Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
[tex]A=w\ell[/tex]
Where w is the width and l is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to t, where w and l are both functions of t:
[tex]\displaystyle \frac{dA}{dt}=\frac{d}{dt}\left[w\ell][/tex]
By the Product Rule:
[tex]\displaystyle \frac{dA}{dt}=\frac{dw}{dt}\ell +\frac{d\ell}{dt}w[/tex]
Since we know that dl/dt = 6 and that dw/dt = 5:
[tex]\displaystyle \frac{dA}{dt}=5\ell + 6w[/tex]
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
[tex]\displaystyle \frac{dA}{dt}=5(12)+6(4)=84\text{ cm}^2\text{/s}[/tex]
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Can I get some help with this question? I have attempted several times and failed.
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Answer:
B. relative maximum of 8.25 at x=2.5
Step-by-step explanation:
A quadratic of the form ax²+bx+c has an absolute extreme at x=-b/(2a). For your quadratic, that is ...
x = -5/(2(-1)) = 5/2
The value of the extreme is ...
f(5/2) = (-5/2 +5)(5/2) +2 = 25/4 +2 = 33/4 = 8.25
The negative leading coefficient tells you the graph opens downward, so the extreme is a maximum.
The function has a relative maximum of 8.25 at x = 2.5.
__
A graphing calculator can show this easily.
PlEaSe HelP mEakwhtb4qhnga
Answer:
d. y = x + 6
Step-by-step explanation:
Equation of AD can be written in the slope-intercept form, y = mx + b
First, find the slope (m) and y-intercept (b) of line AD.
✔️Slope (m) = change in y/change in x
Using two points on line AD, (-5, 1) and (0, 6):
Slope (m) = (6 - 1)/(0 - (-5))
Slope (m) = 5/5
m = 1
✔️y-intercept (b) is the point where the line cuts across the y-axis = 6
b = 6
✔️To write the equation, substitute m = 1 and b = 6 into y = mx + b
y = 1(x) + 6
y = x + 6
RJM Enterprises is a manufacturer of consumer electronics products. The industry is very competitive, and RJM has seen its profits fall in recent years, including an operating loss of $16,328 last year. RJM was able to turn that around this year by aggressively cutting costs. The summarized financial results for RJM are shown below:
Answer: hello your question has some missing data attached below is the missing data
answer :
∑ Volume variance = $55272
∑ Sales price variance = $41944 ( F )
Step-by-step explanation:
First step : prepare a flexible budget data for the current year using the formulae below
flexible budget = Actual units * Budgeted rate
and
Sales price variance = Actual - Budgeted data
Attached below is the Table showing the evaluation of sales price variance and volume variance
A researcher wants to investigate the effects of environmental factors on IQ scores. For an initial study, she takes a sample of 400 people who grew up as the only child. She finds that 48.5% of them have an IQ score over 100. It is known that 50% of the general population has an IQ score exceeding 100.(a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people.(b) Find the standard deviation of p.(c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400. Round answer to 4 decimal places.
Answer:
a) p = 0.5.
b) s = 0.025.
c) 0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
It is known that 50% of the general population has an IQ score exceeding 100. Sample of 400.
This means that [tex]n = 400, p = 0.5, s = \sqrt{\frac{0.5*0.5}{400}} = 0.025[/tex]
(a) Find the mean of p, where p is the proportion of people with IQ scores over 100 in a random sample of 400 people
By the Central Limit Theorem, p = 0.5.
(b) Find the standard deviation of p.
By the Central Limit Theorem, s = 0.025.
(c) Compute an approximation for P(p is greater than or equal to 0.485), which is the probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
This is 1 subtracted by the p-value of Z when X = 0.485. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.485 - 0.5}{0.025}[/tex]
[tex]Z = -0.6[/tex]
[tex]Z = -0.6[/tex] has a p-value of 0.2743.
1 - 0.2743 = 0.7257.
0.7257 = 72.57% probability that there will be 48.5% or more individuals with IQ scores over 100 in a random sample of 400.
Solve for X in the triangle. Round your answer to the nearest TENTH. (LISTING BRAINLIST PLZ HELP)
Answer:
2.3 =x
Step-by-step explanation:
We know the opposite and adjacent sides.
Since this is a right triangle, we can use trig functions
tan 38 = opp/ adj
tan 38 = x/3
3 tan 38 = x
2.34385688= x
To the nearest tenth
2.3 =x
Answer:
x ≈ 3.9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA [Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 38°
Opposite Leg = x
Adjacent Leg = 5
Step 2: Solve for x
Substitute in variables [tangent]: tan38° = x/5[Multiplication Property of Equality] Multiply 5 on both sides: 5tan38° = xRewrite: x = 5tan38°Evaluate: x = 3.90643Round: x ≈ 3.9The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true? The domain of the function is all real numbers less than or equal to −2. The domain of the function is all real numbers less than or equal to 9. The range of the function is all real numbers less than or equal to −2. The range of the function is all real numbers less than or equal to 9.
Answer:
D
Step-by-step explanation:
We have the quadratic function:
[tex]f(x)=-x^2-4x+5[/tex]
First, the domain of all quadratics is always all real numbers unless otherwise specified. You can let x be any number and the function will be defined.
So, we can eliminate choices A and B.
Note that since the leading coefficient is negative, the parabola will be curved downwards. Therefore, it will have a maximum value. This maximum value is determined by its vertex, which is (-2, 9).
Since it is curving downwards, the maximum value of the parabola is y = 9. It will never exceed this value. Therefore, the range or the set of y-value possible is always equal to or less than 9.
So, the range of the function is all real numbers less than or equal to 9.
Our answer is D.
It is not C because the maximum value is dependent on y and not x.
Helpppplpppp
Which choice is equivalent to the product below?
Answer:
6
Step-by-step explanation:
=>root(2) x root(3) x root(6)
=>root(2x3) x root(6)
=>root(6) x root(6)
=>6
Consider the following sample data: x 12 18 20 22 25 y 15 20 25 22 27 Click here for the Excel Data File a. Calculate the covariance between the variables. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Answer:
The covariance between the variables is 21.10 and the Correlation coefficient is 0.9285.
Step-by-step explanation:
Hence,
identify the 3D shape :)thank you
If you folded the figure up, you would have a prism where the parallel bases are right triangles. Each lateral face is a rectangle.
It might help to imagine a room where the floor and ceiling are triangles (they are identical or congruent triangles). Each wall of this room is one of the rectangles shown.
a. Chéo hóa ma trận A .
b. Từ kết quả câu a, hãy tính 10 A .
If 10 miles is 70% of the distance,
what is the total distance?
If a rectangular prism has a length of 3 1/2 in and a width of 9 in and a height of 3 1/2, what would the surface area be?
The surface area is 150.5 in
Answer:
The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].
Step-by-step explanation:
The formula for finding the surface area of a rectangular prism is this :
A=2(wl + hl + hw)
l = 3.5, w = 9, h = 3.5
Now we substitute those values in and solve for A.
A = 2 · ( 9 · 3.5 + 3.5 · 3.5 + 3.5 ·9) = 150.5
The surface area of this rectangular prism is 150.5 [tex]inches^{2}[/tex].
Hope this helps, please mark brainliest. Have a great day!
Given that the length of the figure below is x + 2, its width is
2- 2, and its perimeter is 24, solve for 2.
Answer:
hear is your answer in attachment please give me some thanks
The quotient of 36 and 9 multiplied by 7
Answer:
6
Step-by-step explanation:
6*9 = 54
6*6 = 36
6*7 = 42
5'1 in height plus 7 cm how tall am I ?
Answer:
5.313 ft (about 5'3.75")
What is the slope of the line represented by this equation?
-3x + 8y = 12
A -8/3
B -3/8
C 3/8
D 8/3
Answer:
C. 3/8
Step-by-step explanation:
[tex] - 3x + 8y = 12 \\ \therefore 8y =3x + 12 \\ \therefore \: y = \frac{3}{8} x + 12 \\ equating \: it \: with \\ y = mx + b \: we \: find: \\ m = \frac{3}{8} \\ \therefore \: slope = \frac{3}{8} [/tex]
The answer above is wrong I took the test. It's in the picture below!
Work out the following, giving your answers in their simplest form:
b) 5/9 ÷ 5
Answer:
5/9÷55/9×1/51/9Hope it helps youAnswer:
Since i m not sure of the equation i have dont both possible ways :)
Step-by-step explanation:
b)
(5/9) ÷ 5
[tex]= \frac{5}{9} \div 5\\\\=\frac{\frac{5}{9}}{5}\\\\=\frac{5}{9 \times 5}\\\\=\frac{1}{9}[/tex]
5/(9÷5)
[tex]=\frac{5}{9 \div5}\\\\= \frac{5}{\frac{9}{5}}\\\\=\frac{5 \times 5}{9}\\\\=\frac{25}{9}[/tex]
[(4 x 2) + (2 x 3)] ÷ 2 x 5 =
Answer:
1.4
Step-by-step explanation:
= [(4 x 2) + (2 x 3)] ÷ 2 x 5
= [8 + 6] / 10
= 14 / 10
= 1.4
1.3.33 Question Help A certain triangle has a perimeter of 3078 mi. The shortest side measures 71 mi less than the middle side, and the longest side measures 371 mi more than the middle side. Find the lengths of the three sides. The shortest side is mi long.
Answer:
the shortest side is 855 miles long.
Step-by-step explanation:
a + b + c = 3078 miles
a = b - 71
c = b + 371
=>
(b-71) + b + (b+371) = 3078
3b + 300 = 3078
3b = 2778
b = 926 miles
a = 926 - 71 = 855 miles
c = 926 + 371 = 1297 miles
The numbers 1, 2, 3 , and 4 are drawn one at a time from the set {0, 1, 2, …, 9}. If these four numbers are drawn with replacement, what is the probability that 14 − 23 is an even number?
Use the formula for simple interest, I = Prt, to find the indicated quantity. Assume a 360 day year.
1 = $24; P = $1200; t = 90 days; r = ?
r=% (Simplify your answer.)
Answer:
r = 8%
Step-by-step explanation:
Given that,
Interest, I = $24
Principal, P = $1200
Time, t = 90 days = 90/360 = 1/4 years
We need to find the rate.
We know that,
The simple interest is given by :
[tex]I=\dfrac{Prt}{100}[/tex]
Put all the values,
[tex]r=\dfrac{100I}{Pt}\\\\r=\dfrac{100\times 24}{1200\times \dfrac{1}{4}}\\\\r=8\%[/tex]
So, the rate is 8%.
A bin of 50 manufactured parts contains 3 defective parts and 47 non-defective parts. A sample of size 6 parts is selected from 50 parts. Selected parts are not replaced. How many different samples are there of size six that contain exactly 2 defective parts? What is the probability that a sample contains exactly 2 defective parts?
Answer:
535,095 different samples of size six that contain exactly 2 defective parts.
0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
As the order of the parts is not important, the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different samples are there of size six that contain exactly 2 defective parts?
2 defective from a set of 3, and 4 non-defective from a set of 47. So
[tex]D = C_{3,2}*C_{47,4} = \frac{3!}{2!1!}*\frac{47!}{4!43!} = 535095[/tex]
535,095 different samples of size six that contain exactly 2 defective parts.
What is the probability that a sample contains exactly 2 defective parts?
The total number of samples is:
[tex]T = C_{50,6} = \frac{50!}{6!44!} = 15890700[/tex]
Then...
[tex]p = \frac{D}{T} = \frac{535095}{15890700} = 0.0337[/tex]
0.0337 = 3.37% probability that a sample contains exactly 2 defective parts.
Do the following lengths form a right triangle?
Answer:
yes, this forms a right angle
The length of duration, in minutes, of earthquakes in California has been recorded for future analysis and information. An earthquake expert claims that the average duration of earthquakes in California is 0.5 minutes. To investigate the validity of this claim a random sample of 6 earthquakes were taken and the sample mean and the sample standard deviation were 1.15 and 0.308 minutes, respectively. Construct a 98% confidence interval and determine if the researcher`s claim can be rejected.
a. 98% C.l.is (0.727, 1.573). One can reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.
b. 98% C.I. is (0.727, 1.573). One cannot reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.
c. 98% C.I. is (0.755, 1.545). One can reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.
d. 98% C.I. is (0.755, 1.545). One cannot reject the expert's claim tha thte true average duration of earthquakes in California is 0.5 minutes.
Answer:
The answer is "(0.727, 1.573)".
Step-by-step explanation:
The confidence interval of 98 percent is C.I = (0.727, 1.573). You might disregard the statement of the experts that the genuine average duration in California of earthquakes is 0.5 minutes.
[tex]C.I = \bar{x}\pm t_{\frac{\alpha }{2}}\times \frac{s }{\sqrt{n}}\\\\[/tex]
[tex]= 1.15 + 3.365 \times 0.12574\\\\= 1.15 + 0.4231\\\\= (0.7269, 1.5731)[/tex]
What is the value of x for x +20 x=22
Answer:
x(1+20)=22
21x=22
x= 22/21
x= 1.05
Step-by-step explanation:
Answer:
2!!!
Step-by-step explanation:
the person is wrong.. 2+20=22
Find the critical value ta/2 needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
(a) For level 90% and sample size 8.
(b) For level 99% and sample size 11.
(c) For level 95% and sample size 25.
(d) For level 99.5% and sample size 10.
Answer:
1.894
3.169
2.064
3.690
Step-by-step explanation:
A.) 90% ; sample size = 8
Degree of freedom, df = n - 1
t(1 - α/2, 7) = t0.05, 7 = 1.894
B.) 99% ; sample size = 11
Degree of freedom, df = n - 1
t(1 - α/2, 10) = t0.005, 10 = 3.169
C.) 95% ; sample size = 25
Degree of freedom, df = n - 1
t(1 - α/2, 24) = t0.025,24 = 2.064
(D.) 99.5% and sample size 10.
Degree of freedom, df = n - 1
t(1 - α/2, 9) = t0.0025,9 = 3.690
The width of a rectangle, in feet, is represented by (3x + 2). The length of the rectangle, in feet, is represented by (5x + 4). Find the perimeter of the rectangle.
Which relations represent functions?
Input
Output
3
5
-b
9
d
Input
Output
7
-3
y
5
Input
Output
John
52
what does the equation inverse of the function found in part b represent in the contract of the problem ? explain your answer .
context to question - At a carnaval , you pay $15 for admission plus $3 for each ride that you go on .
Answer:
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The inverse function is to calculate the number of rides; given the amount paid
Step-by-step explanation:
Given
[tex]Admission = 15[/tex]
[tex]Ride = 3[/tex] per ride
Required
Explain the inverse function
First, we calculate the function
Let x represents the number of rides
So:
[tex]f(x) = Admission + Ride * x[/tex]
[tex]f(x) = 15 + 3 * x[/tex]
[tex]f(x) = 15 + 3x[/tex]
For the inverse function, we have:
[tex]y = 15 + 3x[/tex]
Swap x and y
[tex]x = 15 + 3y[/tex]
Make 3y the subject
[tex]3y = x - 15[/tex]
Make y the subject
[tex]y =\frac{x}{3} - 5[/tex]
Replace y with the inverse function
[tex]f^{-1}(x) =\frac{x}{3} - 5[/tex]
The above is to calculate the number of rides; given the amount paid
Which is more economical: purchasing the economy size of a detergent at 3 kilograms for $3.15 or purchasing the regular size at 720 grams for 60c?
Answer:
Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.
Step-by-step explanation:
Which is more economical?
Whichever situation has the lowest price per kilogram.
3 kilograms for $3.15
3.15/3 = $1.05 per kilogram.
720 grams for 60c
0.6/0.72 = $0.83 per kilogram.
Due to the lower price per kilogram, purchasing the regular size at 720 grams for 60c is more economical.