Answer: D
Step-by-step explanation:
i think so
A psychologist theorized that people could hear better when they have just eaten a large meal. Twenty individuals were randomly assigned to eat either a large meal or a small meal. After eating the meal, their hearing was tested. Assuming hearing ability was measured on an interval scale and that the scores were normally distributed, the research hypothesis would be ________ and the most appropriate statistic for testing the research hypothesis would __________
A. non-directional; t-test for independent means
B. directional; t-test for independent means
C. non-directional; t-test for dependent means
D. directional; t-test for dependent means
The correct research hypothesis and distribution is directional, t-test for independent means.
What is the research hypothesis?The research hypothesis that "people can hear better when they have just eaten a large meal" is a directional hypothesis because it predicts the direction of the effect (i.e., hearing ability will improve after a large meal).
The appropriate statistical test to use would be a t-test for independent means, which compares the means of two independent groups to determine if there is a statistically significant difference between them.
Therefore, the correct answer is B. Directional; t-test for independent means.
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Find the maximum/minimum value of the quadratic function q² + 22q = y - 85 by
completing the square method.
O-36
O-48
C
-24
-64
Step-by-step explanation:
To find the maximum/minimum value of the quadratic function q² + 22q = y - 85, we can complete the square as follows:
q² + 22q = y - 85
q² + 22q + 121 = y - 85 + 121 (adding (22/2)² = 121 to both sides)
(q + 11)² = y + 36
Now, we have a square of a binomial on the left side, which means the minimum value of the quadratic function is y + 36, and it occurs when (q + 11) = 0. Thus, the minimum value is:
y + 36 = 36 - 85 = -49
Similarly, the maximum value of the quadratic function occurs when (q + 11) = 0, but this time the value of y will be as large as possible. The largest possible value of y occurs when STU is a permutation of the digits 9, 8, and 7 (since PQR must be 4, 0, and 3 in some order). Thus, the maximum value is:
y + 36 = 9 + 8 + 7 - 85 + 36 = -25
Therefore, the options are incorrect and the correct answers are:
Minimum value: -49
Maximum value: -25
Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. (Round your answer to three decimal places.)
Answer:
1.066 (3 d.p.)
Step-by-step explanation:
The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:
[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]
where:
r(x) is the distance from the axis of rotation to x.h(x) is the height of the solid at x (the height of the shell).[tex]\hrulefill[/tex]
We want to find the volume of the solid formed by revolving a region, R, around the y-axis, where R is bounded by:
[tex]y=\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}[/tex]
[tex]y=0[/tex]
[tex]x=0[/tex]
[tex]x=1[/tex]
As the axis of rotation is the y-axis, r(x) = x.
Therefore, in this case:
[tex]r(x)=x[/tex]
[tex]h(x)=\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}[/tex]
[tex]a=0[/tex]
[tex]b=1[/tex]
Set up the integral:
[tex]\displaystyle 2\pi \int^{1}_0x \cdot\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
Take out the constant:
[tex]\displaystyle 2\pi \cdot \dfrac{1}{\sqrt{2\pi}}\int^{1}_0x \cdot e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
[tex]\displaystyle \sqrt{2\pi}\int^{1}_0x \cdot e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
Integrate using the method of substitution.
[tex]\textsf{Let}\;u=-\dfrac{x^2}{3}\implies \dfrac{\text{d}u}{\text{d}x}=-\dfrac{2x}{3}\implies \text{d}x=-\dfrac{3}{2x}\;\text{d}u[/tex]
[tex]\textsf{When}\;x=0 \implies u=0[/tex]
[tex]\textsf{When}\;x=1 \implies u=-\dfrac{1}{3}[/tex]
Rewrite the original integral in terms of u and du:
[tex]\displaystyle \sqrt{2\pi}\int^{-\frac{1}{3}}_0x \cdot e^{u}\cdot -\dfrac{3}{2x}\;\text{d}u[/tex]
[tex]\displaystyle \sqrt{2\pi}\int^{-\frac{1}{3}}_0 -\dfrac{3}{2}e^{u}\; \text{d}u[/tex]
[tex]-\dfrac{3\sqrt{2\pi}}{2}\displaystyle \int^{-\frac{1}{3}}_0 e^{u}\; \text{d}u[/tex]
Evaluate:
[tex]\begin{aligned}-\dfrac{3\sqrt{2\pi}}{2}\displaystyle \int^{-\frac{1}{3}}_0 e^{u}\; \text{d}u&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^u\right]^{-\frac{1}{3}}_0\\\\&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^{-\frac{1}{3}}-e^0\right]\\\\&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^{-\frac{1}{3}}-1\right]\\\\&=1.06582594...\\\\&=1.066\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the solid is approximately 1.066 (3 d.p.).
[tex]\hrulefill[/tex]
[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x(+\;\text{C})$\end{minipage}}[/tex]
Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin
The coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.
How to find dilated coordinate of A and B?To find the coordinates of the points A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:
[tex]$$(x', y') = (5(x - 0), 5(y - 0)) = (5x, 5y)$$[/tex]
where (x, y) are the original coordinates of the point, and (x', y') are the new coordinates after the dilation.
For point A(1, 2), the new coordinates A' are:
[tex]$$(x_A', y_A') = (5(1), 5(2)) = (5, 10)$$[/tex]
Therefore, the coordinates of point A' are (5, 10).
For point B(-2, -1), the new coordinates B' are:
[tex]$$(x_B', y_B') = (5(-2), 5(-1)) = (-10, -5)$$[/tex]
Therefore, the coordinates of point B' are (-10, -5).
Therefore, the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.
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For the graph, find the average rate of change on the intervals given
See attached picture b
We cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function.
Define the term graph?The visual representation of mathematical functions or data points on a Cartesian coordinate system is an x-y axis graphic. The vertical or dependent variable is represented by the y-axis, while the horizontal or independent variable is represented by the x-axis. The difference between the change in output values and the change in input values is known as the average rate of change of a function over a period.
Let's assume that the function is denoted by f(x). Then, the average rate of change on the interval (a, b) can be calculated as
average rate of change = (f(b) - f(a)) / (b - a)
Using this formula, we can calculate the average rate of change on the given intervals as follows:
For the interval (-3, -2):
average rate of change = [tex]\frac{[f(-2) - f(-3)]}{[-2 - (-3)]}[/tex]
For the interval (1, 3):
average rate of change = [tex]\frac{(f(3) - f(1))}{(3 - 1)}[/tex]
For the interval (-1, 1):
average rate of change = [tex]\frac{(f(1) - f(-1))}{ (1 - (-1))}[/tex]
Note that we cannot determine the actual value of the average rate of change without knowing the function f(x) or having a graph of the function. If you provide the function or the graph, I can help you find the actual values of the average rate of change on these intervals.
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What the values of angles B and C?
The value of b is 73° as opposite angles of congruent sides are equal in an isosceles triangle.
What dοes a math angle mean?An angle is created by cοmbining twο rays (half-lines) that have a cοmmοn terminal. The angle's vertex is the latter, while the rays are alternately referred tο as the angle's legs and its arms.
What is fundamental angle?An angle within a shape that has the shape's base as οne οf its sides is knοwn as the base angle οf a shape in geοmetry. Cοnsider the triangle in the image as an example. We can οbserve that the triangle's base side is made up οf an angle B side and an angle C side. As a result, the triangle's base angles are angles B and C.
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Find all the values of
arcsin −√3/2
Select all that apply:
a.π3
b.5π6
c.11π6
d.5π3
e.2π3
f.7π6
g.4π3
Answer:
g
Step-by-step explanation:
The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.
Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2
However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.
In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:
sin(π - π/3) = sin(2π/3) = √3/2
This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:
sin(π + π/3) = sin(4π/3) = -√3/2
This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.
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Answer:
We know that sin(π/3) = √3/2, so we can write:
arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ
where n is an integer.
Therefore, the values of arcsin(-√3/2) are:
a. π/3 + 2nπ
c. 11π/6 + 2nπ
e. 2π/3 + 2nπ
f. 7π/6 + 2nπ
So, options a, c, e, and f are all correct.
Brianna Wallen lives in Denver, Colorado, where the rate of assessment is 29% of market value. The tax rate is 81.16 mills. The county tax assessor determined that the market value of her home is $438,300. What is the real estate tax on her home?
Step 1 Find the assessed value. Step 2 Express the tax rate as a decimal. Step 3 Find the real estate tax
The real estate tax on Brianna Wallen's home is $37,934.83.
What is property tax?Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.
The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.
The tax is calculated using the given formula:
Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)
Substituting the given values we have:
Tax = (0.29 x $438,300) x (81.16 / 1000)
Tax = $37,934.83
Hence, the real estate tax on Brianna Wallen's home is $37,934.83.
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My little cousin needs help with this can anyone help please.
I’m busy with my tests and I don’t have the time to explain.
Answer:
I don't knowI am sorry I will let someone else answer
Step-by-step explanation:
What is the meaning of "the homotopy classes of paths from x to x in a space X"?
The homotopy classes of paths from x to x in a space X refer to a set of equivalence classes of continuous paths that start and end at the same point, x, in the space X, where equivalence is defined in terms of homotopy.
What is the homotopy about?In other words, for any two paths, there exists a continuous transformation (called a homotopy) between them such that the endpoints remain fixed. Two paths are said to be homotopic if they can be continuously deformed into each other while keeping their endpoints fixed. The set of all paths that are homotopic to each other forms an equivalence class.
The homotopy classes of paths from x to x are important in algebraic topology, as they provide a way to study the topological structure of a space by analyzing the properties of the paths within it. They can also be used to define higher algebraic structures such as the fundamental group and higher homotopy groups.
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construct shear and bending diagrams for the following beams. show your equations used to create the plots. p p p p l/2 l/4 l/4 p p p l/3 l/3 l/3
The shear force and bending moment diagrams for the given beam will have multiple segments of different shapes and slopes, reflecting the variation of loads along the length of the beam.
To construct the shear and bending diagrams for the given beam, we need to analyze the beam for the different sections where the load is applied. We can break down the beam into five sections:
Leftmost section (0 ≤ x ≤ L/4)
Second section (L/4 < x ≤ L/2)
Third section (L/2 < x ≤ 5L/12)
Fourth section (5L/12 < x ≤ 7L/12)
Rightmost section (7L/12 < x ≤ L)
We can use the equations for shear and bending moments to create the plots:
For section 1: 0 ≤ x ≤ L/4
The shear force diagram will be constant since there is no load applied in this section. The bending moment diagram will be a sloping line, which will be zero at x = 0 and will increase linearly with x as we move toward the right end of the section.
For section 2: L/4 < x ≤ L/2
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a maximum value at the midpoint of the section.
For section 3: L/2 < x ≤ 5L/12
The shear force diagram will start from the value of P at x = L/4 and remain constant up to x = L/2. At x = 5L/12, a load of P/3 is added, causing the shear force to increase suddenly. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local minimum at x = 5L/12.
For section 4: 5L/12 < x ≤ 7L/12
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. The bending moment diagram will be a cubic curve, which will be zero at x = L/4 and L/2, and will have a local maximum at x = 7L/12.
For section 5: 7L/12 < x ≤ L
The shear force diagram will start from the value of P + P/3 at x = 5L/12 and remain constant up to x = 7L/12. At x = L/3, a load of P/3 is added, causing the shear force to decrease suddenly. The bending moment diagram will be a parabolic curve, which will be zero at x = L/4 and L/2 and will reach a minimum value at the midpoint of the section.
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. If h> 3 and h - 2g= 0, which of
the following must be true?
A. g> 2.5
B. g> 1.5
C. g <0.5
D. g <1.5
E. g>2
By linear equality , g >1.5 is must be true.
What are equality and inequality along a line?
Equal (=) is the symbol used in linear equations. Example. Using the inequality symbols (>,, is greater than or equal to, and is less than or equal to), linear inequalities are expressed.
x - 5 > 3x - 10 is an illustration of a linear inequality. As the larger than symbol is employed in this inequality, the LHS is strictly greater than the RHS. After being solved, the inequality appears as 2x 5 x (5/2).
If h> 3 and h - 2g= 0
H=2g
2g>3
g >1.5
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The population of a certain city was 3,846 in 1996. It is expected to decrease by about 0.27% per year. Write an exponential decay function, and use it to approximate the population in 2022.
Answer:
To write an exponential decay function for this situation, we can use the formula:
P(t) = P₀e^(rt)
where:
P(t) = the population at time t
P₀ = the initial population
r = the annual rate of decrease (as a decimal)
t = time in years
We are given P₀ = 3,846 and r = -0.0027 (since the population is decreasing).
To approximate the population in 2022, we need to find t, the number of years from 1996 to 2022. That is:
t = 2022 - 1996 = 26 years
Now we can plug in the values we have:
P(t) = 3,846 e^(-0.0027t)
To find P(2022), we plug in t = 26:
P(26) = 3,846 e^(-0.0027(26))
≈ 3,200.62
Therefore, we can approximate the population of the city in 2022 to be about 3,201 people.
Answer:
3,101
Step-by-step explanation:
Please hit brainliest if this helped!
To write an exponential decay function for the population of the city, we can use the formula:
P(t) = P₀e^(-rt)
where P(t) is the population at time t, P₀ is the initial population, r is the decay rate, and e is the base of the natural logarithm.
In this problem, P₀ = 3,846 and r = 0.0027 (0.27% expressed as a decimal). We want to find the population in 2022, which is 26 years after 1996.To use the formula, we need to convert 26 years to the same time units as the decay rate. Since the decay rate is per year, we can use 26 years directly. Therefore, the exponential decay function for the population is:
P(t) = 3,846e^(-0.0027t)
To find the population in 2022 (t = 26), we substitute t = 26 into the function:
P(26) = 3,846e^(-0.0027*26) ≈ 3,101
Therefore, the population in 2022 is approximately 3,101.
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show that the properties of a probability distribution for a discrete random variable are satisfied.
The properties of a probability distribution for a discrete random variable ensure that the probabilities assigned to each possible value of the variable are consistent with the axioms of probability and allow for meaningful inference and prediction.
The properties of a probability distribution for a discrete random variable are.
The probability of each possible value of the random variable must be non-negative.
The sum of the probabilities of all possible values must equal 1.
The probability of any event A is the sum of the probabilities of the values in the sample space that correspond to A.
These properties are satisfied because the probabilities of each possible value of a discrete random variable are defined in such a way that they are non-negative and sum to 1. Additionally, any event A can be expressed as a collection of possible values of the random variable, and the probability of A is then computed as the sum of the probabilities of those values.
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Change the following equation of a line into slope-intercept form.
y + 4 = 2x
Answer:
Step-by-step explanation:
[tex]y=2x-4[/tex] (slope-intercept form is [tex]y=mx+b[/tex] where m=gradient
and b is where line intercepts y-axis)
let be the space spanned by the two functions and . find the matrix of the linear transformation from into itself with respect to the basis .
When space is spanned by the two functions of linear transformation from into itself with respect to the basis we need to apply T to each basis vector vi to get the column vectors T(vi) = [T(vi)]B.
where [T(vi)]B is the coordinate vector of T(vi) with respect to the basis B. Arrange the column vectors [T(v1)]B, [T(v2)]B, ..., [T(vn)]B into a matrix. This matrix is the matrix of T with respect to the basis B.
In this case, you have two functions that span a vector space, so you need to specify the basis B. Once you have chosen the basis, you can apply the above steps to find the matrix of the linear transformation.
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Michelle and Robert constructed a wooden bridge for ATVs over a deep creek on the edge of their property. To recuperate the cost of the materials, they decided to charge an annual toll of $8 to each of the 120 members of a local club. A survey showed that for every $1 the toll is increased, 4 members wouldn't use the bridge anymore. What is the best toll charge to allow them to recuperate the cost of the materials the fastest?
Answer:
the answer is $10
Step-by-step explanation:
trust that
I will mark you brainiest!
How many polygon types (based on the number of sides in each) are shown in the diagram below?
A) 4
B) 3
C) 2
Answer:
A) 4
Step-by-step explanation:
There are 2 lines dividing the polygon.
The first two on the top are triangles.
The two on the bottom are irregular polygons.
Added up, that's 4 polygons according to the line distribution.
Math
rade> Y.9 Solve two-step equations: complete the solution GK7
2(p+ 4) = 12
P + 4 =
Social studies
Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
Р
Submit
Recommendations
Divide both sides by 2
Subtract 4 from both sides
P = 2 is the answer to the equation 2(p + 4) = 12.
Is it an equation or an expression?An expression is made up of a number, a variable, or a combination of a number, a variable, and operation symbols. Two expressions are combined into one equation by using the equal symbol. For illustration: When you add 8 and 3, you get 11.
Divide the two among the terms between the parenthesis:
2p + 8 = 12
Add 8 to both sides of the equation, then subtract 8:
2p + 8 - 8 = 12 - 8
2p = 4
multiply both sides by two:
2p/2 = 4/2 \sp = 2
p = 2 is the answer to the equation 2(p + 4) = 12 as a result.
Simply put p = 2 back into the equation and simplify to obtain p + 4:
[tex]p + 4 = 2 + 4 = 6[/tex]
Hence, p + 4 = 6.
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Find the derivative of f(x) = -2x^3 by the limit process…
Answer:
f'(x) = -6x^2
f'(-5) = -150
f'(0) = 0
f'(√17) = -102
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than 0.28°C. Round your answer to 4 decimal places
The probability of obtaining a reading greater than 0.28°C is 0.3897.
What is standard normal distribution ?
The standard normal distribution is a specific type of probability distribution that has a mean of 0 and a standard deviation of 1. It is also called the Z-distribution or the Gaussian distribution.
The standard normal distribution is commonly used in statistics and probability theory to make comparisons and calculations across different normal distributions. To use the standard normal distribution for calculations involving a normal distribution with a different mean and standard deviation, the data must be standardized by subtracting the mean and dividing by the standard deviation.
According to the question:
To solve this problem, we need to standardize the value of 0.28°C using the standard normal distribution formula:
z = (x - mu) / sigma
where:
x = 0.28°C
mu = 0°C
sigma = 1.00°C
Substituting the values, we get:
z = (0.28 - 0) / 1.00
z = 0.28
Now, we need to find the probability of obtaining a reading greater than 0.28°C, which is the same as finding the area to the right of z = 0.28 on the standard normal distribution curve. We can use a standard normal distribution table or calculator to find this area.
Using a calculator or software, we find that the probability of obtaining a reading greater than 0.28°C is 0.3897, rounded to 4 decimal places.
Therefore, the probability of obtaining a reading greater than 0.28°C is 0.3897.
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PLEASE HELP ME!!! Type the correct answer in each box. Use T for true and F for false.
Complete the truth table for the contrapositive of a conditional statement.
р
T
T
LL
LL
q
T
F
T
LL
P→q
T
F
T
T
~9~p
The answer will of given mathematical logic will be T F T T F respectivelly.
What fundamental ideas underlie mathematical logic?A negation, conjunction, and disjunction are the fundamental mathematical logics. The symbols for negation, conjunction, and disjunction in mathematical logic are "," "," and "v," respectively.
What is the purpose of mathematical logic?Logical proofs frequently employ mathematical logic. Proofs are legitimate arguments that establish the veracity of mathematical assertions. A series of statements make up an argument. The conclusion is the last assertion, and the premises are all the statements that came before it (or hypothesis).
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The complete truth table is shown in the below diagram.
≈ q → ≈ p: True False True True
Define the conditional statement for contrapositive?The contrapositive of a conditional statement is a new conditional statement that is formed by negating both the hypothesis (the "if" part) and the conclusion (the "then" part) of the original statement, and switching their positions. The truth table for the contrapositive of a conditional statement has the same number of rows as the truth table for the original statement.
For example, if the original statement is "If it is raining, then the ground is wet", then the contrapositive would be "If the ground is not wet, then it is not raining."
According to the given table the contrapositive of a conditional statement q and p is defines as;
True
False
True
True
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How do you write 0.048 as a percentage?
Write your answer using a percent sign (%).
Answer:
0.048 in %
Step-by-step explanation:
firstly: remove the decimal point
= 48/1000
secondly : Simplify
48/1000*100
=48/10
=4.8%
The cost of manufacturing a molded part is related to the quantity produced during a production run. When 100 parts are produced, the cost is $300. When 104 parts are
produced, the cost is $324. What is the average cost per part?
OA $0.23 per part
B. $6 per part
OC. $0.17 per part
OD. $7 per part
Answer:
B. $6 per part
Step-by-step explanation:
The average cost per part can be computed as follows
Average Cost = (324-300)/(104-100)
= 24/4
=$6
Answer: B. $6 per part
Question 2 of 3
Which subtraction equation shows how to subtract
4
2
12
−
2
8
12
using equivalent fractions? i need help
Answer:
Step-by-step explanation:
your given is not cleared repost it then post
can someone please help me asap!!! ill mark brainlistt...
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the length of two sides of the triangle (the legs) and we need to find the length of the hypotenuse.
Let's label the sides of the triangle:
The shorter leg is the vertical side opposite the angle marked 55 degrees, so let's call it "a".
The longer leg is the horizontal side adjacent to the angle marked 55 degrees, so let's call it "b".
The hypotenuse is the side opposite the right angle, so let's call it "c".
Using trigonometry, we can determine the value of "a" and "b":
a = b * tan(55°) (since tangent = opposite/adjacent, we solve for opposite which is "a" in this case)
a = 100 * tan(55°) = 100 * 1.428 = 142.8
b = 100
Now, we can use the Pythagorean theorem to find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 142.8^2 + 100^2
c^2 = 20484.84 + 10000
c^2 = 30484.84
c = sqrt(30484.84)
c ≈ 174.6
Therefore, the length of the hypotenuse is approximately 174.6 units (the units are not given in the problem, but we can assume they are consistent with the units used for the given values of "a" and "b").
The problem does not specify the orientation or scale of the graph, but we can assume that it is a right triangle with the angle marked 55 degrees in the upper left corner.
The vertical side (the shorter leg) of the triangle should be labeled with a length of approximately 142.8 units (assuming the units used for the problem are consistent with the values given for "a" and "b"). The horizontal side (the longer leg) should be labeled with a length of 100 units.
The hypotenuse (the side opposite the right angle) should be drawn as a diagonal line connecting the endpoints of the vertical and horizontal sides. The hypotenuse should be labeled with a length of approximately 174.6 units.
The angle marked 55 degrees should be labeled as such, and the other two angles of the triangle (the right angle and the angle opposite the longer leg) should be labeled accordingly.
Let Vector r = LeftAngleBracket 4, negative 2, 1 RightAngleBracket.and Vector r = LeftAngleBracket 3, 4, negative 1 RightAngleBracket.. Select the graph that shows the correct representation of Vector r + vector s. and select the correct magnitude of the resulting vector. Check all that apply.
Use the vector law of addition to get the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].
What is the resulting vector and its magnitude?
Vector addition can be defined as the sum of two or more vectors of corresponding components.
It is given that,
[tex]\vec{r}= < 4, -2 > \\\vec{s}= < 3,4,-1 >[/tex]
Given vectors can also be written as,
[tex]\vec{r}=4i-2j\\\vec{s}=3i+4j-k[/tex]
Add above vectors as follows:
[tex]\vec{r}+\vec{s}=(4i-2j)+(3i+4j-k)\\\\=(7i+2j-k)[/tex]
Therefore,
[tex]\vec{r}+\vec{s}= < 7,2,-1 >[/tex]
Show the resulting vector as follows:
Now calculate the magnitude of the vector [tex](\vec{r}+\vec{s})[/tex]
[tex]|\vec{r}+\vec{s}|=\sqrt{(7)^2+(2)^2+(-1)^2}\\=\sqrt{49+4+1}\\=\sqrt{54}\\=3\sqrt{6}[/tex]
Hence the resulting vector is [tex](7i+2j-k)[/tex] and magnitude of resulting vector is [tex]3\sqrt{6}[/tex].
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G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5
Answer:
Math Quotient Verification
G For each ordered pair, determine whether it is a solution to the system of equations. 9x+2y=-5 2x-3y=-8 (x, y) (1, -7) (0, -4) (5,6) (-1,2) Is it a solution? Yes No X 5
To check if an ordered pair is a solution to a system of equations, we substitute the values of x and y into both equations and see if both equations are satisfied.
Let's check each ordered pair one by one:
(1, -7):
9x + 2y = -5 becomes 9(1) + 2(-7) = -5, which is false.
2x - 3y = -8 becomes 2(1) - 3(-7) = -8, which is true.
Therefore, (1, -7) is not a solution to the system of equations.
(0, -4):
9x + 2y = -5 becomes 9(0) + 2(-4) = -8, which is false.
2x - 3y = -8 becomes 2(0) - 3(-4) = 12, which is false.
Therefore, (0, -4) is not a solution to the system of equations.
(5, 6):
9x + 2y = -5 becomes 9(5) + 2(6) = 41, which is false.
2x - 3y = -8 becomes 2(5) - 3(6) = -8, which is true.
Therefore, (5, 6) is not a solution to the system of equations.
(-1, 2):
9x + 2y = -5 becomes 9(-1) + 2(2) = -11, which is false.
2x - 3y = -8 becomes 2(-1) - 3(2) = -8, which is true.
Therefore, (-1, 2) is not a solution to the system of equations.
Therefore, the answer is "No" for all the ordered pairs given in the problem.
(please mark my answer as brainliest)
do you mind helping me with this?
Answer:
125
Step-by-step explanation:
We Take
625 / 5 = 125
So, the answer is 125
to calculate the workload of a resource that serves different flow unit types, one must know which of the following?
The workload of the resource is 20.5 units.
To calculate the workload of a resource that serves different flow unit types, one must know the amount of flow units, the processing time for each flow unit, and the number of resources available. This is best calculated using Little's Law, which states that the average number of flow units in a system is equal to the average rate of flow units multiplied by the average time they spend in the system.
For example, if a resource is serving 3 flow unit types, A, B and C, with 10, 8 and 5 units respectively, and a processing time of 2 minutes, 1 minute and 3 minutes respectively, with 2 resources available, the workload can be calculated as follows:
Workload = (10*2 + 8*1 + 5*3) / 2
= 41 / 2
= 20.5 units
Therefore, the workload of the resource is 20.5 units.
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Complete question
What are the flow unit types that the resource is serving?