,y,z) = L(x,y,z) over the region R.
The linearization of f(x,y,z) at Po is L(xyz)=_______
Answer:
L(xyz) = ( 1 , 3 , -7 )
L = x + 3y - 7z -3
Step-by-step explanation:
f (x,y,z) = xy + 2yz - 3xz
f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)
f (3,1,0) = 3
fx = y - 3z
f (3,1,0) = (1) - 3 (0)
fx = 1
fy = x + 2z
f (3,1,0) = (3) - 2 (0)
fy = 3
fz = 2y - 3x
f (3,1,0) = 2 (1) - 3 (3)
fz = -7
Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
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What’s the correct explanation for this question?
Step-by-step explanation:
=> The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid
=> The volume of a cone can be found by V = 1/3(Ab)(H) where Ab is base area and H is the height of the cone
The difference between both is that is it's base. A cone has a polygonal base while a pyramid has a tetragonal base
The length of a rectangular driveway is five feet more than three times the width. The area is 350ft2. Find the width and length of the driveway.
Answer:
width -- 10 ftlength -- 35 ftStep-by-step explanation:
We can let x represent the width. Then the length will be represented by (3x+5), a value 5 more than 3 times the width.
The area is the product of length and width, so is ...
A = (3x +5)(x) = 3x^2 +5x
To make the area 350, we can find the value of x from ...
3x^2 +5x = 350
This can be solved a number of ways. One of them is "completing the square".
3(x^2 +5/3x) = 350
We choose to divide by 3 and add the square of half the x-coefficient.
x^2 +5/3x +(5/6)^2 = (350/3) + (5/6)^2
(x +5/6)^2 = 4225/36 . . . . simplify
x +5/6 = ±√(4225/36) = ±10 5/6 . . . . take the square root
x = 10 or -11 2/3 . . . . subtract 5/6
The positive solution is the one of interest: x = 10.
The driveway is 10 ft wide and 35 ft long.
Sean tossed a coin off a bridge into the stream below. The path of the coin can be represented by the equation h = -16t2 + 72t + 100. what is the height of the bridge
Answer:
100
Step-by-step explanation:
When t=0 (no time has passed), the coin is at height 100. This means the bridge must be 100 units high for this to be possible.
Answer:
100
Step-by-step explanation:
:3
A swimming pool is to be drained. The pool is shaped like a Rectangular prism with length 12m , with 10 m, and depth 3m. Suppose water is pumped out of the pool at a rate of 18 m3 per hour.if the pool starts completely full , how many hours does it take to empty the pool ?
Answer:
20 hours
Step-by-step explanation:
first calculate volume:
12x10x3=360
then divide by 18
360/18=20
So 20 hours in total
if p=7,q=5,r=3 find value of p2+q2-r2
Answer: The value is 18.
Step-by-step explanation:
Since we already know what p, q, and r equal, we can use what we know and plug in the numbers:
p=7, q=5, and r=3,
p2=7*2=14
q2=5*2=10
r2=3*2=6
In conclusion, 14+10-6=18
The value of p2+q2-r2 is 18.
Answer:
Just simply change the variables with their values
7 x 2 + 5 x 2 - 3 x 2
14 + 10 - 6
24 - 6 = 18
18 is the answer
Hope this helps
Step-by-step explanation:
g Suppose the company operates mine #1 for x1 days and mine #2 for x2 days. Write a vector equation in terms of v1 and v2 whose solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver. Do not solve the equation.
Answer:
The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]
Step-by-step explanation:
Solution
The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.
Thus,
Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.
Now,
If the company operates mine 1 for x1 days and mine #2 for x2 days
Then,
The total output becomes x₁v₁ +x₂v₂ which is the same output to b = [296 2454]
Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]
So, the vector equation becomes x₁v₁ +x₂v₂ = [296 2454]
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 9 minutes. Find the probability that a randomly selected passenger has a waiting time greater than 1.25 minutes.
Answer:
P(greater than 1.25 minutes) = 0.8611 (Approx)
Step-by-step explanation:
Given:
Waiting time = 0 - 9 minutes
Find:
Probability that selected passenger has a waiting time greater than 1.25 minutes.
Computation:
⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =
⇒ P(greater than 1.25 minutes) = [9-1.25] / 9
⇒ P(greater than 1.25 minutes) = [7.75] / 9
⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)
Need help finding the answer
Answer:
D
Step-by-step explanation:
When there is an negative sign inside in a radical, then we remove that and put out of the radical classifying as "i". Then, reduce 63 into smallest form and we can write it as 9 and 7. 9 is a perfect square of 3 so we put it outside and the answer is D.
the number of ants per acre in the forest is normally distributed with mean 42000 and standard deviation 12275. let x = number of ants in a randomly selected acre of the forest. Round all answers to 4 decimal places where possible. Find the probability that a randomly selectd acre has between 32647 and 43559 ants.
Answer:
0.3182 = 32.81% probability that a randomly selected acre has between 32647 and 43559 ants.
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 42000, \sigma = 12275[/tex]
Find the probability that a randomly selectd acre has between 32647 and 43559 ants.
This is the pvalue of Z when X = 43559 subtracted by the pvalue of Z when X = 32647. So
X = 43559:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{43559 - 42000}{12275}[/tex]
[tex]Z = 0.13[/tex]
[tex]Z = 0.13[/tex] has a pvalue of 0.5517.
X = 32647:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32647 - 42000}{12275}[/tex]
[tex]Z = -0.76[/tex]
[tex]Z = -0.76[/tex] has a pvalue of 0.2236
0.5517 - 0.2236 = 0.3281
0.3182 = 32.81% probability that a randomly selected acre has between 32647 and 43559 ants.
Find all zeros of f(x)=x^3−17x^2+49x−833
Answer:
x = 17 or x = ±7i
Step-by-step explanation:
x³ − 17x² + 49x − 833 = 0
x² (x − 17) + 49 (x − 17) = 0
(x² + 49) (x − 17) = 0
x = 17 or ±7i
Convert 5613, base 10 to
base 8
Answer:
12755 base-8
Step-by-step explanation:
You’re welcome :) please brainliest me btw.
A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 30 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 60 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked:
Answer: 0.66 ft
Step-by-step explanation:
Let assume that the initial position of the worker is x.
Given that the worker walks away with a constant speed of 2 ft/s. Therefore, dx/dt = 2
As the worker moves away, the rope makes a triangle, with width length x and the height length will be 30.
Using pythagorean theorem, the length of rope on this side of the pulley will be √(x² + 30²)
Also, the length of rope on the other side will be 60 - √(x² + 30²),
and the height h of the weight will be 30 - (60 - √(x² + 30²)) = √(x² + 30²) - 30
dh/dt = dx/dt × x/√(x² + 30²)
= 4x/√(x² + 30²)
dh/dt = 4x/√(x² + 30²)
If the worker moves 5ft away, then
dh/dt = (4×5)/√(5² + 30²)
dh/dt = 20/√(25 + 900)
dh/dt = 0.66 ft
The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was selected, and the mean math SAT score was 528. Is the high school justified in its claim? Explain. ▼ No Yes , because the z-score ( nothing) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. (Round to two decimal places as needed.)
Answer:
No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
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.
Unusual
If X is more than two standard deviations from the mean, x is considered unusual.
In this question:
[tex]\mu = 511, \sigma = 119, n = 55, s = \frac{119}{\sqrt{55}} = 16.046[/tex]
A random sample of 55 students from this school was selected, and the mean math SAT score was 528. Is the high school justified in its claim?
If Z is equal or greater than 2, the claim is justified.
Lets find Z.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{528 - 511}{16.046}[/tex]
[tex]Z = 1.06[/tex]
1.06 < 2, so 528 is not unusually high.
The answer is:
No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
The statement that could be made regarding the high school about the justification of its claim would be:
- No, because the z-score of Z = 1.06 is not unusual since it does not lie within the range of a usual event, namely within 2 standard deviations of the mean of the sample means.
Given that,
μ = 511
σ = 119
Sample(n) = 55
and
s = [tex]119/\sqrt{55}[/tex]
[tex]= 16.046[/tex]
As we know,
The claim of the high school could be valid and justified only when
[tex]Z > 2[/tex]
To find,
The value of Z
So,
[tex]Z = (X -[/tex] μ )/σ
by putting the values using Central Limit Theorem,
[tex]Z = (528 - 511)/16.046[/tex]
∵ [tex]Z = 1.06[/tex]
Since [tex]Z < 2[/tex], the claim is not justified.
Learn more about "Standard Deviation" here:
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Combine these radicals. -3sqrt(of81)+sqrt(of16)
Answer:
-23
Step-by-step explanation:
find the square root of 12 to the nearest hundredth
Answer:
\sqrt(12) hope this helped.
Any help would be great
Answer:
[tex]\frac{56}{96}[/tex] is your answer
Step-by-step explanation:
[tex]\frac{7}{12}[/tex]=[tex]\frac{x}{96}[/tex]
to get to 96 you must multiply by 8
and since you did that for the bottom then you need to do the same for the top,
[tex]\frac{56}{96}[/tex] is your answer
2(x+b)= ax + c
In the equation above, a, b, and c are constants. If
the equation has infinitely many solutions, which of
the following must be equal to c?
Α) α
B) 6
C) 2a
D) 26
An architect creates a scale model. The volume of the scale model is 0.1 cubic meters. The volume of the real-world
building is 100,000 cubic meters. What is the ratio of corresponding sides from model to real world?
Answer:
1:0.4641
Step-by-step explanation:
We are told that the scale of the model with respect to the real world is 0.1 cubic meter. This means that for every 1 cubic meter in the real world the model represents 0.1.
They tell us that the real world volume is 100,000, that if we assume a cube, we have to:
V = l ^ 3
l = 100000 ^ (1/3)
l = 46.41
46.41 meters would be each side, now the volume of the model would be:
100,000 * 0.1 = 10,000
Which means that its sides would be:
V = l ^ 3
l = 100000 ^ (1/3)
l = 21.54
We calculate the scale of the sides:
21.54 / 46.41 = 0.4641
Which means that for every 1 meter in the real world the model represents 0.4641 meters.
A fair die is rolled two times. What is the probability that both rolls are 3?
Answer:
1/36
Step-by-step explanation:
For each roll, the probability that the die rolls a 3 is 1/6
So, for it to happen on both dice is 1/6 * 1/6 = 1/36
The probability that an event will repeat its self for independent events is given by the square of the probability of the event occurring
The probability that both rolls are 3s is [tex]\underline{\dfrac{1}{36}}[/tex]Reason:
Number of faces in a fair die = 6 faces
Numbers on the faces of a fair die = 1, 2, 3, 4, 5, and 6
Number of 3s on the face of a fair die = 1
Probability that a roll of a fair die gives the face of 3, P(3) = [tex]\dfrac{1}{6}[/tex]
The probability that two rolls of a fair die are both, is given as follows;
P(Both 3) = P(3 and 3) = P(3 ∩ 3)
The and condition of two independent probabilities is the product of the two probabilities, therefore;
P(3 ∩ 3) = [tex]\dfrac{1}{6} \times \dfrac{1}{6} = \dfrac{1}{36}[/tex]
The probability that both rolls are 3s P(Both 3s) = [tex]\underline{\dfrac{1}{36}}[/tex]
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A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
Please answer this correctly
Answer:
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Step-by-step explanation:
Answer:
The quarter circle's area is 38.47 yard²
Step-by-step explanation:
The area of a full circle is pi * r ²
The area of a quarter circle is 1/4 * pi * r ²
Given:
Use 3.14 for pi
Round to the nearest hundredths.
Perimeter of quarter circle is 24.99 yards
For r you must leave it as 'r' because we do not know it for now...
1. Circumference of a full circle = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * r )
1/2 * 3.14 * r
1.57 * r
3 Since r = 'r'
We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.
4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch
1.57 * r + 2 * r = 24.99
( 1.57 + 2 ) * r = 24.99
3.57 * r = 24.99
Divide left and right of the = sign by 3.57
3.57 / 3.57 * r = 24.99 / 3.57
1 * r = 24.99 / 3.57
r = 7
The area of a quarter circle is 1/4 * pi * r ²
1/4 * pi * 7²
1/4 * 49 * pi
49/4 * pi
49/4 * 3.14
38.465
Round to the nearest hundredths gives 38.47 yard²
The quarter circle's area is 38.47 yard²
Find the area of the triangle
Answer:
54
Step-by-step explanation:
A = (9*12)/2
A = 9*6
A = 54
Answer:54
Step-by-step explanation:
multiply 9 and 12 then divide by 2 because a triangle is half of a square
List the steps taken and find the area of the figure below
6cm
6 CM
6 cm
6 cm
Answer:
36 cm
Step-by-step explanation:
Since all measurements of the figure are the same, that means that this figure is a square. To find the area of a figure multiply length by width. Since this figure is a square and all sides are equal, we multiply 6 by 6 for an area of 36 cm.
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. Two lines labeled f(x) and g(x). Line f(x) passes through points (-4, 0) and (-3, 1). Line g(x) passes through points (-4, 0) and (-3, -3).
A.) 3
B.) 1/3
C.) -1/3
D.) −3
Answer:
Option D.
Step-by-step explanation:
If a line passing through two points, then the equation of line is
[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
It is given that Line f(x) passes through points (-4, 0) and (-3, 1). So, equation of line f(x) is
[tex](y-0)=\dfrac{1-0}{-3-(-4)}(x-(-4))[/tex]
[tex]y=1(x+4)[/tex]
So, function f(x) is
[tex]f(x)=(x+4)[/tex] ...(1)
Line g(x) passes through points (-4, 0) and (-3, -3). So, equation of line f(x) is
[tex](y-0)=\dfrac{-3-0}{-3-(-4)}(x-(-4))[/tex]
[tex]y=-3(x+4)[/tex]
So, function g(x) is
[tex]g(x)=-3(x+4)[/tex] ...(2)
Using (1) and (2), we get
[tex]g(x)=-3f(x)[/tex] ...(3)
It is given that
[tex]g(x)=kf(x)[/tex] ...(4)
On comparing (3) and (4), we get
[tex]k=-3[/tex]
Therefore, the correct option is D.
what is the slope from 1 to 5.3 seconds?
Answer:
3/2
Step-by-step explanation:
The graph rises 3 feet for each 2 seconds to the right. The slope is ...
rise/run = (3 ft)/(2 s) = (3/2) ft/s
The numerical value of the slope is 3/2 or 1.5. The associated units are feet per second.
A triangular plate with base 3 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it. (Round your answer to the nearest whole number. Use 9.8 m/s2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m3.)
Answer:
The hydro-static force [tex]F=245000N[/tex]
Step-by-step explanation:
given data
base = 3 m
height = 5 m
density of water = 1000 kg/m3
Acceleration due to gravity = 9.8
The area if the strip needs to be calculated using similar triangular formula as well as the hydrostatic force
CHECK THE ATTACHMENT BELOW FOR DETAILED EXPLANATION
Identify the word form of this number: 139,204,539,912
One hundred thirty-nine billion, two hundred four million, five hundred thirty-nine thousand, nine hundred twelve.
Hope this helped!
Please answer this correctly
Answer:
0-4: Make it 1 unit tall
5-9: Make it 5 units tall
10-14: Make it 4 units tall
15-19: Make it 1 unit tall
20-24: Make it 2 units tall
Step-by-step explanation:
0-4: 3 (1 number)
5-9: 5, 5, 7, 8, 8 (5 numbers)
10-14: 10, 11, 12, 13 (4 numbers)
15-19: 17 (1 number)
20-24: 22, 23 (2 numbers)
