We can use the Pythagorean theorem to relate the distances between the ladder, wall, and ground. Let's call the distance from the foot of the ladder to the wall "x", and the distance from the top of the ladder to the ground "y". Then, we know that:
x^2 + y^2 = 10^2
We can differentiate this equation with respect to time to get:
2x(dx/dt) + 2y(dy/dt) = 0
We're interested in finding dy/dt, the rate at which the top of the ladder is sliding down the wall. We know that dx/dt = 0.5 ft/s, so we can plug in these values and solve for dy/dt:
2x(dx/dt) + 2y(dy/dt) = 0
2(8)(0.5) + 2y(dy/dt) = 0 (since x = 8 based on the Pythagorean theorem)
dy/dt = -4 ft/s
So the top of the ladder is sliding down the wall at a rate of 4 ft/s.
When the 10-foot ladder is leaning against a vertical wall, it forms a right-angled triangle with the wall and the ground. As Jack pulls the foot of the ladder away from the wall at a rate of 0.5 ft/s, the top of the ladder slides down the wall. To find the rate at which the top of the ladder slides down, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is the distance from the foot of the ladder to the wall, b is the height of the ladder's top from the ground, and c is the length of the ladder (10 feet).
Differentiating both sides with respect to time (t), we get:
2a(da/dt) + 2b(db/dt) = 0
We know that da/dt = 0.5 ft/s. We need to find db/dt, which is the rate at which the top of the ladder slides down the wall. To do this, we need to find the values of a and b at a given moment. Since the problem doesn't provide this information, it's not possible to determine the exact value of db/dt. However, if you have the values of a and b, you can plug them into the equation and solve for db/dt.
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The general form of a member of the reciprocal family is y=a/x-h+k l. Identify the values of a, h, and k in the given function y=5/x-6-2. State the transformations on the graph as a result of a, h, and k
Answer:
bad photo quality
Step-by-step explanation:
The function is transformed by a vertical stretching or compression by a factor of 5, a horizontal shift of 6 units to the right, and a vertical shift of 2 units downward.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
In the given function y = 5/(x - 6) - 2, the values of a, h, and k can be identified as follows:
a = 5
h = 6
k = -2
Now , the original function is y = a/(x - h) + k, and the reciprocal family of this function is y = a/(x - h) + k
And , value of 'a' determines the vertical scaling factor of the reciprocal function
Now , the value of 'h' determines the horizontal shift of the reciprocal function. If 'h' is positive, the graph of the reciprocal function is shifted horizontally to the right
And , if 'k' is negative, the graph is shifted vertically downward
Hence , the transformation of the function is solved
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At appliance store, 37% of customers purchase a wahing machine. 11 % of customers buy both a wahsing machine. 11% of customers buy both waher and a dryer. Find the probability that a customer who buys a washer also buys a dryer
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.
Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.
Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.
Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.
The formula for conditional probability is:
P(D | W) = P(D and W) / P(W)
where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.
Substituting the values we have:
P(D | W) = 0.11 / 0.37
P(D | W) = 0.297
The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.
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A tennis ball is dropped from a certain height. Its height in feet is given by h(t)=−16t^2 +14 where t represents the time in seconds after launch. What is the ball’s initial height?
The initial height of the ball after launch is 14ft.
What is vertical motion?A vertical motion is a motion due to gravity. This means the velocity and height will depend on the acceleration due to gravity.
The height of vertical motion is given as;
H = ut ± 1/2 gt²
where u is the initial velocity and t is the time to reach max height.
The height of a ball is given by;
h(t) = -16t²+14
where t represents the time in seconds after launch.
The initial height after launch is when t = 0
h(t) = -16(0)² +14
h(t) = 14ft
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A newspaper for a large city launches a new advertising campaign focusing on the number of digital subscriptions. the equation s(t)=31,500(1.034)t approximates the number of digital subscriptions s as a function of t months after the launch of the advertising campaign. determine the statements that interpret the parameters of the function s(t).
"t" increases, and the number of digital subscriptions grows exponentially at a rate of 3.4% per month.
How to determine the statements that interpret the parameters of the function s(t).The function s(t) = 31,500(1.034)^t gives an approximation of the number of digital subscriptions s as a function of t months after the launch of the advertising campaign.
The parameters of the function s(t) are:
31,500: This is the initial number of digital subscriptions at t = 0, when the advertising campaign is launched.
1.034: This is the growth rate of the number of digital subscriptions per month. It represents the percentage increase in the number of subscriptions each month due to the advertising campaign. Specifically, each month the number of subscriptions is multiplied by 1.034, which is the same as increasing it by 3.4%.
t: This is the time in months after the launch of the advertising campaign. It is the independent variable of the function that determines the number of digital subscriptions at any given time t.
Statements interpreting the parameters of the function s(t) are:
The initial number of digital subscriptions at t = 0 is 31,500.
For every month after the launch of the advertising campaign, the number of digital subscriptions increases by 3.4%, or a factor of 1.034.
The parameter t represents the time in months after the launch of the advertising campaign. As t increases, the number of digital subscriptions grows exponentially at a rate of 3.4% per month.
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x^3y^2-343y^5
factoring polynomials
The polynomial is factored to y²(x³ - 7³y³)
How to determine the expressionNote that polynomials are described as expressions that are made up of terms, variables, coefficients, factors and constants.
Also, they have a degree greater than one.
Index forms are also seen as forms used to represent values that are too large or small in more convenient forms.
From the information given, we have that;
x³y²-343y⁵
Now, find the cube value of 343, we have;
343 = 7³
Substitute the value
x³y²- 7³y⁵
Factorize the common terms, we have;
y²(x³ - 7³y³)
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Your bank account consists of a checking and savings accounts. Assume your expenses and earnings can be described by a random walk with an equal probability to spend one dollar or to receive one dollar in your checking account at every time interval. You are charged $5 for any transaction from the checking account to the savings account and viceversa. Also, assume that the cost per unit of cash, per unit of time r of keeping cash on hand is equal to $0. 1 dollars for any dollar on hand per time period. Determine:
a. The optimal values of the two thresholds s and S, i. E. , the amount of cash in your checking account restored after each transaction, and the maximum amount of cash in your checking account, respectively.
b. The long run average cost associated to the optimal cash management strategy and to the strategy with the same s but with a maximum amount of cash equal to 2S.
c. Are there any common criticisms of this model?
a. To determine the optimal values of the two thresholds s and S, we can use the Miller-Orr cash management model. The objective is to minimize the total cost of cash management, which includes transaction costs and the opportunity cost of holding cash.
Let's assume that the transaction cost of $5 applies whenever the cash balance in the checking account goes below s or above S. The expected daily cash balance is zero since expenses and earnings are equally likely, and the standard deviation of the cash balance is σ = √(t/2), where t is the time interval.
The optimal value of s is given by:
s* = √(3rT/4C) - σ/2,
where T is the length of the cash management period, and C is the fixed cost per transaction. The optimal value of S is given by:
S* = 3s*,
which ensures that the probability of a cash balance exceeding S is less than 1/3.
Using r = 0.1, T = 1 day, and C = $5, we obtain:
s* = √(30.11/4*5) - √(1/2)/2 = $16.82
S* = 3*$16.82 = $50.47
Therefore, the optimal values of the two thresholds are s* = $16.82 and S* = $50.47.
b. The long run average cost associated with the optimal cash management strategy can be calculated as:
Total cost = (s*/2 + S*) * σ * √(2r/C) + C * E(N),
where E(N) is the expected number of transactions per day. Since expenses and earnings are equally likely, E(N) = (S* - s*)/2 = $16.83. Therefore, the total cost is:
Total cost = ($16.82/2 + $50.47) * √(1/2) * √(2*0.1/$5) + $5 * $16.83 = $1.38 per day.
Now let's consider the strategy with the same s but with a maximum amount of cash equal to 2S. The expected daily cash balance is still zero, but the standard deviation is now σ' = √(t/3). The optimal value of S' is given by:
S' = √(3rT/2C) - σ'/2 = $35.35.
The long run average cost associated with this strategy is:
Total cost' = (s/2 + S') * σ' * √(2r/C) + C * E(N'),
where E(N') is the expected number of transactions per day. Since the maximum amount of cash is now 2S, we have E(N') = (2S - s)/2 = $34.59. Therefore, the total cost is:
Total cost' = ($16.82/2 + $35.35) * √(1/3) * √(2*0.1/$5) + $5 * $34.59 = $1.30 per day.
Therefore, the strategy with the same s but with a maximum amount of cash equal to 2S is slightly more cost-effective in the long run.
c. One common criticism of this model is that it assumes a constant transaction cost, which may not be realistic in practice. In reality, transaction costs may vary depending on the size and frequency of transactions, and may also depend on the banking institution and the type of account. Another criticism is that it assumes a random walk model for expenses and earnings, which may not capture the
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In ΔSTU, s = 360 cm, t = 110 cm and u=450 cm. Find the measure of ∠U to the nearest 10th of a degree.
The measure of angle U to the nearest tenth is 39.6°
What is cosine rule?The cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
C² = a²+b²-2abcosC
450² = 360²+110²+2(110)(360)cosU
202500 = 129600+ 12100+ 79200cosU
202500 = 141700+79200cosU
79200cosU = 202500-141700
79200cosU = 60800
cos U = 60800/79200
cos U = 0.77
U = 39.6°( nearest tenth)
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[tex]CD= \left[\begin{array}{ccc}e1&e2\\e3&e4\\\end{array}\right][/tex]
the determinant of the matrix is e1e4-e3e2
What is the determinant of a matrix?The determinant of a matrix is a scalar value that is a function of the entries. It characterizes some properties of the matrix and the linear map represented by it. The determinant is nonzero if and only if the matrix is invertible and an isomorphism exists.
Determinants are only defined for square matrices and encode certain properties of the matrices.
The determinant of a matrix is defined by the difference betweern the product of the right diagonal to the the product of the left diagonal
From the given question. the determinant of the matrix is e1*e4 -e3-e2 = e1e4-e3e2
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Can someone please help me with this
Calculate the partial derivative ∂z/∂y using implicit differentiation of e* + sin (5x2) + 2y = 0.
(Use symbolic notation and fractions where needed.)
the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:
To calculate the partial derivative ∂z/∂y using implicit differentiation of e* + sin (5x^2) + 2y = 0, we first need to differentiate both sides of the equation with respect to y.
We get:
d/dy(e^z + sin(5x^2) + 2y) = d/dy(0)
Using the chain rule, the left-hand side becomes:
∂(e^z)/∂z * ∂z/∂y + ∂(sin(5x^2))/∂y + 2
We can simplify this by recognizing that ∂(sin(5x^2))/∂y = 0, since sin(5x^2) does not depend on y. Thus, we are left with:
∂(e^z)/∂z * ∂z/∂y + 2 = 0
Now, we need to solve for ∂z/∂y:
∂z/∂y = -2 / ∂(e^z)/∂z
To find ∂(e^z)/∂z, we differentiate e^z with respect to z, giving:
∂(e^z)/∂z = e^z
Substituting this into the expression for ∂z/∂y, we get:
∂z/∂y = -2 / e^z
Therefore, the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:
∂z/∂y = -2 / e^z
Note that we cannot simplify this any further without knowing the value of z.
To find the partial derivative ∂z/∂y using implicit differentiation for the equation e^z + sin(5x^2) + 2y = 0, we will first differentiate the equation with respect to y, treating z as a function of x and y.
Differentiating both sides with respect to y:
∂/∂y (e^z) + ∂/∂y (sin(5x^2)) + ∂/∂y (2y) = ∂/∂y (0)
Using the chain rule for the first term, we get:
(e^z) * (∂z/∂y) + 0 + 2 = 0
Now, solve for ∂z/∂y:
∂z/∂y = -2 / e^z
So, the partial derivative ∂z/∂y for the given equation is:
∂z/∂y = -2 / e^z
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You want your savings account to have a total of $23,000 in it within 5 years. If you invest your money in an account that pays 6.8% interest compounded continuously, how much money must you have in your account now?
You must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.
To achieve a savings account balance of $23,000 in 5 years with an interest rate of 6.8% compounded continuously, you will need to use the formula for continuous compounding: A = P * e^(rt), where A is the future value, P is the principal amount (initial deposit), r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).
In this case, A = $23,000, r = 0.068, and t = 5 years. You need to solve for P, the principal amount:
$23,000 = P * e^(0.068 * 5)
Now, you can solve for P:
P = $23,000 / e^(0.068 * 5)
P ≈ $16,465.55
So, you must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.
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Ruben paints one coat on one wall that us 3 1/2 yards long by 9 feet tall. He then paints one coat on two part walks that are each 4 feet talk by 1 1/2 yards long. What was the total area he paintex?
Ruben painted a total area of [tex]130.5 square feet.[/tex]
To determine the total area that Ruben painted, we need to find the area
of each wall and then add them together. Since the dimensions of the
walls are given in different units (yards and feet), we will first need to
convert them to a common unit.The first wall is 3 1/2 yards long by 9 feet
tall, which is equivalent to 10 1/2 feet long by 9 feet tall (since 1 yard = 3
feet).
The area of this wall is:
[tex]10 1/2 feet * 9 feet = 94.5 square feet[/tex]
The second two walls are each 4 feet tall by 1 1/2 yards long, which is
equivalent to 4 feet tall by 4.5 feet long (since 1 yard = 3 feet).
The area of each of these walls is:
[tex]4 feet* 4.5 feet = 18 square feet[/tex]
Since Ruben painted one coat on each wall, the total area he painted is:
[tex]94.5 square feet + 2 * 18 square feet = 130.5 square feet[/tex]
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The equation a² + b² = c² represents the relationship between the three sides of a right triangle.
Ivan is cutting a piece of fabric for his sewing project in the shape of a right triangle. His right triangle has a leg with
a length of 5 inches and a hypotenuse with a length of 11 inches. What is the length, in inches, of the other leg of
his triangle?
the length, in inches, of the other leg of his triangle is 9. 8inches
How to determine the lengthUsing the Pythagorean theorem which states that the square of the longest leg or side of a given triangle is equal to the sum of the squares of the other two sides of the triangle.
From the information given, we have that;
a² + b² = c² represents the relationship between the three sides of a right triangle
Also,
Hypotenuse side = 11 inches
One of the other side = 5 inches
Substitute the values, we have;
11² = 5² + c²
collect like terms
c² = 121 - 25
Subtract the values
c = √96
c = 9. 8 inches
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Given that BC is tangent to circle A and that BC=3 and AB=5. Calculate
the length of the radius of circle A
The radius of circle A is 4.
From the given information, we can draw a right triangle ABC where BC is the tangent to circle A at point C, AB is the hypotenuse, and AC is the radius of the circle. By the Pythagorean theorem, we have:
AC² + BC² = AB²
Substituting the given values, we get:
AC² + 3² = 5²
AC² = 25 - 9
AC² = 16
Taking the square root of both sides, we get:
AC = 4
Therefore, the length of the radius of circle A is 4.
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Observa las siguientes tablas y analiza los valores que contienen. Después, plantea un problema que pueda resolverse con esos datos, también argumenta por qué una tabla corresponde a la variación lineal y la otra a la variación de proporcionalidad directa.
1 is linear variation and 2 is direct proportionality. In 1 it is linear variation since from the beginning the zeros do not correspond and in 2 if the zeros correspond.
Variation refers to the differences that exist among individuals or groups within a population. These differences can be genetic, environmental, or a combination of both, and can manifest in various traits, such as physical characteristics, behavior, or disease susceptibility.
Genetic variation arises from differences in the DNA sequence among individuals, which can result in different traits being expressed. This variation can occur naturally or be induced by mutations, genetic recombination, or genetic drift. Environmental variation arises from differences in the conditions experienced by individuals or groups, such as differences in climate, nutrition, or exposure to toxins. Environmental variation can also interact with genetic variation to produce complex traits.
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Complete Question:-
Look at the following tables and analyze the values they contain. Then, pose a problem that can be solved with these data, also argue why one table corresponds to linear variation and the other to direct proportional variation.
TABLE 1:
X 0 1 2 3
and 2 17 32 47
TABLE 2:
X 0 1 2 3
AND 0 15 30 45
a group conducting a survey randomly selects adults in a certain region. of the 2,500 adults selected, 1,684 are men.
assuming that men and women have an equal chance of being selected the probability of the adults being chosen this way
by chance is less than 0.01. interpret the results of this calculation
The probability of the adults being chosen this way by chance is less than 0.01 interprets that group is more likely to choose men over women
A group conducting a survey randomly selects adults in a certain region. Of the 2,500 adults selected, 1,684 are men. The men and women have an equal chance The result of the survey is significant at the 0.01 level which means that the probability of group selection being the result of chance is 0.01 or less because the event is least likely to happen the group is more likely to select men over women.
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Solve the equation and check your solution: -2(x + 2) = 5 - 2x
Answer:
I think the answer might be -4 = 3x.
Step-by-step explanation:
-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.
In a survey of 85 people, every fifth person had a pierced ear. How many people had a pierced ear? A 0.5 × 85 B 85 × 15 C 5÷85 D 85-4/5 E 85 × 0.25
Answer:
B
Step-by-step explanation:
Every fifth people means one person from 5 people in total. So when we convert that into numbers, it becomes [tex]\frac{1}{5}[/tex].
And in total there are 85 people involved, so the answer is
[tex]85[/tex] × [tex]\frac{1}{5}[/tex]
Answer:
Step-by-step explanation:
correct asnswer b
Use the known MacLaurin series to build a series for each of the following functions. Be sure to show each step (layer) in expanded form along the way. Write your final answer in proper summation notation
f(x) = (e^2x - 1 - 2x)/2x^2
To build a series for the given function f(x) = (e^(2x) - 1 - 2x)/2x^2, we can start by finding the MacLaurin series for e^(2x) and then manipulate it to obtain the desired series.
The MacLaurin series for e^(2x) is given by:
e^(2x) = Σ (2x)^n / n! for n = 0 to ∞
Expanding the series, we get:
e^(2x) = 1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...
Now, we can substitute this back into the original function:
f(x) = (e^(2x) - 1 - 2x)/2x^2 = (1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ... - 1 - 2x) / 2x^2
Simplifying, we have:
f(x) = (2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...) / 2x^2
Now, we can divide by 2x^2 to obtain the series for f(x):
f(x) = 1/2! + 2x/3! + 2^3x^2/4! + 2^4x^3/5! + ...
Finally, we can write the final answer in proper summation notation:
f(x) = Σ (2^(n-1)x^(n-2)) / n! for n = 2 to ∞
To begin, we can write f(x) as:
f(x) = (1/2x^2)[e^(2x) - 1 - 2x]
Next, we will use the Maclaurin series for e^x, which is:
e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...
Substituting 2x for x, we have:
e^(2x) = 1 + 2x + (4x^2)/2! + (8x^3)/3! + ...
Expanding the first two terms of the numerator in f(x), we have:
f(x) = (1/2x^2)[(1 + 2x + (4x^2)/2! + (8x^3)/3! + ...) - 1 - 2x]
Simplifying, we get:
f(x) = (1/2x^2)[2x + (4x^2)/2! + (8x^3)/3! + ...]
Now we can simplify the coefficients in the numerator by factoring out 2x:
f(x) = (1/x)[1 + (2x)/2! + (4x^2)/3! + ...]
Finally, we can write the series in summation notation:
f(x) = Σ[(2n)!/(2^n*n!)]x^n, n=1 to infinity.
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On a coordinate plane, kite g d e f has points (0, 0), (10, 10), (16, 8), (14, 2). complete the steps to find the area of the kite. what is ge? square root of units what is df? square root of units what is the area of the kite to the nearest unit? square unitson a coordinate plane, kite g d e f has points (0, 0), (10, 10), (16, 8), (14, 2). complete the steps to find the area of the kite. what is ge? square root of units what is df? square root of units what is the area of the kite to the nearest unit? square units
The square root of units is sqrt (80), and the area of the kite to the nearest unit is 74 square units.
To find the area of the kite, we can divide it into two triangles by drawing a diagonal between points (10,10) and (14,2).
First, we need to find the length of this diagonal. We can use the distance formula:
d = sqrt((14-10)^2 + (2-10)^2)
d = sqrt(16 + 64)
d = sqrt(80)
So the length of the diagonal is square root(80) units.
Next, we can find the area of each triangle:
Triangle 1:
Base = 10 units
Height = 10 units
Area = 1/2 * base * height = 1/2 * 10 * 10 = 50 square units
Triangle 2:
Base = 6 units (the difference between the x-coordinate plane of (10,10) and (14,2))
Height = 8 units (the difference between the y-coordinate plane of (10,10) and (16,8))
Area = 1/2 * base * height = 1/2 * 6 * 8 = 24 square units
So the total area of the kite is 50 + 24 = 74 square units.
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Answer:
On a coordinate plane, kite G D E F has points (0, 0), (10, 10), (16, 8), (14, 2).
Complete the steps to find the area of the kite.
What is GE?
Square root of
✔ 320units
What is DF?
Square root of
✔ 80units
What is the area of the kite to the nearest unit?
✔ 80
square units
An architect draws a blueprint of the newly modeled family room she is designing for her basement. The scale she uses is 1 inch = 2.5 feet. If the length of the family room is 8 inches, and the width of the family room is 4 inches, what are the actual dimensions of the family room?
Answer:20 feet by 10 feet
Step-by-step explanation:
The first term of a pattern is 509. The pattern follows the "subtract 7" rule. Which number is a term in the pattern?
A:516
B:500
C:495
D:464
Answer:
C
Step-by-step explanation:
first fine the nth term
a+(n-1)d
509+7n+7
516-7n
then equate the ans to the nth term
495=516-7n
7n=516-495
7n= -21
n= -3
If a person drives his car at the speed of 50 miles per hour, how far can he cover in 2.5 hours?
Match each phrase with the type of inequality it indicates.
The inequalities represented are:
Below - Less than or equal toAbove - Greater thanMore than - Greater thanSmaller Than - Less thanAt most - Less than or equal toAt least - Greater than or equal toNo more than - Less than or equal toNo less than - Greater than or equal toNot to exceed - Less than or equal toMaximum - Less than or equal toWhat is an inequality?In mathematics, an inequality is a statement that two values or expressions are not equal. It is used to compare two values and determine the relationship between them. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).
Inequalities can be solved and graphed on a number line to show all possible solutions that satisfy the inequality. They are commonly used in algebra and calculus to express a range of values for a variable.
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The base of a cone has a radius
of 6 centimeters. The cone is
7 centimeters tall. What is the volume
of the cone to the nearest tenth? Use 3. 14 for it.
A. 260 cm
C. 263. 8 cm3
B. 263. 7 cm
D. 264. 0 cm3
The volume of the cone to the nearest tenth is 263.8 cm^3.
What is the volume, rounded to the nearest tenth, of a cone with a radius of 6 centimeters and a height of 7 centimeters?To find the volume of the cone, we first need to use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
We are given that the radius is 6 centimeters and the height is 7 centimeters, so we can substitute these values into the formula.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
Using the given values, we can plug them into the formula and solve:
V = (1/3)π(6 cm)^2(7 cm)
V ≈ 263.7 cm^3
Rounding this to the nearest tenth gives us the final answer of 263.8 cm^3, which is option (C).
Since 3 is less than 5, we round down, which means the answer is 263.8 cm^3, as shown in option (C).
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Evaluate the following indefinite integrals:
a) ∫ (1/x + 3/x2/- 4/x3 ) dx
b) ∫ (x2+ 2x - 5) / √x dx
c) ∫ x ex dx
a) ∫ (1/x + 3/x^2 - 4/x^3) dx
To solve this indefinite integral, we need to use the power rule and the fact that the derivative of ln(x) is 1/x.
∫ (1/x + 3/x^2 - 4/x^3) dx = ln|x| - 3/x + 2/x^2 + C
b) ∫ (x^2 + 2x - 5) / √x dx
To solve this indefinite integral, we can simplify the integrand by multiplying the numerator and denominator by √x. Then, we can use the power rule and u-substitution.
∫ (x^2 + 2x - 5) / √x dx = ∫ (x^(5/2) + 2x^(3/2) - 5x^(1/2)) dx
= (2/7)x^(7/2) + (4/5)x^(5/2) - (10/3)x^(3/2) + C
c) ∫ x e^x dx
To solve this indefinite integral, we need to use integration by parts.
Let u = x and dv/dx = e^x. Then, we can find v by integrating dv/dx.
v = e^x
Using integration by parts, we get:
∫ x e^x dx = xe^x - ∫ e^x dx
= xe^x - e^x + C
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Yasmin has a bag containing 165 colored beads. her classmates take turns selecting one bead from the bag without looking, recording the color in the table, and replacing the bead. if the bag contained an equal number of each color of bead, for which color is the experimental probability closest to the theoretical probability?
Since there are multiple colors, the theoretical probability of selecting any one color would be 1/total number of colors, which is 1/6.
Theoretical probability is the probability of an event occurring based on all possible outcomes. In this case, if the bag contained an equal number of each color of bead, then the theoretical probability of selecting any one color of bead would be 1/total number of colors.
To find the experimental probability, we need to calculate the number of times each color was selected and divide by the total number of selections. Since each student is replacing the bead, the probability of selecting any one color of bead remains the same. Therefore, the experimental probability of selecting any one color of bead should also be 1/6.
However, due to the randomness of the selection process, the experimental probability may not be exactly equal to the theoretical probability. The color for which the experimental probability is closest to the theoretical probability would be the color that has been selected the most number of times, as this would provide the most accurate representation of the experimental probability.
Therefore, we need to record the number of times each color has been selected and calculate the experimental probability for each color. The color with the experimental probability closest to 1/6 would be the color for which the theoretical probability is closest to the experimental probability.
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Can someone please help me ASAP? It’s due tomorrow. I will give brainliest if it’s correct. Show work.
The difference between the outcomes when selected with or without replacement is B. 10 outcomes.
How to find the number of outcomes ?With Replacement:
When you select two coins with replacement, you put the first coin back in the jar before selecting the second coin. This means that there are 10 possibilities for each selection. So, the number of outcomes for selecting two coins with replacement is 10 x 10 = 100 outcomes.
Without Replacement:
When you select two coins without replacement, you don't put the first coin back in the jar before selecting the second coin. This means that after selecting the first coin, there are 9 coins left in the jar for the second selection. So, the number of outcomes for selecting two coins without replacement is 10 x 9 = 90 outcomes.
Difference = 100 outcomes - 90 outcomes
Difference = 10 outcomes
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The radius of a circle is 18 in. Find its area in terms of pi
Answer:
324π
Step-by-step explanation:
Area of circle = r² · π
r = 18 in
Find its area in terms of pi.
We Take
18² · π = 324π
So, the area of the circle is 324π.
Answer:
A = 324π
Step-by-step explanation:
A = πr²
A = π(18)²
A = π(324)
A = 324π
If a scale dilates a two dimensional object by factors of 2/3 it means that?
If a scale dilates a two-dimensional object by a factor of 2/3, it means that the image of the object will be reduced by a factor of 2/3. In other words, the length and width of the image will be 2/3 of the length and width of the original object.
For instance, consider a rectangle with length L and width W. If we dilate this rectangle by a factor of 2/3, the new length and width of the rectangle will be (2/3)L and (2/3)W, respectively. The area of the new rectangle will be (2/3)L x (2/3)W = (4/9)LW, which is 4/9 of the original area. This means that the image is smaller than the original rectangle, and this type of dilation is called a reduction.
Dilations can be used in different applications of mathematics, such as geometry, trigonometry, and algebra. They are useful for changing the scale or size of an object in a proportional way, without altering its basic shape or characteristics.
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