The inequality to describe the possible values for the total area is 0 ≤ A ≤ 193.11.
The formula for the area of a triangle is A = (1/2)bh, where b is the base and h is the height.
Substituting the given values, we get A = (1/2)(12.3)(31.4) = 193.11 square feet.
To create an inequality for the possible values of A, we can say that A is greater than or equal to 0 (since area cannot be negative) and less than or equal to the maximum possible area, which occurs when the base and height are both positive.
Therefore, the inequality to describe the possible values for the total area is 0 ≤ A ≤ 193.11.
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Evaluate the expression (-3)(4)(-6)
A project under consideration has a 10-year projected life. The initial investment for the project is estimated to have a mean of $10,000 and a standard deviation of $1,000. The annual receipts are independent, with each year’s expected return having a mean of $1,800 and a standard deviation of $200. MARR is 12 percent. Assuming that initial investment and annual receipts are independent and normally distributed, estimate the probability that the present worth is negative using NORM.INV function in excel.
This value represents the present worth below which the probability is 0.5, indicating a negative present worth.
To estimate the probability that the present worth is negative using the NORM.INV function in Excel,
we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.
The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).
Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),
where t is the year. We then sum up these present values for each year.
We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.
Since we have a mean and standard deviation for the present worth,
we can calculate the corresponding probability of a negative present worth using NORM.INV.
This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,
we can estimate the probability that the present worth is negative based on the given data and assumptions.
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Please Help Me, Y=15-X?
Write the quadratic function in the form f(x) = a * (x - h) ^ 2 + kf(x) = - 2x ^ 2 + 4x - 3Then, give the vertex of its graph.
Given
\(f(x)=-2x^2+4x-3\)Solution
\(\begin{gathered} f(x)=-2x^2+4x-3 \\ f(x)=ax^2+bx+c \\ in\text{ vertex form} \\ f(x)=a(x-h)^2+k \\ \\ h=-\frac{b}{2a}=-\frac{4}{2(-2)}=-\frac{4}{-4}=1 \\ \\ k=f(h)^ \\ k=-2(1)^2+4(1)-3 \\ k=-2+4-3 \\ k=2-3 \\ k=-1 \end{gathered}\)The quadratic in vertex form is
\(f(x)=-2\left(x-1\right)²-1\)The vertex is
\(Vertex\text{ }\lparen1,-1)\)Ff
(a) Work out the value of (16/81)^3/4
Answer: 8/27
Step-by-step explanation:
Just evaluate the equation.
Do it in this order: Parenthesis, Exponents, Multiply/Divide, Add/Subtract.
So:
16/81 = 16/81
16/81 To the Power of 3/4 = 0.2^0.75 = 8/27
Please help. I thought I worked it out correctly but the answer is apparently wrong
Answer:
ready-steady paint
Step-by-step explanation:
if he needs 12 tins, and purchased from paint -O mine, he would spend (12/3) X 7.50 = 4 x 7.50 = £30
from ready steady, he can buy 4 for £11. he needs 12.
so he will spend (12/4) X 11 = 3 X 11 = £33. but he can get 15% off. 15% off is the same as multiplying by 0.85.
33 X 0.85 = £28.05.
so he his better purchasing from ready steady paint
find ∅ round to the nearest degree
A. 24°
B. 66°
C. 64°
D. 26°
Answer:
C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cosθ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{7}{16}\) , then
θ = \(cos^{-1}\) (\(\frac{7}{16}\) ) ≈ 64° ( to the nearest degree )
Which postulate can be used to prove the two triangles are congruent if you know that
UQ ≅ AC and QD ≅ AU
The postulate that can be used to prove the two triangles are congruent is (c) None of the other answers are correct
How to prove the congruency of the trianglesThe figure represents the given parameter
There are two triangles in the figure
Such that the triangles are similar triangles or congruent
From the question, we understand that the triangles are congruent
Also, we know that
UQ ≅ AC and QD ≅ AU
There is no point C on any of the triangles
This means that we cannot ascertain the congruency of the triangles
Hence, the true statement is (c)
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Use the law of sines to solve the triangle. If two solutions exist, find both. Found your answers to two decimal places.
URGENT!
c. find the uniform continuous probability for p(25 < x < 45) for u(15, 65). (round your answer to 1 decimal place.)
The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.
To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).
Length of the interval: 45 - 25 = 20
Length of the entire range: 65 - 15 = 50
Now, we divide the length of the interval by the length of the entire range to obtain the probability:
Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4
Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.
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Find the missing sides and angles of this triangle
A square has a perimeter of 48 in. Find the perimeter of a triangle with each side 4 inches longer than the side of the square.
Answer:
48 in.
Step-by-step explanation:
square
P = 4s
4s = 48 in.
s = 12 in.
triangle
s = 12 in. + 4 in.
s = 16 in.
P = 3s = 3(16 in.)
P = 48 in.
i need help with this please!!
Answer:
-5 would Be your answer
Step-by-step explanation:
Determine whether the distribution represents a probability distribution. X 3 6 0.3 0.4 P(X) Oa. Yes b. No 9 0.3 0.1
The distribution does not represent a probability distribution. The correct option is b.
A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).
In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.
Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.
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Determine whether each relation is a function.
Answer:
5-No
6-No
7-Yes
8-Yes
9-No
Step-by-step explanation:
5 has a repeating domain (10 is repeated in the x cord)
6 has a repeating domain (x cord) of -4 twice
7 has No repeating domains (x cord)
8 has no repeating domain
9 All of the domain repeats
two cables are connected to the top of a very tall pole and are pulled tight in opposite directions, then connected the the ground. one cable is 48 feet long, and the other is 63 feet long. the ground distance between them is 80 feet. how tall is the pole, measured to the nearest tenth?
The height of the pole is approximately 64 feet when rounded to the nearest tenth.
To determine the height of the pole, we can use the concept of a right triangle formed by the pole and the two cables. Let's denote the height of the pole as 'h'.
In the given scenario, one cable is 48 feet long and the other is 63 feet long. The ground distance between them is 80 feet. We can visualize this as follows:
A
/|
/ |
h / | 63
/ |
/ |
/ |
/______C
48 B
Here, A represents the top of the pole, B represents the point where the 48-foot cable touches the ground, and C represents the point where the 63-foot cable touches the ground.
Using the Pythagorean theorem, we can establish the following relationship:
\(AB^2 + BC^2 = AC^2\)
Substituting the given values, we get:
\(h^2 + 48^2 = 80^2\\h^2 + 2304 = 6400\\h^2 = 6400 - 2304\\h^2 = 4096\)
Taking the square root of both sides, we find:
h =\(\sqrt{4096}\)
h ≈ 64
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A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What percent of scores are between 42 and 58?A.100%B. about 95.4%C. about 23.85%D. about 47.7%
Step 1. The information that we have is:
The mean:
\(\mu=50\)The standard deviation:
\(\sigma=4\)Step 2. To solve this problem and find what percent of scores are between 42 and 58, we use the empirical rule:
• The empirical rule for normally distributed data tells us that about 68% of the data falls under 1 standard deviation from the mean, about 95% falls under 2 standard deviations from the mean, and 99.7% of the data falls under 3 standard deviations from the mean.
Step 3. The following diagram represents the situation:
The marks on the graph are calculated as follows:
\(\begin{gathered} \mu-\sigma=50-4=46 \\ \mu+\sigma=50+4=54 \\ \mu+2\sigma=50-2\cdot4=50-8=58 \\ \mu-2\sigma=50-2\times4=50-8=42 \end{gathered}\)This is represented in the image:
Step 4. As you can see in the previous graph, 42 and 58 are 2 standard deviations away from the mean, this means that about 95% of the data will be between those values.
The option closest to 95% is B. about 95.4%
Answer: B. about 95.4%
For the function y=4x^2+7x+2, at the point x=4, find the following. (a) the slope of the tangent to the curve (b) the instantaneous rate of change of the function
A. The slope of the tangent to the curve at x=4 is 39.
B. The instantaneous rate of change of the function at x=4 is also 39.
To find the slope of the tangent to the curve at the point x=4, we need to calculate the derivative of the function with respect to x and evaluate it at x=4.
(a) Slope of the tangent:
To find the derivative of the function y=4x^2+7x+2, we can differentiate each term separately using the power rule.
dy/dx = d/dx (4x^2) + d/dx (7x) + d/dx (2)
dy/dx = 8x + 7
Now, we can evaluate the derivative at x=4:
Slope of the tangent at x=4 = dy/dx at x=4 = 8(4) + 7 = 39
Therefore, the slope of the tangent to the curve at x=4 is 39.
(b) Instantaneous rate of change:
The instantaneous rate of change of a function is given by the derivative of the function.
Instantaneous rate of change at x=4 = dy/dx at x=4 = 8(4) + 7 = 39
Therefore, the instantaneous rate of change of the function at x=4 is also 39.
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Omar invests £6000 for 4 years in a savings account. He will get 1.5 % per year compound interest. Work out the total amount of that will be in Omar accounts by the end of the 4 years. Round your answer to the nearest pound.
The answer is either
6361
6369
6360
Or 6368
Answer:
£6368
Step-by-step explanation:
You can start by making a formula, which will be:
100/100=1
1.5/100=0.015
1+0.015=1.015 (your multiplyer)
6000*1.015^n= your money after 4 years
(n represents the number of years)
Now you just put in the number of years:
6000*1.015^4=6368.181304
Now round:
Answed= £6368
the quotient of f and 6
The answer is 6 divided by f
sannie =w=
Product of 4h × 5m is what
Answer:
20hm
Step-by-step explanation:
→ Remember rule a × b = ab
4h × 5m = 20hm
how do I write an equation for a quadratic function represented by a table ?
Answer:
Hello There!!
Step-by-step explanation:
Firstly,select three ordered pairs from the table. Secondly,substitute the first pair of values in to the form of the quadratic equation: f(x) = ax^2 + bx + c and then solve for a.
hope this helps,have a great day!!
~Pinky~
What the midpoint ?
The midpoint formula:
\( \large \boxed{( \frac{x_2 + x_1}{2} , \frac{y_2 + y_1}{2} )}\)
From the graph, the point starts from (-3,2) and ends at (4,-1).
Substitute these points in the formula.
\( \large{( \frac{ - 3 + 4}{2} , \frac{2 - 1}{2}) = ( \frac{1}{2} , \frac{1}{2} )}\)
Hence the midpoint is (1/2,1/2)
Answer
(1/2,1/2) is the midpoint.HELPP FAST IS IT RIGHT
Answer:
Yes it is
Step-by-step explanation:
For a science project, Chase recorded the amount of rainfall for 6 weeks. The line plot shows the amounts of rainfall he recorded. How many inches of rainfall were recorded? (this was to hard to do by myself)
Answer:
2(3/8) + 4/8 + 5/8 + 7/8
= 6/8 + 4/8 + 5/8 + 7/8 = 22/8 = 2 6/8
B is correct.
Help please!!! ASAPPPP
It should be noted that z^4 will be -32 in rectangular form.
How to calculate the valueBased on the information, z = r(cos θ + i sin θ), and provided positive integer n, then it is implied that:
z^n = r^n (cos nθ + i sin nθ)
In this instance, we need to solve for z^4 in rectangular form when z = -2 - 2i. Firstly, we must calculate |z| and arg(z):
|z| = √((-2)^2 + (-2)^2) = 2√2
arg(z) = arctan(-2/-2) = π/4
Leveraging De Moivre's theorem, we can effectively deduce the value of z^4 as:
z^4 = (2√2)^4 (cos (4π/4) + i sin (4π/4))
= 32 (cos π + i sin π)
= -32
Concludedly, z^4 resolved in rectangular form is -32.
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Determine the function which corresponds to the given graph. (3 points)
The asymptote is x = -3.
Answer:
linear graph
Step-by-step explanation:
(depends)
The first three terms of an arithmetic sequence are as follows.
-8, -5, -2
Find the next two terms of this sequence.
-8, -5, -2,
Answer:
1, 4
Step-by-step explanation:
to find the next term in an arithmetic sequence add the common difference d to the previous term.
d = a₂ - a₁ = - 5 - (- 8) = - 5 + 8 = 3
then
a₄ = a₃ + d = - 2 + 3 = 1
a₅ = a₄ + d = 1 + 3 = 4
the next two terms are 1, 4
how to determine if a relation is a function calculator
Answer:
A relation is defined as the collection of inputs and outputs which are related to each other in some way. In case, if each input in relation has accurately one output, then the relation is called a function.
Based on the given relation, we found that it is not a function because it has repeating x-values. Remember, for a relation to be a function, each input (x-value) must correspond to exactly one output (y-value).
To determine if a relation is a function, you need to check if each input (x-value) corresponds to exactly one output (y-value). You can use the following steps:
1. Identify the given relation as a set of ordered pairs, where each ordered pair represents an input-output pair.
2. Check if there are any repeating x-values in the relation. If there are no repeating x-values, move to the next step. If there are repeating x-values, the relation is not a function.
3. For each unique x-value, check if there is only one corresponding y-value. If there is exactly one y-value for each x-value, then the relation is a function. If there is more than one y-value for any x-value, then the relation is not a function.
Let's consider an example relation: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 1: Identify the relation as a set of ordered pairs: {(1, 2), (2, 3), (3, 4), (2, 5)}.
Step 2: Check for repeating x-values. In our example, we have a repeating x-value of 2. Therefore, the relation is not a function.
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Consider functions f and g. f(x)=3 x+1What is the value of f(g(1))
Step-by-step explanation:
f(1)=(3×1)+1=4
so f(g(1)=4