Answer: The distance of Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Step-by-step explanation:
We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:
Intensity(r) = A/r^2
Observer A measures 16 the intensity of observer B.
if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:
Ia = 16Ib
A/(ra)^2 = 16*A/(rb)^2
1/(ra)^2 = 16/(rb)^2
rb^2 = 16*ra^2
and we know that 16 = 4*4 = 4^2
rb^2 = (4*ra)^2
then rb = 4*ra
this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.
The fraction is ra = rb/4
The distance of
Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?
It is 1/4.
Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.
Explanation:Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.
We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.
So, we have:
IntensityA/IntensityB = (dA/dB)^2 = 16
Solving for dA/dB, we find:
dA/dB = sqrt(16) = 4
Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.
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A crate has the shape of a rectangular prism. The area of the base of the crate is 252 square inches. The length of the crate is 4 inches greater than the width. The height is 2 inches less than the width.
What is the volume of the crate in cubic inches?
Answer:
3024 in^3Step-by-step explanation:
let width=x
length=x+4
height=x-2
A=W×L
252=(x)(x+4)
252=x^2 +4x
0=x^2 +4x -252
use quadratic formula
x=14
W=14
L=18
H=12
V=W×L×H
V=(14)(18)(12)
V=3024 in^3Final answer:
To calculate the volume of the crate, solve for the width using the base area and the relation between length and width, then find the height. Multiply length, width, and height to obtain the crate's volume.
Explanation:
To find the volume of the crate, we must first determine the dimensions of the base. We know that the area of the base is 252 square inches, and that the length (L) is 4 inches greater than the width (W).
Therefore, we can express the length as L = W + 4. Since the area of a rectangle is given by length times width (A = L × W), we can write the equation W × (W + 4) = 252.
Step 1: Find the width (w)
Substitute l=w+4 into the first equation:
w² + 4w - 252= 0
Solve the quadratic equation using the quadratic formula:
w = −b ±√ b²−4ac/2a
where a=1, b=4, and c=−252.
w = −4 ± √4²−4 × 1 × −252/2 × 1
w = −4 ± √1024/2
w = −4 ± 32/2
Since the width cannot be negative, we discard the negative solution.
Therefore, w=14 inches.
Step 2: Find the length (l) and height (h)
l=w+4=14+4=18 inches
h=w−2=14−2=12 inches
Step 3: Find the volume (V)
V = l × w × h = 18 × 14 × 12 = 3024 cubic inches.
On the calculator, graph several monomial functions where a = 1 and n is even. For example, y = x4, y = x6, y = x8, and so on. Trace along the functions, then check all of the statements that are true about all of these functions.
The graph opens up.
The graph passes through (0, 0).
The graph is symmetric about the y-axis.
The graph only has 1 x-intercept.
The graph only has 1 y-intercept.
Answer:
All the statement are true about these functions
Step-by-step explanation:
Given any monomial function where a=1 and n is even.
Attached is the graph of [tex]y=x^4 \:\&\: y=x^6[/tex] as a case study.
From the graphs, the following are observed.
The graph opens up since a is positive. The graph passes through (0, 0). The graph is symmetric about the y-axis. i.e whenever (a,b) is on the graph, (-a,b) is also on the graph.The graph only has 1 x-intercept which is 0.The graph only has 1 y-intercept which is 0.To graph monomial functions where a = 1 and n is even, enter the equations into a graphing calculator and observe the graph. The graph opens up, passes through the origin, and is symmetric about the y-axis.
Explanation:To graph the monomial functions where $a=1$ and $n$ is even, we can use a graphing calculator. For example, to graph $y=x^4, y=x^6$, and $y=x^8$, we can enter these equations into the graphing calculator and select an appropriate viewing window. By tracing along these functions, we can make the following observations:
The graph opens up: Since the exponent $n$ in all these functions is even, the leading coefficient $a=1$ does not change the shape of the graph. The even exponent ensures that the graph opens up, similar to the shape of the parabola $y=x^2$.The graph passes through $(0, 0)$: Plugging in $x=0$ in any of these functions will give $y=0$, indicating that the graphs pass through the origin (0,0).The graph is symmetric about the y-axis: Since these functions have an even exponent, they exhibit y-axis symmetry. If a point $(x,y)$ is on the graph, then $(-x,y)$ will also be on the graph.Based on these observations, we can conclude that all of these statements are true about the graph of the monomial functions with $a=1$ and even $n$.
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The stockholders’ equity section of Waterway Corporation consists of common stock ($10 par) $2,050,000 and retained earnings $520,000. A 10% stock dividend (20,500 shares) is declared when the market price per share is $14. Show the before-and-after effects of the dividend on the following.
(a) The components of stockholders’ equity.
(b) Shares outstanding.
(c) Par value per share.
The stockholders' equity section of Waterway Corporation consists of common stock ($10 par) $2,050,000 and retained earnings $520,000. A 10% stock dividend (20,500 shares) is declared when the market price per share is $14. The before-and-after effects of the dividend are as follows...
Explanation:(a) Before the stock dividend, the components of stockholders' equity in Waterway Corporation are common stock ($10 par) $2,050,000 and retained earnings $520,000. After the stock dividend, the common stock would increase by 20,500 shares ($10 x 20,500 = $205,000) and retained earnings would decrease by the same amount since it is used to finance the dividend. So, the new components of stockholders' equity would be common stock ($10 par) $2,255,000 and retained earnings $315,000.
(b) Before the stock dividend, the shares outstanding in Waterway Corporation are not provided in the question. After the stock dividend, the number of shares outstanding would increase by 20,500 shares.
(c) The par value per share of the common stock remains the same before and after the stock dividend, which is $10 per share.
Final answer:
A 10% stock dividend for Waterway Corporation, with a par value of $10 and a market price of $14 per share, results in an increase in common stock by $205,000, a decrease in retained earnings by the same amount, an increase of 20,500 shares, while the par value per share remains at $10.
Explanation:
When a stock dividend is declared, it affects the stockholders' equity section of a corporation. In the case of Waterway Corporation, a 10% stock dividend is declared when each share has a market price of $14. Since the par value is $10 and there are 20,500 new shares being issued, the total value at par is $205,000 (20,500 shares x $10 par value). This amount is transferred from retained earnings to common stock. No additional capital is generated since it's a stock dividend, not a cash dividend.
Here's the before-and-after effects of the dividend:
(a) Components of stockholders' equity:
Before the dividend:
Common stock: $2,050,000
Retained earnings: $520,000
After the dividend:
Common stock: $2,255,000 (original $2,050,000 + $205,000 from the stock dividend)
Retained earnings: $315,000 (original $520,000 - $205,000 transferred to common stock)
(b) Shares outstanding:
Before the dividend: Assuming each common stock's par value aligns with one share, the company has 205,000 shares ($2,050,000 / $10 par value).
After the dividend: 225,500 shares (205,000 original shares + 20,500 new shares issued)
(c) Par value per share:
The par value per share remains unchanged at $10, as the stock dividend does not affect the par value.
Let W be the region bounded by z=100−y^2, y=10x^2, and the plane z=0. Calculate the volume of W as a triple integral in the order dzdydx. (Give your answer in exact form. Use symbolic notation and fractions where needed.)
To calculate the volume of the region W, set up and evaluate a triple integral over the given region. Identify the bounds, write the triple integral, find the limits of integration, and evaluate the integral.
Explanation:To calculate the volume of the region W, we need to set up and evaluate a triple integral. We will integrate over the region defined by the given inequalities. Let's break it down step by step:
Step 1:Identify the bounds of the region:
From the plane z=0, we have 0 ≤ z.From the equation y = 10x^2, we have 0 ≤ y ≤ 10x^2.From the equation z = 100 - y^2, we have 0 ≤ 100 - y^2 ≤ z.Step 2:Write the triple integral:
∫∫∫ f(x,y,z) dz dy dx
Step 3:Find the limits of integration:
For dz: 0 ≤ z ≤ 100 - y^2For dy: 0 ≤ y ≤ 10x^2For dx: Find the bounds where the region is defined. This can be done by solving the equations y = 10x^2 and z = 100 - y^2 for x.Step 4:Evaluate the integral:
Integrate the function f(x,y,z) over the given limits. The function f(x,y,z) will depend on the specific problem you are trying to solve.
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The volume of the region bounded by z = 100 - y², y = 10x², and the plane z = 0, is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.
To find the volume of the region W bounded by z = 100 - y², y = 10x², and the plane z = 0, we need to evaluate a triple integral in the order dz dy dx. We can start by setting up the integral:
We first identify the boundaries for z. Since z is between 0 and 100 - y², the inner integral limits are 0 to 100 - y².Next, we determine the limits for y. Given y = 10x², we see that y ranges from 0 to 100 (since 100 = 10x² implies y = 100).Finally, we find the limits for x. Solving y = 100 for x in terms of x² = 10 gives us the bounds of -√(10) to √(10).Thus, the triple integral is:
[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} \int_{0}^{100-y^2} dz \, dy \, dx \][/tex]
First, we integrate with respect to z:
⇒ [tex]\[ \int_{0}^{100-y^2} dz = (100-y^2) - 0 = 100 - y^2 \][/tex]
This reduces our integral to:
[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} (100 - y^2) \, dy \, dx \][/tex]
Next, we integrate with respect to y:
⇒ [tex]\[ \int_{0}^{100} (100 - y^2) \, dy = 100y - \frac{y^3}{3} \bigg|_{0}^{100}[/tex]
⇒ [tex]100(100) - \frac{(100)^3}{3} = 10000 - \frac{1000000}{3}[/tex]
⇒ 10000 - 333333.33 = [tex]\frac{20000}{3}[/tex]
Finally, we integrate with respect to x:
⇒ [tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \left( \frac{20000}{3} \right)[/tex] [tex]dx = \frac{20000}{3} \left[ x \right]_{-\sqrt{10}}^{\sqrt{10}}[/tex]
⇒ [tex]\frac{20000}{3} ( 2\sqrt{10})[/tex] = [tex]\frac{40000 \sqrt{10}}{3}[/tex]
Therefore, the volume of W is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.
The average age of three people is 25. If two of the people are 22, how old is the third person...?
A.23
B.25
C.28
D.31
E. None correct
Answer:
D
Step-by-step explanation:
SEX
Question
What is the answer
Answer:
0.0228, Hope that useful for you.
Step-by-step explanation:
Because of " the scores...normally distributed of a mean 310 and the standard deviation 12", we can use the Central limit theorem.
That means:
([tex]P(X>334)= P(\frac{X-E(X)}{SD(X)}>\frac{334-310}{12})= P(Z>2)= 1-P(Z\leq 2)= \\1- 0.9772= 0.0228[/tex]
What is the volume of the prism below height is 5 length is 7 width is 8
Answer:
B. 280 units cubed
Step-by-step explanation:
Multiply all of the numbers together
Suppose you travel at 70 mph for 520 miles. How many hours will take you to reach your destination
Answer:
7.4
Step-by-step explanation:
To calculate the time taken to travel a certain distance at a certain speed, use the formula: Time = Distance/Speed. In this case, to travel 520 miles at 70 miles per hour, it would take approximately 7.43 hours or 7 hours and 26 minutes.
Explanation:The subject of this question is about calculating time based on speed and distance in a real-world context. To find out how many hours it will take you to reach your destination travelling at 70 miles per hour for 520 miles, we use the formula: Time = Distance / Speed. In this context, the distance is 520 miles and the speed is 70 miles per hour. Insert these values into the formula, you get: Time = 520 / 70 which gives you approximately 7.43 hours. This means it would take you about 7 hours and 26 minutes to reach your destination, if you were traveling at a consistent speed of 70 miles per hour.
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Select the indicated angle of rotation in standard position.
A positive angle coterminal to 132°
A. 492° B. 497°
C. 502° D. 487°
A positive angle cotermincal to 132° is .
For a positive angle coterminal to 127°, select Graph B (with angle measurement of 492°). For the angle 79°, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.
A positive angle coterminal to 127° can be found by adding 360° to it, since coterminal angles are separated by full rotations:
1.First Positive Coterminal Angle:
[tex]\( 127° + 360° = 487° \)[/tex] (This is not one of the choices provided.)
2.Second Positive Coterminal Angle:
[tex]\( 487° + 360° = 847° \)[/tex] (This is beyond the range of the options provided.)
However, if we look for a coterminal angle between 360° and 720°, we find:
[tex]\( 127° + 360° = 487° \)[/tex], which is closer to 492° given in Graph B.
For the angle 79°:
1.Positive Coterminal Angles:
- Add 360° for the first positive coterminal angle:
[tex]\( 79° + 360° = 439° \)[/tex]
- Add another 360° for the second positive coterminal angle:
[tex]\( 79° + 720° = 799° \)[/tex]
2. Negative Coterminal Angles:
- Subtract 360° for the first negative coterminal angle:
[tex]\( 79° - 360° = -281° \)[/tex]
- Subtract 720° for the second negative coterminal angle:
[tex]\( 79° - 720° = -641° \)[/tex] (However, this is not the nearest negative coterminal angle.)
The first negative coterminal angle is already the nearest, so the second negative coterminal angle is actually the original angle itself, which is 79° (since subtracting 0° gives us the same angle).
So, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.
complete question given below:
Which function is not continuous
Answer:
A not continueous function
Step-by-step explanation:
has a range
Find the area of a circle with a circumference of 12.56 units.
Answer:
12.55
Step-by-step explanation:
Answer:
[tex]Area\,\,of\,\,the\,\, circle=12.56\,\, units ^2[/tex]
Step-by-step explanation:
Circumference of the circle= 12.56 units
[tex]Circumference=2\times\pi \times r[/tex]
As,
[tex]\pi =\dfrac{22}{7}=3.14[/tex]
[tex]2\pi r=12.56\\\\2\times 3.14 \times r=12.56\\\\6.28\times r=12.56\\\\r=\dfrac{12.56}{6.28} \\\\r=2\,\,units[/tex]
Area of a circle= [tex]=\pi \times r^2[/tex]
[tex]=3.14\times 2^2\\\\\=3.14\times 4\\\\=12.56\,\, units ^2[/tex]
Ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores. 88%, 73%, 97%, 76%, 90%, 80% Which measure of center would best represent Ari’s grade? the mean the median both the mean and the median neither the mean nor the median
Answer:
There is no difference. Because the mean of Ari's tests equals his median score of his six tests. mean = 84% median = 84%
Step-by-step explanation:
88%, 73%, 97%, 76%, 90%, 80%
organize by low to high
73%, 76%, 80%, 88%, 90%, 97%
The median here is (80 + 88)/2 = 84%
let us find the mean
mean = [73% + 76% + 80% + 88% + 90% + 97% ]/6
mean = 504/6 = 84%
There is no difference. Because the mean of Ari's tests equals his median score of his six tests. mean = 84% median = 84%
which is another way to write 10 minutes after 9?
Answer:
quarter past 9
Step-by-step explanation:
Answer:09:10
Step-by-step explanation:
10 minutes after 9 can be written as
09:10
What is the side length of a cube with a volume of 64 mm3?
Cube V = s3
Answer:
4mm edge 2021
Step-by-step explanation:
find the length of side XZ in the right triangle shown
Answer:35 meters
Step-by-step explanation:
Answer:
35 meters
Formula:
a^2+b^2=c^2
12^2+b^2=37^2
Simplify this complex fraction
Answer:
18
Step-by-step explanation:
6 ÷ 1/3
Change the whole number to a fraction
6/1 ÷ 1/3
Copy dot flip
6/1 * 3/1
18/1
18
Answer:
18
Step-by-step explanation:
6 ÷ 1/3
Change the whole number to a fraction
6/1 ÷ 1/3
Copy dot flip
6/1 * 3/1
18/1
18
Neil has three partial full cans of white paint they contains 1/3 gallon 1/5 gallon 1/2 gallon of paint and how much paint does Niall have in all
Answer:
1 and 1/30 gallons of paint
Step-by-step explanation:
Write down the number that is equal to the fifth power of 10
Answer:
100000
Step-by-step explanation:
[tex] {10}^{5} = 100000[/tex]
[tex]10 \times 10 \times 10 \times 10 \times 10 = 100000[/tex]
Solve for x in the equation x squared + 4 x minus 4 = 8
Answer:
solution is : x = -6 and x = 2
Step-by-step explanation:
Answer:
the answer is A
Step-by-step explanation:
his situation is the same for questions 2 - 6. A few years ago, a census bureau reported that 67.4% of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. The city council is debating a plan to offer tax breaks to first-time home buyers in order to encourage people to become homeowners. They decide to adopt the plan on a 2-year trial basis and use the data they collect to make a decision about continuing the tax breaks. Since this plan costs the city tax revenues, they will continue to use it only if there is strong evidence that the rate of home ownership is increasing. What would a Type I error be?
Answer:
Type 1 Error: Stating 'American families owing house< 67.4%', when it = 67.4%
And, implementing the tax break for first time home buyers, due to the error
Step-by-step explanation:
Null Hypothesis [H0] : American families owing house = 67.4%
Alternate Hypothesis [H1] : American families owing house < 67.4%
Type 1 error is he rejection of an actually true null hypothesis.
In this case, it means : Results reject H0 in favour of H1 & state that 'american families owing house < 67.4% ; when actually null hypothesis, i.e 'american families owing house = 67.4%' is true.
This would imply that city council might extend the tax breaks for first time home buyers because of the type 1 error in the case. When, it is actually not needed as per the true data status.
PLEASEEEEE HELPP MEEE WITH NUMBER 13!!!!!!
QUESTION: (IN BOLDED SHOWN IN THE 2 PICTURES)
Answer:
∠1 = 31°
∠2 = 43°
Step-by-step explanation:
All triangles have a sum of 180°
Since we know this, then we know that in the end, the sum of the two triangles should both have a sum of 180° each.
∠2 equals 43° because it corresponds to ∠C and corresponding angles have the same measurement.
Now we can find the measurement of ∠1 by using the big triangle.
180 - (106 + 43)
180 - (149)
31°
So, the measurement of ∠1 is 31°.
Now, let's check our work.
Big triangle:
106 + 43 + 31 = 180
Small triangle:
43 + 31 + 106 = 180
The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested. However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made. Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a 95% confidence interval to judge whether the two indenters result in different measurements.
Answer:
Check the explanation
Step-by-step explanation:
Let X denotes steel ball and Y denotes diamond
[tex]\bar{x_1}[/tex] = 1/9( 50+57+......+51+53)
=530/9
=58.89
[tex]\bar{x_2}[/tex]= 1/9( 52+ 56+....+ 51+ 56)
=543/9
=60.33
difference = d =(60.33- 58.89)
=1.44
[tex]s^2=1/n\sum xi^2 - n/(n-1)\bar{x}^2[/tex]
s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2
=31686/8 - 9/8( 3468.03)
=3960.75 - 3901.53
=59.22
s1 = 7.69
s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2
=33295/8 - 9/8 (3640.11)
=4161.875 - 4095.12
=66.75
s2 =8.17
sample standard deviation for difference is
s=[tex]\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}[/tex]
= [tex]\sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}[/tex]
= [tex]\sqrt{1007.76/16}[/tex]
=7.93
sd = [tex]s*\sqrt{(1/n1)+(1/n2)}[/tex]
=[tex]7.93*\sqrt{(1/9)+(1/9)}[/tex]
=7.93* 0.47
=3.74
For 95% confidence level [tex]Z (\alpha /2)[/tex] =1.96
confidence interval is
[tex]d\pm Z(\alpha /2)*s_d[/tex]
=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)
=(1.44 - 7.35 , 1.44 + 7.35)
=(-2.31, 8.79)
There is sufficient evidence to conclude that the two indenters produce different hardness readings.
Need answer has soon has possible no need to explain
Answer:
7, -7
Step-by-step explanation:
The coordinates of the point on a coordinate grid are -2,6. the point is reflected across the x-axis to obtain a new point. the coordinates of the reflected point are
Answer:
(-2,-6)
Step-by-step explanation:
The rule for reflecting across the x axis is multiply the y coordinate by -1. Your x coordinate stays the same.
(x,y)---->(x,-y)
(-2,6)---> (-2,-6)
14k of tomatoes cost $126. how much would 36k cost?
Answer:
I think it's 2,772
Step-by-step explanation:
I did
36-14=22
Then I did 22× $126
hi
if 14 = 126
36 = ?
: 36*126 /14 = 324
. A factory manufactures widgets using three machines, A, B, and C. Of the total output, machine A is responsible for 30%, machine B for 20%, and machine C for the rest. It is known from previous experience with the machines that 10% of the output from machine A is defective, 5% from machine B, and 3% from machine C. A bolt is chosen at random from the production line and found to be defective. What is the probability that it came from machine A? Round your final answers to three decimal places.
Answer:
0.545 = 54.5% probability that it came from machine A
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Defective.
Event B: Coming from machine A.
Machine A is responsible for 30%
This means that [tex]P(B) = 0.3[/tex]
10% of the output from machine A is defective
This means that [tex]P(B|A) = 0.1[/tex]
Probability of being defective:
Machine A is responsible for 30%. Of those, 10% are defective.
Machine B is responsible for 20%. Of those, 5% are defective.
Machine C is responsible for 100 - (30+20) = 50%. Of those, 3% are defective. Then
[tex]P(A) = 0.3*0.1 + 0.2*0.05 + 0.5*0.03 = 0.055[/tex]
Finally:
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.3*0.1}{0.055} = 0.545[/tex]
0.545 = 54.5% probability that it came from machine A
Which statements are true about the shapes? Select three options.
Figure A is a cylinder. Figure B is a cone. Figure C is a sphere. Figure D is a pyramid with rectangular base.
A Figure A is a cylinder.
B Figure B is a square pyramid.
C Figure C has no bases.
D Figure D is a triangular prism.
E Figure D has four lateral faces that are triangles.
The correct options are:
A, C and E.
What is a shape?Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many categories. The forms are often enclosed by an outline or border that is composed of points, lines, curves, etc.
As per the given data:
We are given some shapes in the diagram, and we are also given the type of the shape, we have to identify the correct options out of the given options.
Figure A is a cylinder.
This is correct, as the figure correctly resemble a cylinder.
Figure B is a square pyramid.
This is incorrect, as the figure resembles a cone.
Figure C has no bases.
This is correct, as the figure correctly resemble a sphere and it has no base.
Figure D is a triangular prism.
This is incorrect, as the figure resembles a rectangular prism.
Figure D has four lateral faces that are triangles.
This is correct, as the figure correctly resemble a rectangular prism with four lateral faces that are triangles.
Hence, the correct options are:
A, C and E.
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Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. x 1 2 3 4 5 P(x) 0.70 0.15 0.10 0.02 (a) Find P(4). (b) Find the probability that a car has at least 3 occupants. (c) Find the probability that a car has fewer than 3 occupants. (d) Compute the mean µX. (e) Compute the standard deviation σX.
Answer:
a) P(4)=0.03
b) P(x≥3)=0.15
c) P(x<3)=0.85
d) µX=1.52
e) σX=1.69
Step-by-step explanation:
The question is incomplete:
The variable X has the following probability distribution:
x 1 2 3 4 5
P(x) 0.7 0.15 0.10 0.03 0.02
a) The probability P(x=4) can be read from the table
[tex]P(4)=0.03[/tex]
b) The probability that there are at least 3 occupants in the car is P(x≥3).
[tex]P(x\geq3)=P(3)+P(4)+P(5)\\\\P(x\geq3)=0.10+0.03+0.02\\\\P(x\geq3)=0.15[/tex]
c) The probability that a car has fewer than 3 occupants (P(x<3)) is:
[tex]P(x<3)=1-P(x\geq3)=1-0.15=0.85[/tex]
d) The mean can be calculated as:
[tex]\mu_x=\sum_{i=1}^5p_i\cdot x_i\\\\\mu_x=0.7*1+0.15*2+0.10*3+0.03*4+0.02*5\\\\\mu_x=0.7+0.30+0.30+0.12+0.10\\\\ \mu_x=1.52[/tex]
e) The standard deviation can be calculated as:
[tex]\sigma_x=\sqrt{\sum_{i=1}^5p_i(x_i-\mu_x)^2}}\\\\ \sigma_x=\sqrt{0.7(1-1.52)^2+ 0.15(2-1.52)^2+ 0.1(3-1.52)^2+ 0.03(4-1.52)^2 +0.02(5-1.52)^2}\\\\ \sigma_x=\sqrt{0.7*0.2704+0.15*0.2304+0.1*2.1904+0.03*6.1504+0.03*12.1104}\\\\\sigma_x=\sqrt{0.18928+0.06912+0.65712+0.738048+1.21104}\\\\ \sigma_x=\sqrt{2.8646}\\\\ \sigma_x=1.69[/tex]
The graph of the probability distribution of X is a bar graph. The mean of X is 1.65 and the standard deviation can be calculated using the variance formula. The probability that a car has at least 3 occupants is 0.12 and the probability that a car has fewer than 3 occupants is 0.85.
Explanation:The graph of the probability distribution of X is a bar graph where the x-axis represents the number of occupants and the y-axis represents the probability. You will have bars at x = 1, 2, 3, 4, and 5 with heights of 0.70, 0.15, 0.10, 0.02 respectively.(i) To calculate the mean of X, you multiply each possible value of X by its corresponding probability and sum them up. So, μX = 1*0.70 + 2*0.15 + 3*0.10 + 4*0.02 + 5*0 = 1.65. (ii) To calculate the standard deviation, you need to find the variance first. The variance is calculated by squaring the difference between each value of X and the mean, multiplying it by its corresponding probability, and summing them up. The standard deviation is the square root of the variance. (a) To find the probability that a car has at least 3 occupants, you need to sum up the probabilities of X being 3, 4, and 5. So, P(X≥3) = P(3) + P(4) + P(5) = 0.10 + 0.02 = 0.12. (b) To find the probability that a car has fewer than 3 occupants, you need to sum up the probabilities of X being 1 and 2. So, P(X<3) = P(1) + P(2) = 0.70 + 0.15 = 0.85.Farmer Ed has 8,000 meters of fencing & wants to enclose a rectangular plot that borders a river. If farmer Ed does not fence the side along the river, what is the largest area that can be enclosed ?
(answer is on pic but I just need a step by step explanation)
Answer:
largest area that can be enclosed = 8,000,000 m²
Step-by-step explanation:
Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.
Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.
Since we know the amount of fencing available is 8000m, we get:
8000 = x + 2y
solving for x, we have;
x = 8000 - 2y
substitute 8000 - 2y for x into the area equation to give;
A = (8000 - 2y)y distribute
A = -2y² + 8000y
Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,
Thus; y = -b/2a = -8000/[2(-2)] = 2000
x = 8000 - 2(2000) = 4000
A = 4000(2000) = 8,000,000 m²
Which equation could you use to solve for x in the proportion 5
4x - 45
5x - 13
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Complete Question
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?
4 x = 14 4 x = 45 5 x = 13 5 x = 36Answer:
(B) 4x = 45
Step-by-step explanation:
The given proportion is:
[Tex]\dfrac{4}{5}=\dfrac{9}{x}[/TeX]
To find an equivalent expression, let us cross multiply:
4*x=5*9
This gives:
4x=45
The correct option is B.