Answer:
35%
Step-by-step explanation:
[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]
[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]
Answer:
35%
Step-by-step explanation:
I REALLY HOPE I HELPED
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
Translate and solve: 82 less than a is at least -82
Answer:
a≥0
Step-by-step explanation:
a-82≥-82
a≥-82+82
a≥0
I am performing a before and after evaluation on 30 students who have taken a keyboarding class. I want to see if the course improved their words per minute keyed.
Required:
a. State the Null and Alternate Hypothesis.
b. The statistic that I would use is:_________
c. What would my t critical be for this calculation at a 0.10 level of significance?
d. If my t calculated = 1.62, would I reject or fail to reject the null hypothesis?
Answer:
a)
H₀ : µd = 0
H₁ : µd < 0
b)
The test statistic is
tₙ₋₁ = α / s√n
c)
at 0.10 level of significance,
tₙ₋₁ , ₐ
t₃₀₋₁ , ₀.₁₀ = t₂₉, ₀.₁₀ = 1.311
d)
given that T(critical) = 1.62
∴ T(critical) = 1.62 > t₂₉, ₀.₁₀ = 1.311
at 10% level of significance,
REJECT H₀
Since 1.62 > 1.311, we can reject the null hypothesis.
Solve Logarithm 5(2^x+4)=15. Round to the nearest thousandth. A.1.089 B.2.415 C.0.657 D.3.982
[tex]5(2^x+4)=15\\2^x+4=3\\2^x=-1\\x\in\emptyset[/tex]
Answer:
no solutions
Step-by-step explanation:
5(2^x+4)=15
Divide each side by 5
5/5(2^x+4)=15/5
(2^x+4)=3
Subtract 4 from each side
2^x = 3-4
2^x = -1
This cannot happen so there are no solutions
1. Why is money better than a bartering system?
A People might not have items to trade.
B It helps people to agree on the value of something.
C People might lose track of their money.
D Both A and B
E Both B and C
The correct answer is D. Both A and B
Explanation:
Bartering is an economic system in which products are directly exchanged for other products. For example, a pound of oranges is exchanged for a pound of rice. Due to this, in bartering, there is no money or elements such as coins or bills that represent the value of products or services. This system has both advantages and disadvantages in comparison to the use of money.
In terms of disadvantages, bartering implies individuals need products or services they can use to exchange, which might not be possible for all individuals as not all individuals might produce a product or have a product other are interested in. Also, in bartering the value of products varies, for example, a pound of blueberries can be equal to a pound of rice, three pounds of rice, or even half pound of rice, as values change according to the situation of those participating in the exchange. This means, in bartering the value fluctuates and it is more difficult to agree on the value of something, which does not occur if money is used as each product has a defined price which might just vary slightly. According to this, options A and B are advantages of money over bartering.
Determine the Perimeter of the shape #1.
Answer:
56.8
Step-by-step explanation:
7.1*8=56.8
Determine the area of the shape above. The formula for the area of a polygon is: Area = 1/2 (a n s) *
Step-by-step explanation:
Area of a regular polygon is half the apothem times the perimeter, or A = ½ a n s, where a is the apothem, n is the number of sides, and s is the side length.
A = ½ (8.5705 in) (8) (7.1 in)
A = 243.4022 in²
This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!
Answer:
A Maybe
Step-by-step explanation:
Cogntive identification
Unable to answer mathematically or analytically
The Plan of the solid shape is shown by : (A)
What is the Meaning of solid shape?A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.
A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.
solid shapes can take up space in the universe because they are more tangible and realistic.
In conclusion, the Plan of the solid shape is shown by : (A)
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An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 421 422 425 428 431 435 437
438 445 447 448 453 458 462 465
(c) Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.) Note that it is plausible that the given sample observations were selected from a normal distribution and there are no outliers.
(___ , ___)
Does the interval suggest that 441 is a plausible value for true average degree of polymerization?
Yes or No
Does the interval suggest that 451 is a plausible value?
Yes or No
Answer:
Step-by-step explanation:
Form a set of values we get
n = 17
And with the help of a calculator
μ₀ = 438,47
σ = 14,79
Normal Distribution is : N ( 438,47 ; 14,79 )
c)
CI = 95 % means α = 5 % α/2 = 2,5 % α/2 = 0,025
and as n < 30 we should use t-student distribution with n -1 degree of freedom df = 16. t score for 0,025 and 16 s from t-table 2,120
By definition:
CI = [ μ₀ ± t α/2 ; n-1 * σ/√n ]
CI = [ μ₀ ± 2,120* 14,79/√17 ]
CI = [ μ₀ ± 7,60 ]
CI = [ 438,47 ± 7,60 ]
CI = [ 430,87 ; 446,07 ]
95% confidence interval for true average degree of polymerization is [430.87 ; 446.07] and this interval suggest that 441 is a plausible value for true average degree of polymerization and also this interval does not suggest that 451 is a plausible value.
Given :
Sample = [ 418, 421, 421, 422, 425, 428, 431, 435, 437, 438, 445, 447, 448, 453, 458, 462, 465 ]95% confidence interval.The total number of values given is, n = 17
Mean, [tex]\mu_0=438.47[/tex]
Standard Deviation, [tex]\sigma = 14.79[/tex]
The normal distribution is given by: N (438.47 ; 14.79)
If Cl is 95% then [tex]\alpha[/tex] is 5% and [tex]\alpha /2[/tex] is 2.5%
[tex]\alpha /2 = 0.025[/tex]
Now, use t-statistics distribution with (n-1) degree of freedom df = 16
So, the t score for 0.025 and 16 s from t-table 2.120.
[tex]\rm Cl = [\mu_0 \pm t_{\alpha /2};(n-1)\times \dfrac{\sigma}{\sqrt{n} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 2.120\times \dfrac{14.79}{\sqrt{17} }][/tex]
[tex]\rm Cl = [\mu_0 \pm 7.60][/tex]
Cl = [430.87 ; 446.07]
Yes, the interval suggests that 441 is a plausible value for true average degree of polymerization.
No, the interval does not suggest that 451 is a plausible value.
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I really need help here I am super confused
Which of the following steps can be performed so that the square root property may easily be applied to 2x^2=16?(1 point)
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is 16, so divide both sides by 2 before applying the square root property.
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is 16, so divide both sides by 16 before applying the square root property.
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 16 before applying the square root property.
Which of the following steps would not be necessary when using the square root property to solve a quadratic equation?(1 point)
The square root property may be applied only if the constant is positive.
Isolate the quantity being squared.
After applying the square root property, solve the resulting equations. When taking the square root of both sides, use ± on the square root of the constant.
Answer:
The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.
Step-by-step explanation:
In the above question, we are given the expression: 2x^2=16 and we are asked the proper way to apply the square root property.
2x² = 16 is an algebraic equation
To apply square root property to an expression, there must be only one quantity that is squared.
Step 1
We divide both sides by 2
This is because we have to first eliminate the coefficient of x
2x²/2 = 16/2
x² = 8
Step 2
Now that we have eliminated the coefficient of x², we can apply the square root property now because x is the only quantity that is squared.
√x² = √8
x = √8
Therefore, Option 2 which says: "The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property." is the correct option
I need help please help me!
Answer:
36ft³
Step-by-step explanation:
Bottom rectangular prism: 2x2x6=24
Top rectangular prism: 2x2x3=12
24+12=36ft³
Answer:
[tex]\boxed{36ft^3}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for V we need to find the volume of the 2 rectangular prism's given.
Rec#1: 2•3•2 = 12
Rec#2: 6•2•2 = 24
Rec#1 + Rec#2 = V
12 + 24 = 36ft³
Hope this helps :)
A jar contains 8 pennies, 5 nickels and 7 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Be very precise with your answers.
a. Find the probability x = 2 cents.
b. Find the probability x = 6 cents.
c. Find the probability x = 10 cents.
d. Find the probability x = 11 cents.
e. Find the probability x = 15 cents.
f. Find the probability x = 20 cents.
g. Find the expected value of x.
Answer:
a. The probability x = 2 cents = 7/22
b. The probability x = 6 cents = 35/66
c. The probability x = 10 cents = 5/33
d. The probability x = 11 cents= 28/33
e. The probability x = 15 cents = 20/33
f. The probability x = 20 cents = 14/33
g. The expected value of x = 5.9
Step-by-step explanation:
This is a binomial probability distribution. The number of trials is known .
a. The probability x = 2 cents.
Probability ( X=2) P( selecting 2 dimes)= 7C2 / 12c2
= 21 / 66 = 7/22
b. The probability x = 6 cents.
Probability ( X=6) P( selecting a nickel and a dime)= 5C1 * 7C1/ 12c2
= 5*7 / 66 = 35/66
c. The probability x = 10 cents.
Probability ( X=10) P( selecting two nickels )= 5C2 / 12c2)
= 10/ 66 = 5/33
d. The probability x = 11 cents.
Probability ( X=11) P( selecting a penny and a dime)= 8C1 * 7C1/ 12c2)
= 8*7 / 66 = 56/66= 28/33
e. The probability x = 15 cents.
Probability ( X=15) P( selecting a penny and a nickel)= 8C1 * 5C1/ 12c2)
= 8*5 / 66 = 40/66= 20/33
f. The probability x = 20 cents.
Probability ( X=20) P( selecting 2 pennies )= 8C2 / 12c2)
= 28 / 66 = 14/33
g. The expected value of x.
E(X) = np
E(X) = 2 * (8C2+ 5C2+ 7C2)/(8+5+7) = 2( 28+10+21)/20
=2(59)/20= 5.9
A 95% confidence interval for the mean number of television per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, choose true or false.
a. The probability that u is between 1.15 and 4.20 is .95.
b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.
c. 95% of all samples should have x-bars between 1.15 and 4.20 televisions.
d. 95% of all American households have between 1.15 and 4.20 televisions
e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.
f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean.
Answer:
a. False
b. True
c. False
d. False
e.True
f. True
Step-by-step explanation:
The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.
I need help with the following question
Answer:
a. 2
b. x²+10x+26
c. x²+2x+2
Step-by-step explanation:
To find each value, you plug in the x value into the function and solve.
a. 2
f(2)=(2)²-2(2)+2 [combine like terms]
f(2)=4-4+2
f(2)=2
---------------------------------------------------------------------------------------------------------
b. x²+10x+26
f(x+6)=(x+6)²-2(x+6)+2 [use FOIL method and distributive property]
f(x+6)=x²+12x+36-2x-12+2 [combine like terms]
f(x+6)=x²+10x+26
---------------------------------------------------------------------------------------------------------
c. x²+2x+2
f(-x)=(-x)²-2(-x)+2 [combine like terms]
f(-x)=x²+2x+2
How much will $1000 deposited in an account earning 7% interest compounded annually be worth in 20 years? (which formula do I use? I am confused...txs)
Answer:
$3870
Step-by-step explanation:
Hello, the initial deposit is $1000.
After one year, we will get 1000 + 7%*1000= 1000 * ( 1+7%) = 1000 * (1+0.07)
= 1000 * 1.07
And we want to compound it so the second year we will get
[tex]1000 * 1.07 * 1.07 = 1000 * 1.07^2[/tex]
And after n years, we will get
[tex]1000 * 1.07^n[/tex]
In that example, we want to know how much we will get after 20 years, so this is:
[tex]1000 * 1.07^{20}=3869.684462...[/tex]
Thank you.
When interest is compounded, it means that both the interest and the amount deposited will earn interest.
We are to determine the future value of $1000 with annual compounding.
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = amount deposited = $1000
R = interest rate = 7%
N = number of years = 20
$1000 x ( 1.07)^20 = $3,869.68
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The graph of g(x) = x – 8 is a transformation of the graph of f(x) = x. Which of
the following describes the transformation?
(A) translation 8 units down
(B) translation 8 units up
(C) translation 8 units right
(D) translation 8 units left
Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
He expected to have 15 customers each day. To answer whether the number of customers follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10)
What is the chi-squared test statistic? Answers are rounded to the nearest hundredth.
Answer:
The chi - square test can be [tex]\approx[/tex] 0.667
Step-by-step explanation:
From the given data :
The null hypothesis and the alternative hypothesis can be computed as:
Null hypothesis: The number of customers does follow a uniform distribution
Alternative hypothesis: The number of customers does not follow a uniform distribution
We learnt that: Carl recorded the number of customers who visited his new store during the week:
Day Customers
Monday 17
Tuesday 13
Wednesday 14
Thursday 16
The above given data was the observed value.
However, the question progress by stating that : He expected to have 15 customers each day.
Now; we can have an expected value for each customer as:
Observed Value Expected Value
Day Customers
Monday 17 15
Tuesday 13 15
Wednesday 14 15
Thursday 16 15
The Chi square corresponding to each data can be determined by using the formula:
[tex]Chi -square = \dfrac{(observed \ value - expected \ value )^2}{expected \ value}[/tex]
For Monday:
[tex]Chi -square = \dfrac{(17 - 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Tuesday :
[tex]Chi -square = \dfrac{(13- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-2)^2}{15}[/tex]
[tex]Chi - square = \dfrac{4}{15}[/tex]
chi - square = 0.2666666667
For Wednesday :
[tex]Chi -square = \dfrac{(14- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(-1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
For Thursday:
[tex]Chi -square = \dfrac{(16- 15 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )^2}{15}[/tex]
[tex]Chi -square = \dfrac{(1 )}{15}[/tex]
chi - square = 0.06666666667
Observed Value Expected Value chi - square
Day Customers
Monday 17 15 0.2666666667
Tuesday 13 15 0.2666666667
Wednesday 14 15 0.06666666667
Thursday 16 15 0.06666666667
Total : 0.6666666668
The chi - square test can be [tex]\approx[/tex] 0.667
At level of significance ∝ = 0.10
degree of freedom = n - 1
degree of freedom = 4 - 1
degree of freedom = 3
At ∝ = 0.10 and df = 3
The p - value for the chi - square test statistics is 0.880937
Decision rule: If the p - value is greater than the level of significance , we fail to reject the null hypothesis
Conclusion: Since the p - value is greater than the level of significance , we fail to reject the null hypothesis and conclude that there is insufficient evidence to show that the number of customers does not follows a uniform distribution.
Answer:.67
Step-by-step explanation:
What is the mulitplicative rate of change for the exponential function f(x) = 2 (5over2) to the negative x power ?
Answer:
2/5
Step-by-step explanation:
f(x) = 2(5/2)^-x = 2(2/5)^x
The multiplicative rate of change is the base of the positive exponent, 2/5.
STUCK Basic geometry A for senior year school
Answer:
(C) A reflection across a horizontal line and a horizontal translation
Step-by-step explanation:
We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.
Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.
Hope this helped!
10-
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
8-
(2,6)
-6
O x = 2
4
O x = 6
-2
-10 -3 -6 -22
2
4
B
8
10
X
O y = 2
O y = 6
(-34)
(814)
8
WO
Answer:
x = 2
Step-by-step explanation:
This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.
The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given is a line that passes through the points (-8, -4) and (8, -4).
This line is parallel to the X axis.
A line parallel to X axis has the equation y = b.
The y coordinate is -4 throughout the line.
So equation of the line is y = -4.
A line perpendicular to the given line will be parallel to Y axis.
Parallel lines to Y axis has the equation of the form x = a.
Line passes through the point (2, 6).
x coordinate will be 2 throughout.
So the equation of the perpendicular line is x = 2.
Hence the required equation is x = 2.
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In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
In terms of the trigonometric ratios for ΔABD, what is the length of line segment BD?
Answer:
[tex] BD = c*sin(A) [/tex]
[tex] BD = c*cos(B) [/tex]
[tex] BD = b*tan(A) [/tex]
Step-by-step explanation:
∆ABD is a right triangle.
Recall: trigonometric ratios of any right triangle can easily be understood or remembered with the acronym, SOHCAHTOA.
SOH => sin(θ) = opposite/hypotenuse
CAH => Cos(θ) = adjacent/hypotenuse
TOA = tan(θ) = opposite/adjacent
Thus, the length of segment BD, in terms of trigonometric ratios for ∆ABD can be done as follows:
Let BD = x
AB = c
AD = b
=>The sine ratio for the length of line segment BD = x, using SOH.
θ = A
Opposite = DB = x
hypotenuse = AB = c
[tex] sin(A) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*sin(A) = x [/tex]
[tex] BD = x = c*sin(A) [/tex]
=>The Cosine ratio for the length of line segment BD = x, using CAH
θ = B
Adjacent = DB = x
hypotenuse = AB = c
[tex] cos(B) = \frac{x}{c} [/tex]
Make x the subject of formula.
[tex] c*cos(B) = x [/tex]
[tex] BD = x = c*cos(B) [/tex]
=>The Tangent ratio for the length of line segment BD = x, using TOA
θ = A
Adjacent = DB = x
hypotenuse = AD = b
[tex] tan(A) = \frac{x}{b} [/tex]
Make x the subject of formula.
[tex] b*tan(A) = x [/tex]
[tex] BD = x = b*tan(A) [/tex]
This??? What is wrong with it?
Answer:
15.8 sq. in. of paper will be required.
Step-by-step explanation:
The problem is that a drinking cup does not have a cover, so only the lateral surface area counts.
I.e. We need only the first term.
A = pi r l = pi * 1.5 * sqrt(3^2+1.5^2)
= 15.81 sq. in.
Another trader would like to carry out a hypothesis test about stocks that offer dividends. Why is this hypothesis test right-tailed? Select the correct answer below: This is a right-tailed test because a direction is not specified. This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value. This is a right-tailed test because a direction is specified. The population parameter is less than the specified value. More information is needed.
Answer:
This is a right-tailed test because a direction is specified. The population parameter is greater than the specified value.
Step-by-step explanation:
The hypothesis testing technique is used to test an assumption regarding population parameter. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. A right tailed test is where the most of data is in the right side. This is one tailed test where the direction is specified.
Someone please help me ASAP
Answer:
x > -7/3
Step-by-step explanation:
-3x+8 < 15
Subtract 8 from each side
-3x+8-8 < 15-8
-3x < 7
Divide by 3 remembering to flip the inequality
-3x/-3 > 7/-3
x > -7/3
Answer:
[tex]x <-\frac{7}{3}[/tex]
Draw the function
[tex]y = \tan(x) [/tex]
on the interval [-pi, pi]
Answer:
The answer is in the photo below. The interval is (-pi, pi) and the function is y = tanx.
Find a • b. a = 5i + 7j, b = -4i + 3j 1 41
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
Find the maximum and minimum values of the function f(x,y)=2x2+3y2−4x−5 on the domain x2+y2≤100. The maximum value of f(x,y) is:
First find the critical points of f :
[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]
[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]
[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]
so the point (1, 0) is the only critical point, at which we have
[tex]f(1,0)=-7[/tex]
Next check for critical points along the boundary, which can be found by converting to polar coordinates:
[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]
Find the critical points of g :
[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]
[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]
[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]
where n is any integer. We get 4 critical points in the interval [0, 2π) at
[tex]t=0\implies f(10,0)=155[/tex]
[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]
[tex]t=\pi\implies f(-10,0)=235[/tex]
[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]
So f has a minimum of -7 and a maximum of 299.
Max believes that the sales of coffee at his coffee shop depend upon the weather. He has taken a sample of 5 days. Below you are given the results of the sample.
Cups of Coffee Sold Temperature
350 50
200 60
210 70
100 80
60 90
40 100
A. Which variable is the dependent variable?
B. Compute the least squares estimated line.
C. Compute the correlation coefficient between temperature and the sales of coffee.
D. Predict sales of a 90 degree day.
Answer:
1. cups of coffee sold
2.Y = 605.7 - 5.943x
3. -0.952
4. 70.84
Step-by-step explanation:
1. the dependent variable in this question is the cups of coffee sold
2. least square estimation line
Y = a+bx
we have y as the cups of coffee sold
x as temperature.
first we will have to solve for a and then b
∑X = 450
∑Y = 960
∑XY = 61600
∑X² = 35500
∑Y² = 221800
a = ∑y∑x²-∑x∑xy/n∑x²-(∑x)²
a = 960 * 35500-450*61600/6*35500-450²
a = 6360000/10500
= 605.7
b = n∑xy - ∑x∑y/n∑x²-(∑x)²
= 6*61600 - 450*960/6*35500 - 450²
= -5.943
the regression line
Y = a + bx
Y = 605.7 - 5.943x
3. we are to find correlation coefficient
r = n∑xy - ∑x∑y multiplied by√(n∑x²-(∑x)² * (n∑y² - (∑y)²)
= 6*61600 -960*450/√(6*35500 - 450²)*(6*221800 - 960²)
=-62400/√4296600000
= -62400/65548.5
= -0.952
4. we have to predict sales of a 90 degree day fro the regression line
Y = 605.7 - 5.943x
y = 605.7 - 5.943(90)
y = 605.7 - 534.87
= 70.84
What is the midline equation of the function h(x) = -4 cos(5x - 9) - 7?
Answer: Midline equation: y = -7
Step-by-step explanation: This function is a sinusoidal function of the form:
y = a.cos(b(x+c))+d
Midline is a horizontal line where the function oscillates above and below.
In the sinusoidal function d represents its vertical shift. Midline is not influenced by any other value except vertical shift. For that reason,
Midline, for the function: [tex]h(x) = -4cos(5x-9) - 7[/tex] is y=d, i.e., [tex]y=-7[/tex]
Answer:
y=-7
Step-by-step explanation:
Mr. Vazquez determines that the area of a bathroom in his house is 25 square feet less than 1/5 of the area of the living room. If the bathroom measures 35 square feet, what is the area of the living room?\
Answer:
300 SF
Step-by-step explanation:
just took the test
