Answer:
The area of the rectangle increasing at the rate of 140 cm²/s
Step-by-step explanation:
Rectangle area:
A rectangle has two dimensions, length l and width w.
It's area is:
A = l*w.
When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?
We apply implicit differentiation to solve this question:
[tex]A = l*w[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
Length is 20, so [tex]l = 20[/tex].
Width is 10, so [tex]w = 10[/tex]
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.
This means that [tex]\frac{dl}{dt} = 8, \frac{dw}{dt} = 3[/tex]
So
[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
[tex]\frac{dA}{dt} = 20*3 + 10*8 = 140[/tex]
Area in cm².
So
The area of the rectangle increasing at the rate of 140 cm²/s
We wish to see if the dial indicating the oven temperature for a certain model of oven is properly calibrated. Four ovens of this model are selected at random. The dial on each is set to 300 °F, and, after one hour, the actual temperature of each is measured. The temperatures measured are 305 °F, 310 °F, 300 °F, and 305 °F. Assuming that the actual temperatures for this model when the dial is set for 300° are Normally distributed with mean μ, we test whether the dial is properly calibrated at 5% of significance level.
Actual Temp: 305, 310, 300, 305
Required:
a. Based on the data, calculate the sample standard deviation and standard error of X bar (round them into two decimal places) Standard Deviation: Standard Error:
b. What is a 95% confidence interval for μ? (upper and lower bound)
c. Provide your test statistic and P-value
d. State your conclusion clearly (statistical conclusion and its interpretation).
e. Even if 5% of significance level looks like default of test, we can use different significance levels as well. If we change the significance level into 10% (= 0.1), how does it affect your conclusion?
Answer:
a. Standard deviation: 4.082
Standard error: 2.041
b. The 95% confidence interval for the actual temperature is (298.5, 311.5).
Upper bound: 311.5
Lower bound: 298.5
c. Test statistic t=2.45
P-value = 0.092
d. There is no enough evidence to claim that the dial of the oven is not properly calibrated. The actual temperature does not significantly differ from 300 °F.
e. If we use a significance level of 10% (a less rigorous test, in which the null hypothesis is rejected with with less requirements), the conclusion changes and now there is enough evidence to claim that the dial is not properly calibrated.
This happens because now the P-value (0.092) is smaller than the significance level (0.10), given statististical evidence for the claim.
Step-by-step explanation:
The mean and standard deviation of the sample are:
[tex]M=\dfrac{1}{4}\sum_{i=1}^{4}(305+310+300+305)\\\\\\ M=\dfrac{1220}{4}=305[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{3}\cdot [(305-(305))^2+(310-(305))^2+(300-(305))^2+(305-(305))^2]}\\\\\\ s=\sqrt{\dfrac{1}{3}\cdot [(0)+(25)+(25)+(0)]}\\\\\\ s=\sqrt{\dfrac{50}{3}}=\sqrt{16.667}\\\\\\s=4.082[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=305.
The sample size is N=4.
When σ is not known, s divided by the square root of N is used as an estimate of σM (standard error):
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{4.082}{\sqrt{4}}=\dfrac{4.082}{2}=2.041[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
The t-value for a 95% confidence interval and 3 degrees of freedom is t=3.18.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=3.18 \cdot 2.041=6.5[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 305-6.5=298.5\\\\UL=M+t \cdot s_M = 305+6.5=311.5[/tex]
The 95% confidence interval for the actual temperature is (298.5, 311.5).
This is a hypothesis test for the population mean.
The claim is that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=300\\\\H_a:\mu\neq 300[/tex]
The significance level is 0.05.
The sample has a size n=4.
The sample mean is M=305.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.028.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.082}{\sqrt{4}}=2.041[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{305-300}{2.041}=\dfrac{5}{2.041}=2.45[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=4-1=3[/tex]
This test is a two-tailed test, with 3 degrees of freedom and t=2.45, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t>2.45)=0.092[/tex]
As the P-value (0.092) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °F does not significantly differ from 300 °F.
If the significance level is 10%, the P-value (0.092) is smaller than the significance level (0.1) and the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the actual temperature of the oven when the dial is at 300 °C does not significantly differ from 300 °C.
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
Required:
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
Answer:
a) 0.32 = 32% probability that your bid will be accepted
b) 0.72 = 72% probability that your bid will be accepted
c) An amount in excess of $15,400.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
This means that [tex]a = 10400, b = 15400[/tex]
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
You will win if the competitor bids less than 12000. So
[tex]P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32[/tex]
0.32 = 32% probability that your bid will be accepted
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
You will win if the competitor bids less than 14000. So
[tex]P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72[/tex]
0.72 = 72% probability that your bid will be accepted
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
His bid is uniformly distributed between $10,400 and $15,400.
So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.
I need help please help me
Answer:
4
Step-by-step explanation:
10-2(1)=8 which is >=4
10-2(2)=6 which is >=4
10-2(3)=4 which is >=4
10-2(4)=2 which isn't >=4
Therefore 4 doesn't satisfy the inequality
Answer:
4
Step-by-step explanation:
Let's test each possibility.
10-2(1)≥4
10-2=8 so it works
10-2(2)≥4
10-4=6 so it works
10-2(3)≥4
10-6=4 so it works
10-2(4)≥4
10-8=2
2<4 so it dosen't fit the solution
John works 21 hours a week and earns $157.50. How much does john earn per hour?
Answer:
D. $7.50
Step-by-step explanation:
$157.50 / 21 hours = $7.50 per hour
what is the value sin(?)= cos 28
Answer: 62
Step-by-step explanation:
Using the fact that cos(90-x)=sin(x) we get that 90-x=28, so x=62 and the answer is simply 62.
Hope that helped,
-sirswagger21
Jack uses triangles in the construction of bridges, such as the one shown below. A triangle has angles G, 72 degrees, and blank. The exterior angle to the blank angle is 133 degrees. What is the measure of Angle?
Answer: The answer is 61
Step-by-step explanation: did it on 2020 edg pls mark me brainliest
Answer:
61
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
Arc EF = 11.30
Step-by-step explanation:
For Circle A
S = r∅
18.08=(8)∅
Where ∅ is the angle subtended by the Arc
So
∅ = 18.08/8
∅ = 2.26 (in radians)
Now
For Circle C
S = r∅
S = (5)(2.26)
S = 11.30
Adam drew a line that was 6 4/10 inches long. If he drew a second line that was 2 2/3
inches longer, what is the length of the second line? Answer as a mixed number.
Answer:
The length of the second line is [tex]9\frac{1}{15}[/tex] inches
Step-by-step explanation:
Given
Length of first line = [tex]6\frac{4}{10}[/tex] inches
Length of second line = [tex]2\frac{2}{3}[/tex] inches longer
Required
Length of second line.
Let the length of the second line be represented by x.
From the question, x is [tex]2\frac{2}{3}[/tex] inches longer than the first line;
This implies that:
[tex]x = 2\frac{2}{3} + 6\frac{4}{10}[/tex]
Convert both fractions to improper fractions
[tex]x = \frac{8}{3} + \frac{64}{10}[/tex]
Take LCM
[tex]x = \frac{80 + 192}{30}[/tex]
[tex]x = \frac{272}{30}[/tex]
Convert to mixed fraction
[tex]x = 9\frac{2}{30}[/tex]
Reduce fraction to lowest term
[tex]x = 9\frac{1}{15}[/tex]
Hence, the length of the second line is [tex]9\frac{1}{15}[/tex] inches
Simplify -2(-5) - 7 + 1(-3)
Answer:
Step-by-step explanation:
BRUH YOU STUPID
Answer:
0
[tex] \\ solution \\ - 2( -5) - 7 + 1( - 3) \\ = 10 - 7 + ( - 3) \\ = 10 - 7 - 3 \\ = 3 - 3 \\ = 0 \\ hop \: it \: helps...[/tex]
Jose purchased 4/9 pound of peanut and 7/11 pounds of raisins find the total weight of his purchase
Answer:
The total weight of his purchase is 1.08 pounds
Step-by-step explanation:
To find the total weight of his purchase, we sum the weight of each of his purchases.
He purchased:
4/9 pound of peanut.
7/11 pounds of raisins
Total:
The least common multiple between 9 and 11 is 99.
Then
[tex]\frac{4}{9} + \frac{7}{11} = \frac{11*4 + 9*7}{99} = \frac{107}{99} = 1.08[/tex]
The total weight of his purchase is 1.08 pounds
Find f. f ''(θ) = sin(θ) + cos(θ), f(0) = 2, f '(0) = 1 f(θ) =
Answer:
[tex]f(theta)=sin(theta) - cos(theta)[/tex] + C
This is my first time doing a double integral, so im only 90% sure in my answer
Step-by-step explanation:
You pretty much want to take the double integral of sinx + cosx
The anti-derivative of sinx = -cosx
The anti-derivative of cosx = sinx
So f' = -cosx + sinx
Now lets take the integral of f':
The anti-derivative of -cosx = sinx
The anti-derivative of sinx = -cosx
So, f(x) = sinx - cosx
============================================================
Work Shown:
I'll use x in place of theta since its easier to type on a keyboard.
f '' (x) = sin(x) + cos(x)
f ' (x) = -cos(x) + sin(x) + C ..... integrate both sides; dont forget the plus C
f ' (0) = 1
f ' (0) = -cos(0) + sin(0) + C
-cos(0) + sin(0) + C = 1
-1 + 0 + C = 1
C = 1+1
C = 2
So,
f ' (x) = -cos(x) + sin(x) + C
turns into
f ' (x) = -cos(x) + sin(x) + 2
----------------------------
Now integrate both sides of the first derivative to get the original f(x) function
f ' (x) = -cos(x) + sin(x) + 2
f(x) = -sin(x) - cos(x) + 2x + D .... apply integral; D is some constant
f(0) = -sin(0) - cos(0) + 2(0) + D
f(0) = 0 - 1 + 0 + D
f(0) = D - 1
f(0) = 2
D-1 = 2
D = 2+1
D = 3
We have f(x) = -sin(x) - cos(x) + 2x + D update to f(x) = -sin(x) - cos(x) + 2x + 3
----------------------------
So f '' (x) = sin(x) + cos(x) becomes f(x) = -sin(x) - cos(x) + 2x + 3 when f(0) = 2 and f ' (0) = 1
The last step is to replace every x with theta so that we get back to the original variable.
f(x) = -sin(x) - cos(x) + 2x + 3 turns into f(θ) = -sin(θ) - cos(θ) + 2θ + 3
Simplify the expression,
(a3/2)3
Answer:
[tex]a^{\frac{9}{2}}[/tex]
Step-by-step explanation:
[tex]\left(a^{\frac{3}{2}}\right)^3[/tex]
[tex]=a^{\frac{3}{2}\cdot \:3}[/tex]
[tex]=a^{\frac{3}{2}\cdot \frac{3}{1}}[/tex]
[tex]=a^{\frac{9}{2}}[/tex]
you need 418 yards of blue silk to make one bridesmaid’s dress and 358 yards of the same fabric to make another. How many yards of blue silk do you need to make both dresses?
Answer: you would need 776 yards to make both dresses
Step-by-step explanation:
You would need to find the sum of the amount if yards needed for both dresses.
The first dress needs 418 yards
The seconds dress needs 358 yards
418 + 358 = 776
Therefore you would need 776 yards to be able to make both of the dresses
PLEASE HELP MEEEEEE!!!!!
Answer:
Read below
Step-by-step explanation:
To graph the inequality, place an open circle on -2.5 because there is no line under the > sign. Draw the arrow pointing to the right because the inequality reads "x is greater than -2.5.
As for the check box questions, only B and C should be checked. The arrow points right, and the circle is open.
Determine how many lines of sysmmetry each object had. Then determine whether each object has 180 degree rotational symmetry
Answer:
5, yes.
Step-by-step explanation :
Please answer this correctly
Answer:
Step-by-step explanation:
Area = area of rectangle 1 + area of rectangle 2 + area of rectangle 3 +area of triangle
= 8*12 + 12*9 + 19 *5 + (1/2) * 4 *12
= 96 + 108 + 95 + 24
= 323 sq. cm
The office needs 8 new devices worth $8000. The order consists of new computers (C ) which cost $925 each and printers (P) which cost $1125 each. How many of the new devices are computers and how many are printers?
Answer:
The number of computer is 5 and printer is 3
jack is investing 5000 in an account that earns 4% interest compounded annually. Determine to the nearest month when the investment will be worth 8000
Answer:
The nearest time is 15 years or 180 months
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
C. F(x) = 4x² + 1
Step-by-step explanation:
→The function F(x) shifted 1 unit upwards, meaning there needs to be a 1 being added to the function.
→In addition, the function F(x) has grown narrower, compared to the function G(x). This is from the absolute value of a number being greater than 1, which is being multiplied.
This means the correct answer should be "C. F(x) = 4x² + 1."
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Base area = 9 × 13
= 117 square feet
Now
Volume of pyramid = (1/3)(A)(H)
= (1/3)(117)(30)
= 117 × 10
= 1170 cubic feet
Plz help me ASAP it’s important
Answer:
D. 6.3
Step-by-step explanation:
Well you can make a triangle with the line PQ with it's height as 2 and base as 6.
Then you can use the Pythagorean Theorem to find the length of PQ.
a²+b²=c²
2²+6²=c²
4+36=c²
40=c²
c²=40
Square root both sides
c=[tex]\sqrt{40}[/tex]
c≈6.3
Our answer is D. 6.3
Find the general solution to y′′+6y′+13y=0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.
Answer:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Step-by-step explanation:
In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.
For a second order differential equation of type:
[tex]ay''+by'+cy=0[/tex]
Has characteristic equation:
[tex]a r^{2} +br+c=0[/tex]
Whose solutions [tex]r_1 , r_2 ,.., r_n[/tex] are the roots from which the general solution can be formed. There are three cases:
Real roots:
[tex]y(x)=c_1e^{r_1 x} +c_2e^{r_2 x}[/tex]
Repeated roots:
[tex]y(x)=c_1e^{r x} +c_1 xe^{r x}[/tex]
Complex roots:
[tex]y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i[/tex]
Therefore:
The characteristic equation for:
[tex]y''+6y'+13y=0[/tex]
Is:
[tex]r^{2} +6r+13=0[/tex]
Solving for [tex]r[/tex] :
[tex]r_1_,_2= -3 \pm 2i[/tex]
So:
[tex]\mu = 2\\\\and\\\\\lambda=-3[/tex]
Hence, the general solution of the differential equation will be given by:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
A random sample of 100 observations from a population with standard deviation 6868 yielded a sample mean of 113113. Complete parts a through c below. a. Test the null hypothesis that muμequals=100 against the alternative hypothesis that muμgreater than>100, using alphaαequals=0.05. Interpret the results of the test. What is the value of the test statistic?
Answer:
Null hypothesis is rejected,
test statistic= 15.76
Step-by-step explanation:
sample mean= 113,
sample standard deviation= 68
H0: mean of sample =100
Ha: mean of sample > 100
test statistic= (population mean- sample mean)/√(standard deviation/sample size)
test statistic= (113-100)/√(68/100)= 15.76
Degrees of freeedom= 100-1=99
p-value= 1.658 (from t distribution table for DF=99 and alpha=0.05)
Since p-value is smaller than test statistic, null hypothesis is rejected
Please answer this correctly
Answer:
d = 2
Step-by-step explanation:
Using the formula
A=pq/2
Dont forget to click THANKS
Charlotte is creating a triangular pennant with geometry software.
The base measure of the pennant on screen is 550 pixels. The height
is 275 pixels. Charlotte resizes the pennant, keeping the aspect ratio
constant, so the height is 165 pixels. What is the scale factor of the
dilation? What is the base of the pennant?
~~~~~~~~~~~~~~
pls help T-T
Answer:
Base of the Pennant = 330 pixels
Scale Factor =0.6
Step-by-step explanation:
The base measure of the pennant on screen is 550 pixels.
The height is 275 pixels.
[tex]A$spect Ratio=\dfrac{Base}{Height}=\dfrac{550}{275} =2:1[/tex]
If Charlotte resizes the pennant, keeping the aspect ratio constant.
Height = 165 pixels
Therefore:
[tex]\dfrac{Base}{165}=\dfrac{2}{1} \\\\$Base= 2 *165 =330[/tex]
Therefore, the scale factor of the dilation [tex]=\dfrac{330}{550}= \dfrac{165}{275}=0.6[/tex]
Base of the Pennant = 330 pixels
Scale Factor =0.6
True or false: as the value of cosx decreases towards 0, the value of secx increases towards infinity
Answer:
True
Step-by-step explanation:
True or False? A prism must have a triangular or rectangular base.
Answer: No
Step-by-step explanation:
Simple! No. There can be hexagonal, octagonal, and other types of prisms that do not have a triangular/rectangular base.
Hope that helped,
-sirswagger21
The method of Problem 20 can be extended to second order equations with variable coefficients. If y1 is a known nonvanishing solution of y′′ + p(t)y′ + q(t)y = 0, show that a second solution y2 satisfies (y2 /y1 )′ = W (y1 , y2 )/y21 , where W (y1 , y2 ) is the Wronskian of y1 and y2 . Then use Abel’s formula [Eq. (23) of Section 3.2] to determine y2 .
Answer:24y
Step-by-step explanation:
Which of the following are true? If false, explain briefly.a) A P-value of 0.01 means that the null hypothesis is false.b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.c) A P-value of 0.01 is evidence against the null hypothesis.d) A P-value of 0.01 means we should definitely reject the null hypothesis
Answer:
a) false
b) true
c) false
d) false
Step-by-step explanation:
a) p-value is compared with test statistic to either accept or ereject the null hypothesis. There is no fixed p-value to reject the null hypothesis
b) p-value tells us the probabiltiy of finding null hypothesis to be true
c) There is no fixed p-value for nullyfying the the null hypothesis
d) There is no fixed p-value to reject the null hypothesis
X and Y together complete a task in 4 days, Y and Z together in 5 days. If they work independently, who will finish the work in the least time? A. X B. Y C. Z D. Not enough information to decide
Answer:
c, Z
Step-by-step explanation:
x+y=4
y+z=5
y=4-x
4-x+z=5
-x+z=1
z=1+x
