To find the derivative of the function h(p) = -5/(p^2+1), we will use the quotient rule:
h'(p) = [(-5)'(p^2+1) - (-5)(p^2+1)'] / (p^2+1)^2
Simplifying this expression, we get:
h'(p) = (10p) / (p^2+1)^2
To find the values of p such that h'(p) = 0, we will set the numerator equal to 0 and solve for p:
10p = 0
p = 0
Therefore, h'(p) = 0 when p = 0.
To find the values of p in the domain of h such that h'(p) does not exist, we need to find the values of p where the denominator of h'(p) becomes 0:
p^2+1 = 0
This equation has no real solutions, so there are no values of p in the domain of h such that h'(p) does not exist. Therefore, we enter DE (does not exist).
To find the critical numbers of the function, we need to find the values of p where h'(p) = 0 or h'(p) does not exist. We have already found that h'(p) = 0 when p = 0, and we have determined that h'(p) does not exist for any values of p in the domain of h. Therefore, the only critical number of the function is p = 0.
Let's first find the derivative of the given function, h(p) = (p - 5)/(p^2 + 1).
Using the quotient rule, h'(p) = [(p^2 + 1)(1) - (p - 5)(2p)]/((p^2 + 1)^2).
Simplifying, h'(p) = (p^2 + 1 - 2p^2 + 10p)/((p^2 + 1)^2) = (-p^2 + 10p + 1)/((p^2 + 1)^2).
To find the values of p such that h'(p) = 0, set the numerator of h'(p) equal to zero:
-p^2 + 10p + 1 = 0.
This is a quadratic equation, but it does not have any real solutions. Therefore, there are no values of p for which h'(p) = 0, so the answer is DNE.
To find the values of p where h'(p) does not exist, we look for where the denominator is zero:
(p^2 + 1)^2 = 0.
However, this equation has no real solutions, as (p^2 + 1) is always positive. Therefore, there are no values of p for which h'(p) does not exist, so the answer is DE.
Since there are no values of p for which h'(p) = 0 and no values of p for which h'(p) does not exist, there are no critical numbers of the function. The answer is DNE.
Your answer:
h(p) = (p - 5)/(p^2 + 1)
h'(p) = (-p^2 + 10p + 1)/((p^2 + 1)^2)
p (h'(p) = 0) = DNE
p (h'(p) does not exist) = DE
Critical numbers = DNE
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The value of a sculpture depreciates by 20% each year. Today it is worth £650. How much was it worth 3 years ago? Give your newer to the nearest penny.
The sculpture was worth £332.80 three years ago when it depreciates by 20% each year
To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.
First, we need to calculate how much the sculpture would be worth after one year of depreciation:
650 - (0.20)(650) = 520
This means that after the first year, the sculpture would be worth £520.
Next, we can calculate the value of the sculpture after the second year of depreciation:
520 - (0.20)(520) = 416
After two years, the sculpture would be worth £416.
Finally, we can calculate the value of the sculpture after the third year of depreciation:
416 - (0.20)(416) = 332.8
Therefore, the sculpture was worth £332.80 three years ago.
To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:
650 = x[tex](1-0.20)^{2}[/tex]
Simplifying this equation, we get:
x = 650 / [tex]0.80^{2}[/tex] = 332.80
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A poll used a sample of randomly selected car owners. Within the sample, the mean time of ownership for a single car was years with a standard deviation of years. Test the claim by the owner of a large dealership that the mean time of ownership for all cars is less than years. Use a 0. 05 significance level
If t is less than -1.699, we reject the null hypothesis.
To test the claim by the owner of the large dealership, we will use a one-sample t-test with the following hypotheses:
Null Hypothesis: H0: µ >= µ0 (The population mean time of ownership is greater than or equal to µ0)
Alternative Hypothesis: Ha: µ < µ0 (The population mean time of ownership is less than µ0)
where µ is the population mean time of ownership, µ0 is the claimed mean time of ownership by the owner of the dealership.
The significance level is α = 0.05.
We can calculate the t-value as:
t = ([tex]\bar{x}[/tex] - µ0) / (s / √n)
where [tex]\bar{x}[/tex] is the sample mean time of ownership, s is the sample standard deviation, n is the sample size.
Plugging in the values given in the problem, we get:
t = ([tex]\bar{x}[/tex] - µ0) / (s / √n) = (5.7 - µ0) / (1.8 / √n)
Since the alternative hypothesis is one-tailed (less than), we need to find the critical t-value from the t-distribution table with n-1 degrees of freedom and a significance level of 0.05. For a sample size of n = 30 (assuming it is large enough), the critical t-value is -1.699.
If the calculated t-value is less than the critical t-value, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
If the calculated t-value is greater than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the mean time of ownership for all cars is less than the claimed mean time of ownership by the owner of the dealership.
So, if we assume that the sample is representative of the population and meets the assumptions of the t-test, we can calculate the t-value as:
t = (5.7 - µ0) / (1.8 / √30)
If t is less than -1.699, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Note that we don't have any information about the claimed mean time of ownership by the owner of the dealership, so we cannot calculate the t-value or make any conclusions.
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Consider the following 8 numbers, where one labelled
x
is unknown. 32
,
46
,
46
,
x
,
35
,
9
,
4
,
38
Given that the range of the numbers is 55, work out 2 values of
x
Two possible values of x are 10 and 40.
To find two possible values of x, we need to first determine the highest and lowest numbers in the set.
Highest number: 46
Lowest number: 4
To get a range of 55, we need the highest number minus the lowest number to equal 55.
46 - 4 = 42
But we know that there are 8 numbers in the set, so the range must be spread out over those 8 numbers. To get an idea of how much each number should increase, we can divide 42 by 7 (the number of gaps between the numbers) to get an average increase of 6.
Now we can use this average increase to find two possible values of x.
1) If x is 6 more than the lowest number (4 + 6 = 10), then the set becomes:
4, 9, 10, 32, 35, 38, 46, 46
And the range is:
46 - 4 = 42
2) If x is 6 less than the highest number (46 - 6 = 40), then the set becomes:
4, 9, 35, 38, 40, 46, 46, 32
And the range is:
46 - 4 = 42
Therefore, two possible values of x are 10 and 40.
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solve for the value of x .
80(x+15)
=60
Answer:
x = [tex]\frac{-57}{4}[/tex]
Step-by-step explanation:
solve for the value of x .
80(x+15)=60
80(x + 15) = 60
80x + 1200 - 60 = 0
80x + 1140 = 0
80x = -1140
x = -1140/80
x = [tex]\frac{-57}{4}[/tex]
Answer:
-14.25
Step-by-step explanation:
Given: 80 (x+15) = 60
Solution: On opening the brackets, we get
> 80x + 80 * 15 = 60
> 80x + 1200 = 60
Then, taking 1200 to the other side of the equation,
80x = 60 - 1200
Therefore, 80x = -1140
Now, dividing both sides by 80, we get:
80x/80 = -1140/80
So, x= -14.25
Hope this helps!
Untitled Question
14 points
2 Chelsea sprinted 120 yards in 18. 5
seconds. One meter is approximately equal
to 1. 1 yards. Which measurement is closest
to the number of meters Chelsea sprinted?
F 109. 1 yd H 64. 9 yd
G 132 yd J 90. 6 yd
7. 4E
G
The measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
To determine the number of meters Chelsea sprinted, we need to convert the distance she sprinted from yards to meters.
Given:
Chelsea sprinted 120 yards.
Conversion:
1 meter is approximately equal to 1.1 yards.
To convert yards to meters, we divide the distance in yards by the conversion factor:
120 yards / 1.1 yards/meter ≈ 109.1 meters.
Therefore, the measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.
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Pythagorean theorem
1. a surveyor walked eight miles north, then three miles west. how far was she from her starting point?
2. a four meter ladder is one meter from the base of a building. how high up the building will the ladder reach?
3. what is the longest line you can draw on a paper that is 15 cm by 25 cm?
4. how long a guy wire is needed to support a 10 meter tall tower if it is faster
the foot of the tower?
5. the hypotenuse of a right triangle is twice as long as one of its legs.the other leg is nine inches long. find the length of the hypotenuse.
The distance traveled by the surveyor is √73 miles. The height of the building that the ladder reaches is √15 meters. The longest line that can be drawn is 5√34 cm. The length of the guy wire that is needed is 5√5 meters. The length of the hypotenuse of the given right triangle is 6√3 inches.
In a right-angled triangle that is a triangle with one of the angles with magnitude 90° following is true according to Pythogaras' Theorem:
[tex]A^2=B^2+C^2[/tex]
where A is the hypotenuse
B is the base
C is the height
1. According to the question,
the distance between the starting and the ending point is the hypotenuse of a right-angled triangle
B = 8 miles
C = 3 miles
A = √(64 + 9)
= √73 miles
2. Hypotenuse in the given question is the length of the ladder, thus,
A = 4 m
B = 1 m
16 = 1 + [tex]C^2[/tex]
C = √15 meters
3. The longest line that can be drawn on the paper is described as the hypotenuse of the triangle
C = √225 + 625
= 5√34 cm
4. The length of the guy wire is the hypotenuse of the triangle.
C = √100 + 25
= 5√5 meters
5. Let the base of the triangle be x
the hypotenuse be 2x
height = 9 inches
[tex]4x^2=x^2[/tex] + 81
[tex]3x^2[/tex] = 81
x = 3√3 inches
Hypotenuse = 2x = 6√3 inches
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Find x.
Round to the nearest tenth:
12 cm
22 cm
42°
x = [? ]°
Law of Sines: sin A
sin B
sin C
а
vt6
b
Enter
The value of x is approximately 61.7 degrees using the Law of Sines.
To find the value of x, we can use the Law of
Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. Mathematically, we can write:
a/sin A = b/sin B = c/sin C
where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.
Using the given information, we can set up the
equation as follows:
12/sin 42° = 22/sin x
Multiplying both sides by sin x°, we get:
sin x = (22/12) x sin 42°
sin x = 1.6977
Taking the inverse sine of both sides, we get:
x* = sin" (1.6977)
x = 61.7°
Rounding to the nearest tenth, we get:
x = 61.7°
Therefore, the value of x is approximately 61.7
degrees.
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The complete question is:
In the given figure , find the X (round to the nearest tenth) , where the sides are marked as 12cm and 22 cm with the angle of 42°.
QUESTION 5/10
24-136
If Chris has car liability insurance, what damage would he be covered for?
HATA
EAN
A. Repairing damage to his own car that was caused by storms
or theft.
C. Repairing damage to his own car that was caused by
another driver who does not have car insurance.
B. Repairing damage to other cars if he got into an accident
that was his fault.
D. Repairing damage to his own car if he got into an accident
that was his fault
Answer:
Step-by-step explanation:
At the start of an experiment there are 50 bacteria in a dish. The bacteria is expected to grow at a rate of 220% each day. What is the best prediction for the bacteria population after 8 days?
The best prediction for the bacteria population after 8 days is approximately 14,301.67 bacteria.
At start experiment are 50 bacteria in dish. The bacteria expected to grow a rate 220% each day. What is the prediction for the bacteria population after 8 days?
To find the predicted population of bacteria after 8 days, we need to apply the given growth rate of 220% per day to the initial population of 50 bacteria for each day, starting from day 1 and continuing to day 8.
For each day, the population of bacteria is expected to be 220% or 2.2 times the population of the previous day. So, we can use the formula:
P = P0 [tex]x (1 + r)^n[/tex]
where P is the predicted population after n days, P0 is the initial population, r is the growth rate per day (as a decimal), and n is the number of days.
Substituting the given values, we get:
P = 50[tex]x (1 + 2.2)^8[/tex]
P ≈ 14,301.67
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Harvey won some money on a
scratch-and-win ticket. Then, he won a
$2 bonus. When he arrived at the counter,
he noticed that he had also won a "triple
your winnings" ticket. As Harvey was
cashing in his prize, the cashier told him
he was the 100th customer, so his total
winnings were automatically doubled. Write two algebraic expressions to
describe Harvey’s winnings
First algebraic expression: x + 2. Second algebraic expression: 6x + 12.
We can represent Harvey's winnings using algebraic expressions.
Let's use the variable 'x' to represent the amount Harvey won on the scratch-and-win ticket. Harvey then won a $2 bonus, so we add 2 to 'x':
1) x + 2
Next, Harvey won a "triple your winnings" ticket, so we need to multiply the current winnings by 3:
2) 3(x + 2)
Finally, as the 100th customer, Harvey's total winnings were doubled:
3) 2 * 3(x + 2)
So, the two algebraic expressions to describe Harvey's winnings are:
1) x + 2 (initial winnings with the $2 bonus)
2) 2 * 3(x + 2) (total winnings after tripling and doubling)
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A triangle with area 28 square inches has a height that is six less than twice the width. Find the height and width of the triangle. [Hint: For a triangle with base b and height h , the area, A , is given by the formula
The height of the triangle is 8 inches and the width is 7 inches.
Find the height and width of a triangle with area 28 square inches, where the height is six less than twice the width.Let's start by using the formula for the area of a triangle:
A = (1/2)bh
where A is the area of the triangle, b is the base, and h is the height.
We are given that the area of the triangle is 28 square inches, so we can write:
28 = (1/2)bh
Next, we are given that the height h is six less than twice the width w. In other words:
h = 2w - 6
Now we can substitute this expression for h into the formula for the area:
28 = (1/2)bw(2w - 6)
Simplifying this equation, we get:
56 = bw(2w - 6)
28 = w(w - 3)
w^2 - 3w - 28 = 0
We can solve this quadratic equation using the quadratic formula:
w = [3 ± √ ([tex]3^2[/tex] - 4(1)(-28))] / 2
w = [3 ± √ (121)] / 2
w = (3 + 11) / 2 or w = (3 - 11) / 2
w = 7 or w = -4
Since a negative width doesn't make sense in this context, we can ignore the second solution and conclude that the width of the triangle is 7 inches.
Now we can use the expression for h in terms of w to find the height:
h = 2w - 6
h = 2(7) - 6
h = 8
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The marginal cost function for a company is given by C'(q) = q^2 - 17q + 70 dollars/unit;
where q is the quantity produced. If C(0) = 650, find the total cost of producing 20 units. What is the fixed cost and what is the total variable cost for this quantity? Fixed cost = Variable Cost of producing 20 units =
Total cost of producing 20 units =
The problem involves analyzing the cost of production for a company that produces a certain quantity of units. Specifically, we are given the marginal cost function C'(q) = q^2 - 17q + 70, where q is the quantity produced, and we need to find the total cost of producing 20 units, as well as the fixed cost and variable cost for this quantity. To find the total cost, we need to integrate the marginal cost function from 0 to 20, which will give us the total variable cost. We can then find the fixed cost by subtracting the total variable cost from the initial cost C(0), which is given in the problem. Cost analysis is an important concept in economics and business, and is used to optimize production and pricing decisions for companies. Understanding the relationship between marginal cost, fixed cost, and variable cost is crucial for making informed decisions about production and pricing strategies.
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The marginal cost function for a company is given by C'(q) = [tex]q^2[/tex] - 17q + 70 dollars/unit; where q is the quantity produced. If C(0) = 650, then total cost of producing 20 units = 2,600 dollars. Fixed cost for the quantity = 650 dollars. Variable Cost of producing 20 units = 1,950 dollars
To find the total cost function C(q), integrate the marginal cost function C'(q):
C(q) = ∫[tex](q^2 - 17q + 70)[/tex] dq = [tex](1/3)q^3 - (17/2)q^2 + 70q + K[/tex]
To find the constant K, use the given information: C(0) = 650
650 = [tex](1/3)(0)^3 - (17/2)(0)^2 + 70(0) + K[/tex]
K = 650
So the total cost function is:
C(q) = [tex](1/3)q^3 - (17/2)q^2 + 70q + 650[/tex]
Now, we find the total cost of producing 20 units:
C(20) = [tex](1/3)(20)^3 - (17/2)(20)^2 + 70(20) + 650[/tex]
C(20) = 2,600
Total cost of producing 20 units = 2,600 dollars.
Fixed cost is the cost incurred when producing 0 units, which is given as C(0) = 650 dollars.
To find the total variable cost for producing 20 units, subtract the fixed cost from the total cost:
Variable Cost = Total Cost - Fixed Cost
Variable Cost = 2,600 - 650
Variable Cost = 1,950 dollars
To summarize:
Fixed cost = 650 dollars
Variable cost of producing 20 units = 1,950 dollars
Total cost of producing 20 units = 2,600 dollars
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During a survey of 240 people who own cats, 188 people preferred cat food A to cat food B. Based on these results, in the second survey of 60 people, how many people can be predicted to prefer cat food A?
Based on the first survey results, we can predict that around 47 people in the second survey of 60 people will prefer cat food A over cat food B.
Based on the results of the first survey, 188 out of 240 people preferred cat food A over cat food B. To predict the preference for cat food A in the second survey, we can calculate the proportion of people who preferred cat food A in the first survey and apply it to the sample size of the second survey.
First, find the proportion of people preferring cat food A in the first survey:
Proportion = (Number of people preferring cat food A) / (Total number of people surveyed)
Proportion = 188 / 240
Proportion ≈ 0.7833
Now, apply this proportion to the second survey's sample size of 60 people:
Predicted preference = Proportion × (Sample size of the second survey)
Predicted preference = 0.7833 × 60
Predicted preference ≈ 47
Therefore, based on the first survey results, we can predict that around 47 people in the second survey of 60 people will prefer cat food A over cat food B.
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Write and simplify the integral that gives the arc length of the following curve on the given integral. b. If necessary, use technology to evaluate or approximate the integral. y = -x² -5 on [-1,2]
To find the arc length of the curve y = -x² -5 on the interval [-1,2], we use the formula to evaluate:
L = ∫√(1 + (dy/dx)²) dx
where dy/dx is the derivative of y with respect to x.
First, we find dy/dx:
dy/dx = -2x
Next, we substitute dy/dx into the formula and simplify:
L = ∫√(1 + (-2x)²) dx
L = ∫√(1 + 4x²) dx
To evaluate this integral, we can use a trigonometric substitution. Let x = (1/2)tanθ, then dx = (1/2)sec²θ dθ. Substituting, we get:
L = ∫√(1 + 4(1/2)²tan²θ)(1/2)sec²θ dθ
L = (1/2)∫sec³θ dθ
To integrate sec³θ, we use integration by parts:
u = secθ, du/dθ = secθ tanθ
dv/dθ = sec²θ, v = tanθ
∫sec³θ dθ = secθ tanθ - ∫tan²θ secθ dθ
= secθ tanθ - ∫secθ dθ + ∫sec³θ dθ
Rearranging, we get:
2∫sec³θ dθ = secθ tanθ + ln|secθ + tanθ|
Therefore:
L = (1/2)(secθ tanθ + ln|secθ + tanθ|) + C
To evaluate L on the interval [-1,2], we need to find θ when x = -1 and x = 2. Using the substitution x = (1/2)tanθ:
When x = -1, θ = -π/4
When x = 2, θ = π/3
Substituting these values into the equation for L and simplifying, we get:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Therefore, the integral that gives the arc length of the curve y = -x² -5 on the interval [-1,2] is:
L = (1/2)(2√2 + ln(3 + 2√3) + π/4)
Note: If technology is used to evaluate or approximate the integral, the answer may differ slightly due to rounding errors.
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A sterling silver platter is made up of a mixture of silver and copper. The ratio of silver to copper is 37:3 by mass. If the platter has a mass of 600 grams, what is the mass, in grams, of the copper in the platter?
A) 18
B) 45
C) 222
D) 555
The mass of copper in the platter is 45 grams, which corresponds to option (B).
What is ratio ?
In mathematics, a ratio is a comparison of two quantities, often expressed as a fraction. Ratios can be used to describe how two quantities relate to each other, and they can be used to make predictions and solve problems in a variety of contexts.
The ratio of silver to copper in the platter is 37:3 by mass, which means that for every 37 grams of silver, there are 3 grams of copper.
Let's call the mass of silver in the platter "s" and the mass of copper "c". We know that the total mass of the platter is 600 grams, so:
s + c = 600
We also know that the ratio of silver to copper is 37:3, which means that:
s÷c = 37÷3
We can use this second equation to solve for s in terms of c:
s:c = 37:3
s = (37÷3)c
Now we can substitute this expression for s into the first equation:
s + c = 600
(37÷3)c + c = 600
(40÷3)c = 600
c = (3÷40) * 600
c = 45
Therefore, the mass of copper in the platter is 45 grams, which corresponds to option (B).
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Can someone please help me ASAP? It’s due tomorrow.
Answer: m*n
Step-by-step explanation:
Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y) = 3ex sin(y), (0, 1/3), v = (-5, 12) V = D,FO, 1/3) = 12-973 10 x Need Help? Read It Watch
The directional derivative of the function f(x,y) in the direction of the vector v at the point (0,1/3) is:
Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38
To find the directional derivative of the function f(x, y) = 3e^x sin(y) at the point (0, 1/3) in the direction of the vector v = (-5, 12), we first need to calculate the gradient of the function, which is a vector containing the partial derivatives with respect to x and y.
The partial derivative with respect to x:
∂f/∂x = 3eˣ sin(y)
At point (0, 1/3), ∂f/∂x = 3e⁰ sin(1/3) = 3 sin(1/3)
The partial derivative with respect to y:
∂f/∂y = 3eˣ cos(y)
we first need to find the gradient of f at that point:
∇f = [∂f/∂x, ∂f/∂y] = [3ex sin(y), 3ex cos(y)]
Evaluated at (0,1/3), we get:
∇f(0,1/3) = [0, 3e/2
At point (0, 1/3), ∂f/∂y = 3e⁰ cos(1/3) = 3 cos(1/3)
So the gradient vector is ∇f = (3 sin(1/3), 3 cos(1/3)).
Next, we need to normalize the direction vector v:
|v| = √((-5)² + (12)²) = 13
Normalized vector v: (-5/13, 12/13)
Finally, we calculate the directional derivative (D_vf) as the dot product of the gradient vector and the normalized direction vector:
D(vf)= ∇f • (-5/13, 12/13) = (3 sin(1/3) × (-5/13)) + (3 cos(1/3) × (12/13))
D(vf) = (-15/13) sin(1/3) + (36/13) cos(1/3)
That is the directional derivative of the function at the given point in the direction of the vector v
Duf(0,1/3) = ∇f(0,1/3) · u = [0, 3e/2] · [-5/13, 12/13] = (3e/2)(12/13) ≈ 1.38
Therefore, the directional derivative of f(x, y) in the direction of v at the point (0,1/3) is approximately 1.38.
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(−2x−1)(−3x 2 +6x+8)
The value of y varies directly with x. When y = 75, x=1/2. What is the value of y, when x is 2 1/2
Answer:
y=60
Step-by-step explanation:
y=kx75=k×1/275=1/2k75÷1/2=1/2k÷1/2k=150y=kxy=150×2 1/2y= 60This question is kinda confusing :(
state the parent function of g(x) and describe how the graph of (x) is related to its parent function (questions 3,4,5)
The parent functions of the function equations are x³, x⁴ and x²
Stating the parent functionsThe transformed functions 3 - 5 represent the given parameter
To derive the parent functions, we need to determine the degree of the transformed and use this degree as a guide
By definition, the degree of a function is the highest power in the function
So, we have
Question 3
g(x) = (1/2x + 2)³ + 5
The degree here is 3
This means that the function is a cube function
The parent function of a cube function is y = x³
So, the parent function is g(x) = x³
Question 4
g(x) = x⁴ - 4
The degree here is 4
This means that the function is a polynomial function shifted down by 4 units
The parent function of this is y = x⁴
So, the parent function is g(x) = x⁴
Question 5
g(x) = 1/2(x - 1)² - 4
The degree here is 2
This means that the function is a quadratic function
The parent function of a quadratic function is y = x²
So, the parent function is g(x) = x²
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Kevin and his family are going camping.the tent has a width of 20ft,and the sides are 12ft long.how high is the tent in the middle?round to nearest tenth
Therefore , the solution of the given problem of unitary method comes out to be length (12 ft) that is less than its width (20 ft), which is the case with the tent.
What is a unitary method?The well-known simple approach, real variables, and any crucial elements from the very initial And specialised inquiry can all be used to finish the work. Customers may then be given another chance to try the product in response. If not, significant impacts on our understanding of algorithms will vanish.
Here,
The hypotenuses of two right triangles created by halving the triangle can be viewed as the two sides of the triangle. Next, we have
=> h² = (12/2)² - (20/2)²
=> h² = 36 - 100
=> h² = -64
The fact that the outcome is bad indicates that we made a mistake. In this instance, it is because a legitimate triangular prism cannot be formed using the specified dimensions.
A triangular prism cannot have a length (12 ft) that is less than its width (20 ft), which is the case with the tent.
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In a student poll of 38 boys and 42 girls,
15 boys and 20 girls said they like science
fiction books. Based on this information,
Answer:40-45 percent
Step-by-step explanation:
explenation
252-(18x8)
Ross says that he does not need parenthesis. Is he correct?
Yes
Step-by-step explanation:PEMDAS explains the order that operations are done.
PEMDAS
PEMDAS stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. This is the order of operations. Always start with operations inside parentheses, then exponents, then multiplication and division, and the last operations are addition and subtraction. In the problem above, parentheses come first, so means start with 18 x 8 and then do subtraction afterward.
Without Parentheses
Take the new expression, 252 - 18 x 8. Following the order of operations, multiplication goes first. This means multiply 18 x 8 first and then subtract. This order of operations is the same with or without parentheses. Since multiplication comes before subtraction, parentheses are not needed.
A cylinder has a radius of 2 ft and a hight of 6 ft. What is the total surface area using 3.14 as pi.
The total surface area of a cylinder is the sum of the areas of its top and bottom circles, along with the area of its lateral surface (the curved surface that connects the two circles).
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
The formula for the area of a circle is:
Area of circle = πr^2
Using these formulas, we can calculate the total surface area of the cylinder as follows:
Area of top and bottom circles = 2 × π × r^2
= 2 × 3.14 × 2^2
= 25.12 square feet
Lateral surface area = 2 × π × r × h
= 2 × 3.14 × 2 × 6
= 75.36 square feet
Total surface area = Area of top and bottom circles + Lateral surface area
= 25.12 + 75.36
= 100.48 square feet
Therefore, the total surface area of the cylinder is 100.48 square feet.
The sixth-graders at Ayana's school got to choose between a field trip to a museum and a field trip to a factory. 39 sixth-graders picked the museum. If there are 50 sixth-graders in all at Ayana's school, what percentage of the sixth-graders picked the museum?
Answer:
78% of sixth-graders picked a field trip to a museum.
Step-by-step explanation:
39 out of 50 kids picked the museum field trip. This is 39/50. We can change this like so:
39/50 × 2/2
= 78/100
78/100 is 78% (because percent literally means "per hundred)
Another way is to just divide. 39/50 means 39 ÷ 50.
39 ÷ 50 is .78 then times by 100 to change to a percent. This works for all kinds of fractions.
78% of sixth graders at Ayana's school selected the museum field trip.
A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 64 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 124 kWh. At a = 0. 01, can you support the claim? Complete parts (a) through (e)
(a) State the null and alternative hypotheses.
Null Hypothesis: The mean monthly residential electricity consumption in the region is less than or equal to 880 kWh.
Alternative Hypothesis: The mean monthly residential electricity consumption in the region is greater than 880 kWh.
(b) Determine the test statistic.
We need to use a one-tailed t-test because the alternative hypothesis is one-tailed.
t = (x - μ) / (σ / √n) = (900 - 880) / (124 / √64) = 2.581
(c) Find the p-value.
Using a t-table or a calculator, we can find the p-value associated with a t-value of 2.581 and 63 degrees of freedom: p-value = 0.007
(d) State the conclusion.
The p-value is less than the significance level of 0.01, which means that we reject the null hypothesis. We have enough evidence to support the claim that the mean monthly residential electricity consumption in the region is more than 880 kWh.
(e) Interpret the conclusion in the context of the problem.
Based on the sample data, we can conclude that the mean monthly residential electricity consumption in the region is likely to be greater than 880 kWh. However, we cannot say for sure whether this conclusion would hold true for the entire population.
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If Ethan’s monthly expenses are $1160 and his debt to income ratio is 0. 8, what is his monthly salary?
Ethan's monthly salary is $1450.
Ethan's monthly salary, we can use the debt to income ratio formula, which is calculated by dividing monthly debt expenses by monthly income.
Given:
Monthly expenses = $1160
Debt to income ratio = 0.8
Let's assume Ethan's monthly salary as S.
We can set up the equation using the debt to income ratio formula:
Debt to income ratio = Monthly expenses / Monthly income
0.8 = $1160 / S
To solve for S (monthly salary), we can rearrange the equation:
S = $1160 / 0.8
Dividing $1160 by 0.8 gives us:
S ≈ $1450
Therefore, Ethan's monthly salary is approximately $1450.
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based on a random sample of 1505 us adults, we built a confidence interval for the proportion of us adults that say the country's best days are still ahead The 95% confidence interval is from 0.588 to 0.612. Select the statement below that correctly interprets this confidence interval. We are 95% confident that the sample proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 We are 95% confident that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612. 95% of the population proportions of US adults that believe owning a house is very important to their quality of life will fall within this interval. The probability that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 is 0.95.
The correct interpretation of the given confidence interval is: We are 95% confident that the population proportion of US adults that say the country's best days are still ahead is between 0.588 and 0.612.
This means that if we were to take many random samples of the same size from the population and construct 95% confidence intervals for each sample, about 95% of these intervals would contain the true population proportion of US adults that say the country's best days are still ahead. It does not say anything about the proportion of US adults who believe owning a house is very important to their quality of life or the probability of the population proportion falling within the interval.
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19. Write a proof in two-column form for the Corresponding Angles Theorem. Given: pill q Prove: m/1 = m/5 Statements Pll q given Reasons aler
Corresponding Angles Theorem: If a transversal intersects two parallel lines, then the corresponding angles formed are congruent.
Statements Reasons
1. ∠1 and ∠3 are corresponding angles Given
2. m//n Given
3. ∠1 and ∠2 are congruent Alternate Interior Angles Theorem
4. ∠2 and ∠3 are congruent Alternate Interior Angles Theorem
5. ∠1 ≅ ∠2 and ∠2 ≅ ∠3 Substitution (from statements 3 and 4)
6. ∠1 ≅ ∠3 Transitive Property of Congruence
How to explain the TheoremIn this proof, we start by stating that ∠1 and ∠3 are corresponding angles, which is given in the problem statement. We also know that m and n are parallel lines, which is also given.
Then, we apply the Alternate Interior Angles Theorem to show that ∠1 and ∠2, as well as ∠2 and ∠3, are congruent.
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