Answers
Related Questions
Greta has watched 30 minutes of a movie. This is 20%
of the entire movie. How long is the movie?
Answers
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
Answers
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.
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?
Answers
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]
More about the integration link is given below.
https://brainly.com/question/18651211
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)
Answers
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
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.
Answers
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.
The score distribution shown in the table is for all students who took a yearly AP statistics exam. An AP statistics teacher had 6565 students preparing to take the AP exam. Though they were obviously not a random sample, he considered his students to be "typical" of all the national students. What's the probability that his students will achieve an average score of at least 3?
Answers
Answer:
Step-by-step explanation:
The question is incomplete because the data is missing, i.e. the probability that you will score 5, 4, 3, 2, 1.
But it is resolved as follows:
[tex]P(x\geq 3) = P(\frac{x - m}{\frac{sd}{\sqrt{n} } } \geq \frac{3 - m}{\frac{sd}{\sqrt{n} }})\\\\[/tex]
where m is the mean and sd is the standard deviation.
the m is calculated by the sum of the multiplication of the score by the probability of this
that is to say,
score probability
5 0.2
4 0.3
3 0.1
2 0.3
1 0.1
m = 5*0.2 + 4*0.3 + 3*0.1 + 2*0.3 + 1*0.1
m = 3.2
However, the standard deviation will be calculated by
sd = [tex]\sqrt{\\}[/tex]∑[tex](x - m)^{2}*p[/tex]
that is, knowing the mean already, we can calculate the standard deviation, following the example:
sd =[tex]\sqrt{[(5-3.2)^2] *0.2 + [(4-3.2)^2] *0.3 + [(3-3.2)^2] *0.1 + [(2-3.2)^2] *0.3 + [(1-3.2)^2] *0.1 }[/tex]
sd = [tex]\sqrt{1.76}[/tex]
sd = 1.327
And also n = 5, because it's 5 scores. We replace in the initial equation:
[tex]P(x\geq 3) = P(Z \geq \frac{3 - 3.2}{\frac{1.327}{\sqrt{5} }})\\\\[/tex]
[tex]P(x\geq 3) = P(Z \geq -0.337)\\\\\\[/tex]
Therefore for the example the number z is -0.337, which if in the normal distribution table corresponds to 0.3520, that is the probability that the average is at least 3, for the example is 35.20 %.
Use the given information to find the minimum sample size required to estimate an unknown population mean μ.
How many business students must be randomly selected to estimate the mean monthly earnings of business students at one college? We want 95% confidence that the sample mean is within $140 of the population mean, and the population standard deviation is known to be $569.
Answers
A minimum sample size of 64 business students must be randomly selected to estimate the mean monthly earnings with 95% confidence within $140 of the true population mean, given the population standard deviation of $569.
Explanation:To find the minimum sample size required to estimate an unknown population mean μ with a certain level of confidence, we can use the formula:
n = (Z*σ/E)^2
Where:
n is the sample sizeZ is the Z-score corresponding to the desired confidence levelσ (sigma) is the population standard deviationE is the margin of errorFor a 95% confidence level, the Z-score is approximately 1.96. The population standard deviation σ is given as $569. The margin of error E is $140.
Plugging these values into the formula, we get:
n = (1.96*569/140)^2
n = (1114.44/140)^2
n = (7.96)^2
n = 63.4
Since the sample size must be a whole number, we would round up to the next whole number which gives us a minimum sample size of 64 business students that must be randomly selected to estimate the mean monthly earnings of business students at one college with the desired precision and confidence level.
Final answer:
To estimate the population mean with a 95% confidence level and a margin of error of $140, we use the formula n = (Z*σ/E)^2 with σ = $569. Using the z-score for 95% confidence (1.96), the calculation yields 119.44, which we round up to 120 business students needed for the sample.
Explanation:
Calculating Minimum Sample Size for Estimating a Population Mean
To determine the minimum sample size needed to estimate the mean monthly earnings of business students at one college with 95% confidence and a margin of error of $140, we use the formula for the sample size (n). The formula is derived from the properties of a normal distribution and the central limit theorem and is as follows:
n = (Z*σ/E)^2
where:
Z is the z-score corresponding to the desired confidence level (1.96 for 95% confidence),
σ (sigma) is the population standard deviation, and
E is the desired margin of error.
Plugging in the given values of σ = $569 and E = $140, we find:
n = (1.96 * 569 / 140)^2
n ≈ (10.924)^2
n ≈ 119.44
Since we cannot survey a fraction of a person, we round up to the nearest whole number. Therefore, 120 business students must be randomly selected to achieve the desired precision.
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?
Answers
Answer:
22%
Step-by-step explanation:
Answer:
22% tax bracket
Step-by-step explanation:
HELP !!! 10 points !!!! plz hurry
Answers
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
what is the midpoint of segment shown below?(-1,5) and (6,5)
Answers
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
Identify the polygon and classify it as regular or irregular.
Answers
Answer:
That should be pentagon, irregular
(5 sides which are not equal)
Hope this helps!
:)
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
Answers
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.
Learn more about the survey here:
https://brainly.com/question/17373064
#SPJ5
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?
Answers
Answer:
No
Step-by-step explanation:
I got it right on Instruction
Answer:
its No trust me
Step-by-step explanation:
A school has two kindergarten classes. There are 21 children in Ms. Toodle's kindergarten class. Of these, 17 are "pre-readers" children on the verge of reading. There are 19 children in Mr. Grimace's kindergarten class. Of these, 13 are pre-readers. Using the plus four confidence interval method, a 90% confidence interval for the difference in proportions of children in these classes that are pre-readers is -0.104 to 0.336.
1. Which of the following statements is correct?
a. This confidence interval is not reliable because the samples are so small.
b. This confidence interval is of no use because it contains 0, the value of no difference between classes.
c. This confidence interal is reasonable because the sample sizes are both at least 5.
d. This confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population
Answers
Answer:
The correct answer is option (d).
Step-by-step explanation:
From the given example, the statement that is correct is, this confidence interval is not reliable because these samples cannot be viewed as simple random samples taken from a larger population.
This is because, In this scenario or setup, all the students are already part of the data. This is not a sample from a l population that is larger, but probably, the population itself.
Please helppp
What is the point-slope form of a line with slope 2 that contains the point
(1, 3)?
Answers
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
Find the area of a circle with a circumference of 12.56 units.
Answers
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
Answers
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
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length which statements about the two rectangular solids are true is it the bases are congruent the solids are similar and the ratio of the volume volumes of the first solid solid is eight One the volume of the first solid is twice as much is the volume of the second solid and if the dimensions of the second solid RX by X by H the first
Answers
Answer: A, D, E
Step-by-step explanation
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 49.0 and 54.0 minutes. Find the probability that a given class period runs between 50.75 and 51.25 minutes. Find the probability of selecting a class that runs between 50.75 and 51.25 minutes.
Answers
Answer:
The probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
Step-by-step explanation:
Let the random variable X represent the lengths of the classes.
The random variable X is uniformly distributed within the interval 49.0 and 54.0 minutes.
The probability density function of X is:
[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b,\ a<b[/tex]
Compute the probability that a given class period runs between 50.75 and 51.25 minutes as follows:
[tex]P(50.75<X<51.25)=\int\limits^{51.25}_{50.75}{\frac{1}{54-49}}\, dx\\\\=\frac{1}{5}\times [x]^{51.25}_{50.75}\\\\=\frac{51.25-50.75}{5}\\\\=0.10[/tex]
Thus, the probability that a given class period runs between 50.75 and 51.25 minutes is 0.10.
Answer: 0.050
I just did it and i got it right.
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.
Answers
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.
To learn more about shape, click:
brainly.com/question/28978432
#SPJ3
PLEASEEE HELPPP MEEE
solve for x
ANSWER CHOICES
a= -8
b= 2
c= 8
d= -6
Answers
Answer:
WHAT IS THE QUESTION WHAT IS X IN WHAT EQUATION!!!!!!!!
Step-by-step explanation:
Answer:
plzz i asked for brainliest on ur other question
Step-by-step explanation:
In which form is the following function written?
y= - 2(x - 3)(x+5)
Answers
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]
In Bangladesh, approximately 50.6% of the population is male and 49.4% of the population is female. By the Law of Large Numbers, we can take this to mean that the probability that a randomly selected birth is that of a male child is 0.506 and the probability that a randomly selected birth is that of a female child is 0.494. In a randomly selected family with six children, what is the probability that at most 2 of the children are boys? What is the expected number of boys in a randomly selected family with six children?
Answers
Answer:
A) 0.015
B) 4 bous6
Step-by-step explanation:
That at most 2 of the selected children are male means that number of male must be less than or equal to 2
Pr (male) = 0.506
Pr (female) = 0.494
Pr (at most 2 males) = 0.506 x 0.506 x 0.494 x 0.494 x 0.494 x 0.494 = 0.015
Expected number of boys in a randomly selected number of 6 is
0.506 x 6 = 3.03
We round off to 4 boys
An office supply company manufactures paper clips, and even tolerates a small proportion of those paper clips being ‘defective’ (or incorrectly shaped and/or twisted) in its outgoing product. (The company reasons that paper clips are so cheap, users will simply discard the occasional defective paper clip they might find in a box.) The average proportion of ‘defective’ paper clips is known to be 2% when the paper clip manufacturing process is ‘in control’. To monitor this issue, what should be the value of the upper control limit of a p-chart if the company plans to include 25 paper clips in each of its samples and use z-value of 3.0 to construct the chart? g
Answers
Answer:
0.104 (10.4%)
Step-by-step explanation:
[tex]UCL = \bar{p}+z(\sigma)[/tex]
[tex]\sigma = p(1-)) Vn = 1.02(1-202)) 5[/tex] = 0.028
[tex]\thereforeUCL = .02+(3x0.028)[/tex] = 0.104
[tex]\thereforeUCL[/tex]= 10.4%
If p=2(a+b), then b=
Answers
Solving the equation p = 2(a + b) for b involves two steps: first dividing each side by 2, then subtracting 'a' from each side. This results in the final equation 'b = (p/2) - a'.
Explanation:To solve the equation p = 2(a + b) for b, you would first divide each side by 2 to isolate 'a + b'.
This gives you p/2 = a + b. Next, to isolate 'b', you would subtract 'a' from each side of the equation.
This gives you b = (p/2) - a, which is your final, simplified expression for 'b' in terms of 'p' and 'a'.
Learn more about Solving Equations here:https://brainly.com/question/18322830
#SPJ11
Round 506.57915 to the nearest hundredth.
Answers
Answer:
506.58
Step-by-step explanation:
Your welcome ;w;
What is the mean 9, 8, 12, 6, 10
Answers
Answer:
Mean = sum of elements/number of elements = (9 + 8 + 12 + 6 + 10)/5 = 9
Hope this helps!
:)
Answer:
9
Step-by-step explanation:
The mean is also called the average
Add up all the number
(9+8+ 12+ 6+ 10)
45
Then divide by the number of numbers
45/5 = 9
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?
Answers
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.
) You want to rent an unfurnished one-bedroom apartment after you graduate from high school. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $940. The margin of error for a 95% confidence interval is $160. Find the 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community. Write your answer in this format: x to y
Answers
Answer:
$780 to $1100
Step-by-step explanation:
A confidence interval has two bounds. A lower bound and an upper bound. They are dependent of the sample mean and of the margin of error M.
In this problem:
Sample mean: $940
Margin of error: $160
The lower end of the interval is the sample mean subtracted by M. So it is 940 - 160 = $780
The upper end of the interval is the sample mean added to M. So it is 940 + 160 = $1100
So the answer is
$780 to $1100
Answer:
[tex]940-160=780[/tex]
[tex]940+160=1100[/tex]
So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100
Step-by-step explanation:
For this case we can define the following random variable X as the monthly rent and we know the following properties given:
[tex]\bar X= 940 [/tex] represent the sample mean
[tex] ME = 160[/tex] represent the margin of error
n = 10 represent the sample size
The confidence interval for the true mean is given by:
[tex] \bar X \pm z_{\alpha/2} \sqrt{\frac{\sigma}{\sqrt{n}}}[/tex]
And is equivalent to:
[tex]\bar X \pm ME[/tex]
And for this case if we replace the info given we got:
[tex]940-160=780[/tex]
[tex]940+160=1100[/tex]
So then we are 95% confident that the true mean for the monthly rent is between 780 and 1100
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
Answers
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).
Learn more about the quadratic function here:
brainly.com/question/14083225
#SPJ5