Answer:
Less
Step-by-step explanation:
10 = 10
1/2 < 3/4
1/2 = 50%
3/4 = 75%
Answer:
10 1/2 is less than 10 3/4
Step-by-step explanation:
10 1/2 is 10.5
10 3/4 is 10.75
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:
Which equation could you use to solve for x in the proportion 5
4x - 45
5x - 13
Mark this andre un
Save and Exit
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.
A magazine sends out 100,000 survey questionnaires to ask for peoples' opinions on whether they approve of how the federal government is running the country. 4,500 questionnaires were returned voluntarily. The magazine editors find that over 80% of the respondents disapprove of how the federal government is running the country. Which of the following are most likely true? i. Since 4,500 returned questionnaires is a very large number, the results are reliable. Il. The voluntary response makes it likely that the most dissatisfied people were the ones to respond. Ill. The response suffers from undercoverage. A. Il and IlI B. Ionly C. Il only D. Ill only E. I and III only
The requried, Il. The voluntary response makes it likely that the most dissatisfied people were the ones to respond. Ill. The response suffers from under coverage. are true. Option A is correct.
What is a survey?The survey is defined as an activity that took the participation of the public in order to improve the service by taking feedback from the targeted public.
here,
As of the given conditions,
The number of people that returned the voluntaries is not a very large number, while the voluntary response increases the likelihood that the most dissatisfied people responded, the response also suffers from under coverage
.
Thus, Both II and III are correct statements. Option A is correct.
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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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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]
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.
You have decided to relax your work schedule over the next 5 years. Your current income is $92,000 putting you in the 24% Federal Income tax bracket. The tax bracket is 12% for income from $9,526 up to $38,700, 22% for income from $38,701 up to $82,500, and 24% for income from $82,501 to $157,000. If you decrease your annual income by 8% per year over the next 5 years, what Federal tax bracket will you be in after 5 years?
Answer:
22%
Step-by-step explanation:
Answer:
22% tax bracket
Step-by-step explanation:
American adults are watching significantly less television than they did in previous decades. In 2016, Nielsen reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day. 1. Find the probability that an average American adult watches more than 300 minutes of television per day. Answer in three decimal places. 2. Find the probability that an average American adult watches more than 2,000 minutes of television per week. Answer in three decimal places.
Answer:
1. 0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.
2. 100% probability that an average American adult watches more than 2,000 minutes of television per week.
Step-by-step explanation:
To solve this question, we need to understand the poisson distribution and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.
Normal distribution:
Problems of normally distributed samples are solved using 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.
To approximate the Poisson to the normal, we use [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]
1. Find the probability that an average American adult watches more than 300 minutes of television per day.
The mean is 320 minutes per day, so [tex]\lambda = 320, \mu = 320, \sigma = \sqrt{320} = 17.89[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 300. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{300 - 320}{17.89}[/tex]
[tex]Z = -1.12[/tex]
[tex]Z = -1.12[/tex] has a pvalue of 0.131.
1 - 0.131 = 0.869
0.869 = 86.9% probability that an average American adult watches more than 300 minutes of television per day.
2. Find the probability that an average American adult watches more than 2,000 minutes of television per week.
A week has 7 days, so [tex]\lamda = 7*320 = 2240, \mu = 2240, \sigma = \sqrt{2240} = 47.33[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 2000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2000 - 2240}{47.33}[/tex]
[tex]Z = -5.07[/tex]
[tex]Z = -5.07[/tex] has a pvalue of 0
1 - 0 = 1
100% probability that an average American adult watches more than 2,000 minutes of television per week.
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
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:
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]
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]
What value of c makes x2+6x+c a perfect square trinomial? 3,6,9,12
Answer: 9
Step-by-step explanation:
In order to make the expression a perfect square, ,we ate going to add to the expression the square of the half of the coefficient of 6.
x² + 6x + c
= x² + 6x + (6/2)²
= x² + 6x + 3²
= x² + 6x + 9
Therefore, 9 is the required solution that will.make the expression a perfect square.
Answer:
9
Step-by-step explanation.
x² + 6x + 9
= (x+3)(x+3)
= (x + 3)²
it is a perfect square trinomial when c is equal to 9
A tiny but horrible alien is standing at the top of the Empire State Building (which is
443
443443 meters tall) and threatening to destroy the city of New York!
A Men In Black agent is standing at ground level,
18
1818 meters across the street, aiming his laser gun at the alien.
At what angle, in degrees, should the agent shoot his laser gun?
Round your final answer to the nearest tenth.
Please help
Answer:
87.7 degrees.
Step-by-step explanation:
In triangle ABC, attached.
The height of the building |AB|=443 meters
The distance of the agent across the street , |BC|=18 meters
We want to determine the angle at C.
Now,
[tex]Tan C=\dfrac{|AB|}{|BC|} \\C=arctan (\dfrac{|AB|}{|BC|} )\\=arctan (\dfrac{443}{18} )\\=87.67^\circ\\\approx 87.7^\circ $(correct to the nearest tenth)[/tex]
The agent should sfoot his laser gun at an angle of 87.7 degrees.
Identify the polygon and classify it as regular or irregular.
Answer:
That should be pentagon, irregular
(5 sides which are not equal)
Hope this helps!
:)
Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x? StartFraction 5 plus-or-minus 3 StartRoot 11 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction StartFraction 5 plus-or-minus StartRoot 47 EndRoot Over 12 EndFraction StartFraction negative 5 plus-or-minus StartRoot 97 EndRoot Over 12 EndFraction
Answer:
The answer is B
Step-by-step explanation:
The required value of the quadratic function which is determined by the using quadratic formula would be [tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex] which is the correct answer would be an option (B).
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
We have been given that quadratic function as
5x = 6x² – 3
⇒ 6x² - 5x - 3 = 0
Compare the given function to the standard quadratic function
f(x) = ax² + b x + c = 0.
We get a = 6, b = -5 and c = -3
Using the quadratic formula to solve the above quadratic function
[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute the values of a = 6, b = -5 and c = -3 in the quadratic formula
[tex]x = \dfrac{-(-5)\pm\sqrt{-5^2-4\times6\times-3}}{2\times6}[/tex]
[tex]x = \dfrac{5\pm\sqrt{25+72}}{12}[/tex]
[tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]
Therefore, the correct answer would be an option (B).
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Leon started to try to transform the expressions 6g + (g + 2) + 3 to determine if it is equivalent to the expression 6 + 7g. His work is shown below. 6g + (g + 2) + 3 (6g + g) + 2 + 3 associative property 7g + 2 + 3 combine like variable terms Are the expressions 6g + (g + 2) + 3 and 6 + 7g equivalent?
Answer:
No
Step-by-step explanation:
I got it right on Instruction
Answer:
its No trust me
Step-by-step explanation:
HELP !!! 10 points !!!! plz hurry
Answer:
21 sq ft
Step-by-step explanation:
The formula is 0.5bh; b is the length of the base (6) and h is the height (7). So if you plug in those values, you have 0.5(6)(7). Multiply those and you get 21!
Answer:
The area of the triangle is 21 ft (640.08 centimeters)
The area of the rectangle is 120 ft (3657.6 centimeters)
The area of the whole figure is 141 ft (4297.68 centimeters)
Step-by-step explanation:
The area of a triangle is:
[tex]A = \frac{1}{2}bh[/tex] b is the base and h is the height.
Plug in what you have
[tex]A= \frac{1}{2}(6)(7)[/tex] multiply 6 by 7
[tex]A = \frac{1}{2} (42)[/tex] divide 42 by 2
[tex]A = \frac{42}{2}[/tex]
[tex]A = 21[/tex]
Now you have to find the area of the rectangle
The area of a rectangle is:
A = bh
Plug in what you have
A = (10)(12)
A = 120
Now add both areas together to get the area of the whole figure
120 + 21 = 141
In which form is the following function written?
y= - 2(x - 3)(x+5)
Answer:
I believe it is standard form?
Step-by-step explanation:
Answer: y= - 2(x - 3)(x+5) is Factored form
Step-by-step explanation: Quadratic equation forms
Vertex form is y = a(x -h)² + k
Standard form is y = ax² + bx + c
Factored form is [tex]y = a(x + r_{1} )(x + r_{2} )[/tex]
. 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
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
Evaluate the indefinite integral as a power series.
∫ tan−1(x) / x dx
[infinity]
f(x) = C + Σ
n = 0
What is the radius of convergence R?
Answer:
- The integral of arctan(x)/x =
C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).
- The radius of convergence is R = 1/x
Step-by-step explanation:
First note that
tan^(-1)x = arctan(x)
And
arctan(x) = Σ [(-1)^n. x^(2n+1)]/(2n+1). From n = 0 to infinity
arctan(x)/x = Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity
∫arctan(x)/x dx = ∫{Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity}dx
= ∫{Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.∫x^(2n)dx
= {Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.x^(2n+1)/(2n+1) + C
= C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).
To obtain the radius of convergence, we apply the ration test
R = Limit as n approaches infinity |a_n/a_(n+1)|
a_n = (-1)^n.x^(2n+1)]/(2n+1)²
a_(n+1) = (-1)^(n+1).x^(2(n+1)+1)]/(2(n+1)+1)²
|a_n/a_(n+1)| = (2(n+1) + 1)²/(2n+1)².x
= (1/x)[1 + 2/(2n+1)]
R = Limit as n approaches infinity |a_n/a_(n+1)|
= R = Limit as n approaches infinity (1/x)[1 + 2/(2n+1)]
R = 1/x
The integration of the arctan (x)/x is C + Σ [(-1)^n x^(2n+1)]/(2n+1)² where n is from 0 to ∞. The radius of convergence is R = 1/x
What is integration?It is the reverse of differentiation.
The indefinite integral is a power series that will be
[tex]\rm \int \dfrac{\tan^{-1}x }{ x} \ dx[/tex]
We know that the arctan is given as
[tex]\rm \tan^{-1} x = \dfrac{\sum [(-1)^n \ x^{2n+1}]}{(2n+1)}\\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ x^{2n})]}{(2n+1)}\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n}[/tex]
Then we have
[tex]\rm \int \dfrac{\tan^{-1} x }{x}\ dx= \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n} dx\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \int x^{2n}\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)^2} x^{2n + 1} + C[/tex]
To obtain the radius of convergence, then the ration test
[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{a_n}{a_{n+1}}\\\\\\a_n = \dfrac{(-1)^n \ x^{2n+1} }{(2n+1)^2}\\\\\\a_{n+1} = \dfrac{(-1)^{n+1} \ x^{2(n+1)+1} }{(2(n+1)+1)^2}\\\\\\ \dfrac{a_n}{a_{n+1}} = \dfrac{1}{x}(1+\dfrac{2}{2n+1})[/tex]
Then we have
[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{1}{x}(1+\dfrac{2}{2n+1})\\\\\\R = \dfrac{1}{x}[/tex]
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what is the midpoint of segment shown below?(-1,5) and (6,5)
Answer:
(2.5,5)
Step-by-step explanation:
The x coordinate of the midpoint is found by averaging the x coordinates
(-1+6)/2 = 5/2 = 2.5
The y coordinate of the midpoint is found by averaging the y coordinates
(5+5)/2 = 10/2 = 5
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
Please helppp
What is the point-slope form of a line with slope 2 that contains the point
(1, 3)?
Answer:
y=2x+1
Step-by-step explanation:
A(1;3) and m=2
y-yA=m(x-xA)
y-3=2(x-1)
y-3=2x-2
y=2x+1; or 2x-y+1=0
Need answer has soon has possible no need to explain
Answer:
7, -7
Step-by-step explanation:
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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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.
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.
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.