Answer:
Is needed 16 fluid oz of water to fill in 2 cups of water
Step-by-step explanation:
1 cup have 8 fluid oz
2 cups = 2 * 8 fluid oz = 16 fluid oz
Final answer:
The recipe requires 2 cups of water, which is equivalent to 16 fluid ounces since there are 8 fluid ounces in one cup.
Explanation:
To calculate how many fluid ounces of water is needed if a recipe requires 2 cups of water, you need to understand the unit equivalence between cups and fluid ounces. One cup is equivalent to 8 fluid ounces. Since the recipe requires 2 cups, you will multiply the number of cups by the unit equivalence to find the total number of fluid ounces.
Here is the calculation:
2 cups × 8 fluid ounces/cup = 16 fluid ounces
Therefore, the recipe requires 16 fluid ounces of water.
A diver's elevation is -5 feet relative to sea level. A
school of fish is swimming at an elevation of -12 feet.
What is the difference in elevation between the diver
and the school of fish?
Answer:
-7 feet
Step-by-step explanation:
To find the difference in elevation between the diver and the school fish SUBTRACT the elevation of the diver from that of the fish
i.e. difference in elevation = -12 - (-5)
= -12 + 5
= -7 feet
Final answer:
The difference in elevation between the diver at -5 feet and the school of fish at -12 feet is 7 feet, calculated by taking the absolute value of their elevations' difference.
Explanation:
The question asks for the difference in elevation between a diver and a school of fish, with the diver at -5 feet and the fish at -12 feet relative to sea level. To find the difference in elevation, you subtract the diver's elevation from the fish's elevation.
Here is the calculation:
School of fish elevation: -12 feetDiver's elevation: -5 feetDifference in elevation: |-12 - (-5)| = |-12 + 5| = |-7| = 7 feetThe absolute value is used because we are interested in the positive difference in elevation, which is the distance between the two elevations regardless of direction.
Therefore, the difference in elevation between the diver and the school of fish is 7 feet.
Nancy thinks the answer to the question 1/4 divided by -2/3 is 3/8 is next correct explain why or why not be sure to use complete sentences
Answer:
Her sign is in error. The answer is -3/8.
Step-by-step explanation:
Nancy's answer has the correct magnitude. It is obtained by multiplying 1/4 by -3/2. However, the sign of that product will be negative. Nancy has reported a positive answer, so it is incorrect.
Describe the differences between a histogram and a stem-and-leaf display. Check All That Apply A stem-and-leaf display describes the individual observations. A stem-and-leaf display describes the individual observations. A histogram describes the individual observations. A histogram describes the individual observations. A histogram has slightly more information than a stem-and-leaf. A histogram has slightly more information than a stem-and-leaf. A stem-and-leaf display has slightly more information than a histogram.
Answer:
Step-by-step explanation:
A steam and leaf plot is the arrangement of numerical data into different groups with place value. For eg, 17,20,21 is shown as
stem leaf
1 7
2 0,1
A histogram is a bar chart that described frequency distribution.
A stem and leaf plot displays more information than a histogram.
Hence we have the correct answers are:
A stem-and-leaf display describes the individual observations.
A stem-and-leaf display has slightly more information than a histogram.
A stem-and-leaf display provides detailed individual data points and their distribution, while a histogram offers aggregated data into bins, showing the overall data distribution without individual details.
The differences between a histogram and a stem-and-leaf display are significant in how they present data. A stem-and-leaf display retains the individual data values and is beneficial for small datasets, showing the exact values and the frequency of data for each "stem" which provides a clear view of the distribution shape. On the contrary, a histogram groups data into contiguous bins, providing a visual representation of data distribution, showing the spread and most frequent values but without detailing individual data points. Therefore, a stem-and-leaf display has slightly more information than a histogram because it describes individual observations, unlike a histogram that aggregates data into bins.
Proof by Contradiction : Show that √ 2 is irrational.
Answer:
[tex]\sqrt2[/tex] is irrational
Step-by-step explanation:
Let us assume that [tex]\sqrt2[/tex] is rational. Thus, it can be expressed in the form of fraction [tex]\frac{x}{y}[/tex], where x and y are co-prime to each other.
[tex]\sqrt2[/tex] = [tex]\frac{x}{y}[/tex]
Squaring both sides,
[tex]2 = \frac{x^2}{y^2}[/tex]
Now, it is clear that x is an even number. So, let us substitute x = 2u
Thus,
[tex]2 = \frac{(2u)^2}{y^2}\\y^2 = 2u^2[/tex]
Thus, [tex]y^2[/tex]is even, which follows the fact that y is also an even number. But this is a contradiction as x and y have a common factor that is 2 but we assumed that the fraction [tex]\frac{x}{y}[/tex] was in lowest form.
Hence, [tex]\sqrt2[/tex] is not a rational number. But [tex]\sqrt2[/tex] is a an irrational number.
Ax = b: A = ( −2 −1 2 −2 2 3 −4 1 3 ) b = ( −1 −1 4 ) x = ( x1 x2 x3 ) (a) (6 pts) Use the elimination method to find the matrices L and U such that A = LU. (b) (3 pts) Solve the intermediate system Ly = b for the intermediate variable y. (c) (3 pts) Solve the system Ux = y and confirm your solution from Problem 2 above
[tex]\underbrace{\begin{bmatrix}-2&-1&2\\-2&2&3\\-4&1&3\end{bmatrix}}_A\underbrace{\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}}_x=\underbrace{\begin{bmatrix}-1\\-1\\4\end{bmatrix}}_b[/tex]
Multiply [tex]A[/tex] on the left side with the following elimination matrix [tex]E_1[/tex]:
[tex]\underbrace{\begin{bmatrix}1&0&0\\-1&1&0\\-2&0&1\end{bmatrix}}_{E_1}A=\begin{bmatrix}-2&-1&2\\0&3&1\\0&3&-1\end{bmatrix}[/tex]
Multiply [tex]E_1A[/tex] on the left by another elimination matrix [tex]E_2[/tex]:
[tex]\underbrace{\begin{bmatrix}1&0&0\\0&1&0\\0&-1&1\end{bmatrix}}_{E_2}(E_1A)=\begin{bmatrix}-2&-1&2\\0&3&1\\0&0&-2\end{bmatrix}[/tex]
[tex]\implies\boxed{U=\begin{bmatrix}-2&-1&2\\0&3&1\\0&0&-2\end{bmatrix}}[/tex]
Multiply on the left by the inverse of [tex]E_2E_1[/tex]:
[tex](E_2E_1)^{-1}(E_2E_1)A=(E_2E_1)^{-1}U[/tex]
[tex]A=\underbrace{({E_1}^{-1}{E_2}^{-1})}_LU[/tex]
We have
[tex]{E_1}^{-1}=\begin{bmatrix}1&0&0\\1&1&0\\2&0&1\end{bmatrix}[/tex]
[tex]{E_2}^{-1}=\begin{bmatrix}1&0&0\\0&1&0\\0&1&1\end{bmatrix}[/tex]
[tex]\implies\boxed{L=\begin{bmatrix}1&0&0\\1&1&0\\3&1&1\end{bmatrix}}[/tex]
7. When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is "in control" during the period of time in which each sample is selected. Suppose a concrete-block manufacturer samples nine blocks per hour and tests the breaking strength of each. During one-hour’s test, the mean and standard deviation are 985.6 pounds per square inch (psi) and 22.9 psi, respectively. a. Construct a 99% confidence interval for the mean breaking strength of blocks produced
Answer:
A 99% confidence interval for the mean breaking strength of blocks produced is [tex][959.987, 1011.213][/tex]
Step-by-step explanation:
A (1 - [tex]\alpha[/tex])x100% confidence interval for the average break in these conditions It is an interval for the population mean with unknown variance and is given by:
[tex][\bar x -T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}, \bar x +T_{(n-1,\frac{\alpha}{2})} \frac{S}{\sqrt{n}}][/tex]
[tex]\bar X = 985.6psi[/tex]
[tex]n = 9[/tex]
[tex]\alpha = 0.01[/tex]
[tex]T_{(n-1,\frac{\alpha}{2})}=3.355[/tex]
[tex]S = 22.9[/tex]
With this information the interval is determined by:
[tex][985.6 - 3.355\frac{22.9}{\sqrt{9}}, [985.6 - 3.355\frac{22.9}{\sqrt{9}}] = [959.987, 1011.213] [/tex]
Convert 17.42 m to customary units. A.57'-17/8" B. 36-10 1/2" C. 442 1/2" D. 367/8" E. None of these answers is reasonable.
Answer:
Option E - None of these answers is reasonable.
Step-by-step explanation:
To find : Convert 17.42 m to customary units ?
Solution :
The customary units is defined as the measure length and distances in the customary system are inches, feet, yards, and miles.
The options belong to feet and inches.
We have to convert meter into inches, feet.
Meter into feet,
[tex]1 \text{ feet} = 0.3048 \text{ meter}[/tex]
[tex]1 \text{ meter} = \frac{1}{0.3048}\text{ feet}[/tex]
[tex]17.42 \text{ meter} = \frac{17.42}{0.3048}\text{ feet}[/tex]
[tex]17.42 \text{ meter} = \frac{174200}{3048}\text{ feet}[/tex]
[tex]17.42 \text{ meter} =57 \frac{464}{3048}\text{ feet}[/tex]
[tex]17.42 \text{ meter} =57 \frac{58}{381}\text{ feet}[/tex]
Now, Feet into inches
[tex]1 \text{ feet} = 12\text{ inches}[/tex]
[tex] \frac{58}{381} \text{ feet} = 12\times \frac{58}{381}\text{ inches}[/tex]
[tex] \frac{58}{381} \text{ feet} =\frac{232}{381}\text{ inches}[/tex]
i.e. [tex]17.42 \text{ meter} =57\text{ feet }\frac{232}{381}\text{ inches}[/tex]
or [tex]17.42 \text{ meter} =57'\frac{232}{381}''[/tex]
None of these answers is reasonable.
Therefore, Option E is correct.
The clutch linkage on a vehicle has an overall advantage of 24:1. If the pressure plate applies a force of 504lb,how much force must the driver apply to release the clutch.
Answer:
the force that must be applied by the driver to release the clutch is 21 lb
Step-by-step explanation:
Data provided:
clutch linkage on a vehicle has an overall advantage = 24:1
Applied force by the pressure plate = 504 lb
Now,
the advantage ratio is given as:
advantage ratio = [tex]\frac{\textup{Force applied by the pressure plate}}{\textup{Force applied by the driver}}[/tex]
on substituting the respective values, we get
[tex]\frac{\textup{24}}{\textup{1}}[/tex] = [tex]\frac{\textup{504 lb}}{\textup{Force applied by the driver}}[/tex]
or
Force applied by the driver to release the clutch = [tex]\frac{\textup{504 lb}}{\textup24}}[/tex]
or
Force applied by the driver to release the clutch = 21 lb
Hence,
the force that must be applied by the driver to release the clutch is 21 lb
Using the mechanical advantage of the clutch linkage (24:1), the force the driver must apply to release the clutch is calculated to be 21 pounds.
The student has asked about the amount of force a driver must apply to release the clutch in a vehicle, given that the clutch linkage has an overall mechanical advantage of 24:1 and the pressure plate applies a force of 504lb. To find the force the driver needs to apply (Fdriver), we use the relationship provided by the mechanical advantage. Mechanical advantage (MA) is defined as the output force (Fout) divided by the input force (Fdriver). From this, we can formulate the equation MA = Fout / Fdriver, which can be rearranged to solve for the driver's force: Fdriver = Fout / MA.
Substituting the given values:
Fdriver = 504lb / 24
Fdriver = 21lb
Therefore, the driver must apply a force of 21 pounds to release the clutch.
Consider the area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant. (a) Set up the definite integral needed to find the area. (b) Make an appropriate substitution
[tex]y(t)=8\sin(bt)[/tex] has a period of [tex]\dfrac{2\pi}b[/tex], which is to say one "arch" of the curve occurs over the interval [tex]0\le t\le\dfrac\pi b[/tex].
a. Then the area under one such arch is
[tex]\displaystyle\int_0^{\pi/b}8\sin(bt)\,\mathrm dt[/tex]
b. Substitute [tex]u=bt[/tex], so that [tex]\dfrac{\mathrm du}b=\mathrm dt[/tex]. When [tex]t=0[/tex], [tex]u=0[/tex]; when [tex]t=\dfrac\pi b[/tex], [tex]u=\pi[/tex].
Then the integral is
[tex]\displaystyle\frac1b\int_0^\pi8\sin u\,\mathrm du[/tex]
The required area is [tex]\int^{\frac{\pi }{b}}_0 8sin(bt).dt\\[/tex]
The appropriate Substitution is [tex]\dfrac{1}{b} \int^\pi _08sinu.du[/tex]
Given that,
The area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant.
We have to find,
Set up the definite integral needed to find the area.
Make an appropriate substitution.
According to the question,
The area under one arch of the curve y(t) = 8sin(bt) for t ≥ 0 where b is a positive constant.
The curve y(t) = 8sin(bt) has a period of 2π\b, which is one arch of the curve occur over the interval [tex]0\leq t\leq \frac{\pi }{b}[/tex].The area under one arch is given by,
[tex]Area = \int^{\frac{\pi }{b}}_0 8sin(bt).dt\\[/tex]
The required area is [tex]Area = \int^{\frac{\pi }{b}}_0 8sin(bt).dt\\[/tex]
Appropriate Substitute u= bt ,Then,
[tex]\dfrac{du}{b} = dt \\\\when \ t=0, \ and \ u=0\\\\when\ t = \dfrac{\pi }{b}, u = \pi[/tex]
Then,
The required integral is ,
[tex]\dfrac{1}{b} \int^\pi _08sinu.du[/tex]
The appropriate Substitution is [tex]\dfrac{1}{b} \int^\pi _08sinu.du[/tex].
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The numbers 2, 4, 6, and 8 are a set of four consecutive even numbers. Suppose the sum of five consecutive numbers is 320. What is the smallest of the five numbers?
The smallest of five consecutive numbers, whose sum equals 320, is 62. This is determined by setting up an equation where the sum of these numbers equals 320, then solving for the smallest number 'n'.
Explanation:The subject at hand involves understanding patterns within consecutive numbers (numbers that follow each other in order, without gaps). In the given example of four consecutive even numbers 2, 4, 6 and 8, we see that the difference between them is constantly 2.
When it comes to the sum of five consecutive numbers equating to 320, let's presume the first (and smallest) number is 'n'. Therefore, the consecutive numbers would be n, (n+1), (n+2), (n+3) and (n+4). Their sum ought to total 320, so we write the expression n + (n+1) + (n+2) + (n+3) + (n+4) = 320. By simplifying, we receive 5n+10 = 320.
Further simplifying, we subtract 10 from both sides to afford: 5n = 310. Divide 310 by 5 to isolate 'n', which results in 'n' equals 62. Consequently, the smallest of the five consecutive numbers is 62.
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least to greatest
-4/5, -5/4, -4.5, -0.54, -5, -0.4
Answer:
[tex]-5[/tex], [tex]-4.5[/tex], [tex]-\frac{5}{4}[/tex], [tex]-\frac{4}{5}[/tex], [tex]-0.54[/tex] and [tex]-0.4[/tex].
Step-by-step explanation:
We are asked to write the given numbers from least to greatest.
-4/5, -5/4, -4.5, -0.54, -5, -0.4
We know that the more negative number has least value.
Let us convert each number into decimal.
[tex]-\frac{4}{5}=-0.8[/tex]
[tex]-\frac{5}{4}=-1.25[/tex]
We can see that -5 is most negative, so it will be least.
Order from more negative to less negative:
[tex]-5[/tex], [tex]-4.5[/tex], [tex]-1.25[/tex], [tex]-0.8[/tex], [tex]-0.54[/tex] and [tex]-0.4[/tex].
Therefore, the least to greatest numbers would be [tex]-5[/tex], [tex]-4.5[/tex], [tex]-\frac{5}{4}[/tex], [tex]-\frac{4}{5}[/tex], [tex]-0.54[/tex] and [tex]-0.4[/tex].
Given the table below.. Find the following..
a) Find formula for h(t)
b) Find t intercept of function as an ordered pair
c) Find h intercept of function as an ordered pair
Answer:
h(t)=-1/3(x)+50/3
h intercept is (0,50/3)
t intercept is (50,0)
Step-by-step explanation:
Find the slope of the table by using the slope formula then plug in to y-y1=m(x-x1) then solve for y this gives you the formula
sub in y =0 for the x intercept
sub in x=0 for the y intercept
Using data collected between 1957 and 1978, from 15 samples of adults, Professor Rodgers (1982 Social Forces) found that (1) the average level of happiness reported by people under 65 years of age declined from 1957 to 1970. For this same group, the average level of happiness increased slightly from 1970 to 1978. (2) The average level of happiness reported by people age 65 and older increased from 1957 to 1978. A (the) variable(s) in this study is (are)
Answer:
The variable in this study is age.
Step-by-step explanation:
The variable in this study is Age, which has a relationship of cause and effect. Consequently,it is clear that happiness does not depend on the passing of time , but on the age of each group of people.
A = ( −2 −1 2 −2 2 3 −4 1 3 ) b = ( −1 −1 4 ) x = ( x1 x2 x3 ) (a) (2 pts) Write down the augmented matrix (A|b). (b) (4 pts) Use Gauss-Jordan elimination to find the Reduced Row Echelon Form (RREF) of the augmented matrix. (c) (2 pts) What is the rank of A? What is the rank of (A|b) (d) (2 pts) State whether the system is consistent or inconsistent. State how many solutions the system has; if there is/are a solution/s, write it/them down.
Answer:
The augmented matrix is [tex]\left[\begin{array}{ccc|c}-2&-1&2&-1\\-2&2&3&-1\\-4&1&3&4\end{array}\right][/tex]
The Reduced Row Echelon Form of the augmented matrix is [tex]\left[\begin{array}{cccc}1&0&0&-3\\0&1&0&1\\0&0&1&-3\end{array}\right][/tex]
The rank of matrix (A|B) is 3
The system is consistent and the solutions are [tex]x_{1}= -3, x_{2} = 1, x_{3}= -3[/tex]
Step-by-step explanation:
We have the following information:
[tex]A=\left[\begin{array}{ccc}-2&-1&2\\-2&2&3\\-4&1&3\end{array}\right], X=\left[\begin{array}{c}x_{1}&x_{2}&x_{3}\end{array}\right] and \:B=\left[\begin{array}{c}-1&-1&4\end{array}\right][/tex]
1. The augmented matrix is
We take the matrix A and we add the matrix B we use a vertical line to separate the coefficient entries from the constants.
[tex]\left[\begin{array}{ccc|c}-2&-1&2&-1\\-2&2&3&-1\\-4&1&3&4\end{array}\right][/tex]
2. To transform the augmented matrix to the Reduced Row Echelon Form (RREF) you need to follow these steps:
Row operation 1: multiply the 1st row by -1/2[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\-2&2&3&-1\\-4&1&3&4\end{array}\right][/tex]
Row Operation 2: add 2 times the 1st row to the 2nd row[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&3&1&0\\-4&1&3&4\end{array}\right][/tex]
Row Operation 3: add 4 times the 1st row to the 3rd row[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&3&1&0\\0&3&-1&6\end{array}\right][/tex]
Row Operation 4: multiply the 2nd row by 1/3[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&1&1/3&0\\0&3&-1&6\end{array}\right][/tex]
Row Operation 5: add -3 times the 2nd row to the 3rd row[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&1&1/3&0\\0&0&-2&6\end{array}\right][/tex]
Row Operation 6: multiply the 3rd row by -1/2[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&1&1/3&0\\0&0&1&-3\end{array}\right][/tex]
Row Operation 7: add -1/3 times the 3rd row to the 2nd row[tex]\left[\begin{array}{cccc}1&1/2&-1&1/2\\0&1&0&1\\0&0&1&-3\end{array}\right][/tex]
Row Operation 8: add 1 times the 3rd row to the 1st row[tex]\left[\begin{array}{cccc}1&1/2&0&-5/2\\0&1&0&1\\0&0&1&-3\end{array}\right][/tex]
Row Operation 9: add -1/2 times the 2nd row to the 1st row[tex]\left[\begin{array}{cccc}1&0&0&-3\\0&1&0&1\\0&0&1&-3\end{array}\right][/tex]
3. What is the rank of (A|B)
To find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.
Because the row echelon form of the augmented matrix has three non-zero rows the rank of matrix (A|B) is 3
4. Solutions of the system
This definition is very important: "A system of linear equations is called inconsistent if it has no solutions. A system which has a solution is called consistent"
This system is consistent because from the row echelon form of the augmented matrix we find that the solutions are (the last column of a row echelon form matrix always give you the solution of the system)
[tex]x_{1}= -3, x_{2} = 1, x_{3}= -3[/tex]
prove that |a| < b if and only if -b < a < b
Answer:
Since,
[tex]|x|=\left\{\begin{matrix}x &\text{ if } x \geq 0 \\ -x &\text{ if } x < 0\end{matrix}\right.[/tex]
Here, the given equation is,
|a| < b
Case 1 : if a ≥ 0,
|a| < b ⇒ a < b
Case 2 : If a < 0,
|a| < b ⇒ -a < b ⇒ a > - b
( Since, when we multiply both sides of inequality by negative number then the sign of inequality is reversed. )
|a| < b ⇒ a < b or a > - b ⇒ -b < a < b
Conversely,
If -b < a < b
⇒ a < b or a > - b
⇒ a < b or -a < b
⇒ |a| < b
Hence, proved..
Why is a graph that’s symmetric with respect of X-axis is not the graph of function.
Answer:
Because every “x” value has two “y” values.
Step-by-step explanation:
In the graph of a function every value of x has one and only one value of y. So, if we draw a straight line which is parallel to y-axis and it cuts the graph in only one point, this graph will correspond to a function.
In Triangle ABC, angle A is congruent to angle B and
themeasure of angle A is 54. Find the measure of angle C, the value
ofAC and BC.
Answer:
Angle C=72º
Step-by-step explanation:
If two angles are congruent they are equals then angle A is 54º and angle B is 54º and the sum of the internal angles of a triangle is 180º then.
C=180º-54º-54º=72º
To know the value of on AC and BC we have to know the value of the other side AB, to find the values of the sides we can use the law of sines;
[tex]\dfrac{AB}{sin(72)}=\dfrac{BC}{sin(54)}=\dfrac{AC}{sin(54)}[/tex]
Let a,b,,c and x elements in the group G. In each of the following solve for x in terms of a,b,c, and c.
Solve simultaneously x^2 a=bxc^-1 and acx=xac.
Answer with Step-by-step explanation:
We are given that a, b, c and x are elements in the group G.
We have to find the value of x in terms of a, b and c.
a.[tex]x^2a=bxc^{-1}[/tex]
[tex]x^2ac=bxc^{-1}c=bx[/tex]
[tex]x^{-1}x^2ac=x^{-1}bx=b[/tex] ([tex]x^{-1}bx=b[/tex])
[tex]xac=b[/tex]
[tex]xacc^{-1}=bc^{-1}[/tex]
[tex]xa=bc^{-1}[/tex] ([tex]cc^{-1}=[/tex])
[tex]xaa^{-1}=bc^{-1}a^{-1}[/tex]
[tex]x=bc^{-1}a^{-1}[/tex]
b.[tex]acx=xac[/tex]
[tex]acxc^{-1}=xacc^{-1}=xa[/tex] ([tex]cc^{-1}=1,cxc^{-1}=x[/tex])
[tex]axa^{-1}=xaa^{-1}[/tex] ([tex]aa^{-1}=1,axa^{-1}=x[/tex])
[tex]x=x[/tex]
Identity equation
Hence, given equation has infinite solution and satisfied for all values of a and c.
A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 0.02. At the checkpoint, the security system denied a person without security problems 1.5% of the time. Also the security system passed a person with security problems 1% of the time. What is the probability that a random person does not pass through the system and is without any security problems? Report answer to 3 decimal places.
Final answer:
Using the given probabilities, we find that the probability is 0.965, or 96.5%.
Explanation:
To find the probability that a random person does not pass through the system and is without any security problems, we need to calculate the complement of two events: a person being a security hazard and the security system denying a person without security problems.
First, let's calculate the probability of a person being a security hazard:
Probability of a person being a security hazard = 0.02
Next, let's calculate the probability of the security system denying a person without security problems:
Probability of the security system denying a person without security problems = 1.5% = 0.015
To find the probability that a person does not pass through the system and is without any security problems, we can use the formula:
Probability = (1 - probability of being a security hazard) * (1 - probability of the security system denying a person without security problems)
Probability = (1 - 0.02) * (1 - 0.015)
Probability = 0.98 * 0.985
Probability = 0.9653
Therefore, the probability that a random person does not pass through the system and is without any security problems is 0.965, or 96.5% (rounded to 3 decimal places).
Which of the following is equivalent to the set {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}?
(you may select more than one)
Question 4 options:
{x | x is one of the seven wonders of the ancient world}
{x | x is one of the six nobel prize categories}
{x | x is the number of humans who can breathe unassisted underwater}
{x | x is a letter of the alphabet
{x | x is one of the two lead singers of Van Halen}
{x | x is a day of the week}
Answer:
The answer is: {x | x is a day of the week}
Step-by-step explanation:
The mathematical expression {x | x is a day of the week}, uses set theory notation and can be translated as: The set of all x such that x is a day of the week. Since the original set contains all days of the week, therefore it is equivalent to the expression {x | x is a day of the week}.
Final answer:
The correct equivalent set to { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} is {x | x is a day of the week}, as both sets contain the days of the week.
Explanation:
The student has asked which option is equivalent to the set {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}. This set represents the seven days of the week. Therefore, the correct option that is equivalent to this set is {x | x is a day of the week}. All other options listed represent different sets with no connection to the days of the week. When comparing sets for equivalence, we look for a one-to-one correspondence between the members of each set, which is only present in the option directly referring to days of the week.
Convert these decimals into fractions and simplify as much as possible: a) 0.25 b) 0.08 C) 0.400 d) 1.1 e) 3.5
Answer:
When we change a decimal into fraction, then we follow the following steps,
Step 1 : first we write the decimal number with the denominator 1,
Step 2 : Multiply numerator by 10s ( eg 10, 100, 100 etc ) for omitting decimal.
Step 3 : Multiply the denominator ( i.e 1 ) by the same number,
Step 4 : Reduce the fraction in the simplest form if possible by dividing both numerator and denominator by the HCF of numerator and denominator.
a)
[tex]0.25 =\frac{0.25}{1}=\frac{0.25\times 100}{100}=\frac{25}{100}=\frac{25\div 25}{100\div 25}=\frac{1}{4}[/tex]
b)
[tex]0.08 =\frac{0.08}{1}=\frac{0.08\times 100}{100}=\frac{8}{100}=\frac{8\div 4}{100\div 4}=\frac{2}{25}[/tex]
c)
[tex]0.400 =\frac{0.4}{1}=\frac{0.4\times 10}{10}=\frac{4}{10}=\frac{4\div 2}{10\div 2}=\frac{2}{5}[/tex]
d)
[tex]1.1 =\frac{1.1}{1}=\frac{1.1\times 10}{10}=\frac{11}{10}[/tex]
e)
[tex]3.5 =\frac{3.5}{1}=\frac{3.5\times 10}{10}=\frac{35}{10}=\frac{35\div 5}{10\div 5}=\frac{7}{2}[/tex]
Final answer:
To convert decimals into simplified fractions: 0.25 is 1/4, 0.08 is 2/25, 0.400 is 2/5, 1.1 is 11/10 and 3.5 is 7/2. Numbers in scientific notation are written in decimal form by adjusting the decimal point. When rounding to three significant figures, ensure only the first three digits after the leading non-zero digit are kept.
Explanation:
When converting decimals to fractions and simplifying them, it's important to consider the place value of the decimal. Here's how you would convert and simplify the provided decimals:
0.25 can be written as 25/100, which simplifies to 1/4.
0.08 is 8/100, which simplifies to 1/12.5 or 2/25 when expressed as a simplified fraction.
0.400 is 400/1000, which simplifies to 2/5.
1.1 is equivalent to 11/10 or 1 1/10 in mixed number form.
3.5 equals 35/10, which simplifies to 7/2 or 3 1/2 in mixed number form.
For scientific notation, numbers are converted to their decimal forms by moving the decimal point:
5.65 x 10-3 means the decimal point is moved 3 places to the left, giving 0.00565.
9.25 x 10-4 means the decimal point is moved 4 places to the left, resulting in 0.000925.
To write numbers in scientific notation:
4500 becomes 4.5 x 103.
2220000 turns into 2.22 x 106.
0.0035 is 3.5 x 10-3.
0.7 can be written as 7 x 10-1.
858.67 is expressed as 8.5867 x 102.
When rounding to three significant figures:
0.0004505 becomes 4.51 x 10-4 (count starts from the first non-zero digit).
0.00045050 also rounds to 4.51 x 10-4.
For 7.210 x 106, it remains unchanged as it already has three significant figures.
5.00 x 10-6 stays the same, with three significant figures present.
Given the following prescription formula, what is the ratio strength (nearest whole number) of methylcellulose in the finished product? As a ratio is typically expressed as 1:some number, put ONLY the number in the space provided and NOT the 1: portion. DO NOT include any units. • Progesterone 3.8 g • Glycerin 7 mL • 2% methylcellulose solution 50 mL • Cherry syrup ad 90 mL Your Answer: Answer
Answer:
147
Step-by-step explanation:
Given:
Progesterone = 3.8 g
Glycerin = 7 mL
2% methylcellulose solution 50 mL
Cherry syrup ad = 90 mL
Now,
The total volume of the solution = 7 + 50 + 90 = 147 mL
Also,
2% methylcellulose solution 50 mL is concluded as:
the volume of methylcellulose in the solution is 2% of the total volume of the solution
thus,
volume of methylcellulose = 0.02 × 50 mL = 1 mL
Therefore,
Ratio strength of methylcellulose in the finished product
=[tex]\frac{\textup{volume of methylcellulose}}{\textup{ total volume of the solution}}[/tex]
or
= [tex]\frac{\etxtup{1}}{\textup{ 147}}[/tex]
Hence, the answer according to the question is 147
A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 4.00 m/s, and her takeoff point is 1.20 m above the pool. (a) How long are her feet in the air? .3 Incorrect: Your answer is incorrect. s (b) What is her highest point above the board? m (c) What is her velocity when her feet hit the water? m/s
The height of the swimmer's feet in the air at time [tex]t[/tex] is given according to
[tex]y=1.20\,\mathrm m+\left(4.00\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2[/tex]
where [tex]g[/tex] is the magnitude of the acceleration due to gravity (taken here to be 9.80 m/s^2).
a. Solve for [tex]t[/tex] when [tex]y=0[/tex]:
[tex]1.20\,\mathrm m+\left(4.00\dfrac{\rm m}{\rm s}\right)t-\dfrac g2t^2=0\implies\boxed{t=1.05\,\mathrm s}[/tex]
(The other solution is negative; ignore it)
b. At her highest point [tex]y_{\rm max}[/tex], the swimmer has zero velocity, so
[tex]-\left(4.00\dfrac{\rm m}{\rm s}\right)^2=-2g(y_{\rm max}-1.20\,\mathrm m)\implies\boxed{y_{\rm max}=2.02\,\mathrm m}[/tex]
c. Her velocity at time [tex]t[/tex] is
[tex]v=4.00\dfrac{\rm m}{\rm s}-gt[/tex]
After 1.05 s in the air, her velocity will be
[tex]v=4.00\dfrac{\rm m}{\rm s}-g(1.05\,\mathrm s)\implies\boxed{v=-6.29\dfrac{\rm m}{\rm s}}[/tex]
The swimmer's feet are in the air for approximately 0.816 seconds. Her highest point above the diving board is approximately .43 m. She hits the water with a velocity of approximately -8.00 m/s.
Explanation:To answer these questions, we need to use physics equations that describe motion. The swimmer's motion can be broken down into two parts - the upward motion and the downward motion. Let's discuss each with respect to the provided variables.
(a) How long are her feet in the air?
To calculate the time, we can use the equation of motion given by: t = (v_f - v_i)/g where v_f is the final velocity (which is 0 at the highest point), v_i is the initial velocity (4.00 m/s), and g is the acceleration due to gravity (approx -9.81m/s²). The time taken for the upwards journey is: t = (0 - 4)/-9.81 ≈ 0.408 seconds. Since motion up and motion down take the same amount of time, we double this to get the total time: 2*0.408 = 0.816 seconds.
(b) What is her highest point above the board?
Let's use the equation h = v_i * t + 0.5*g*t², where h is the height, t is the time (0.408 seconds), g is the gravity (-9.81 m/s²), and v_i is the initial velocity (4.00 m/s). The highest point above the board is: h = 4*0.408 + 0.5*-9.81* (0.408)² = 1.63 m above the water surface or .43 m above the diving board.
(c) What is her velocity when her feet hit the water?
Here, we can repurpose the equation v_f = v_i + g*t. Notice that the time here is the total time her feet were in the air (0.816 seconds). Using these values we get: v_f = 0 + (-9.81 * 0.816) = -8.00 m/s. She hits the water at a speed of 8.00 m/s.
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Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events. Answer in fraction form or decimal approximation with 4 decimal places: A:{A:{ A 5 does not appear on either die }} B:{B:{ The difference of the numbers is 2 }} C:{C:{ The sum of the numbers is 10 or more }
Step-by-step explanation:
When two dies are tossed, possible outcomes are (1,1) (1,2) ,(1,3) (1,4), (1,5) (1,6),(2,1) (2,2) (2,3) (2,4) (2,5) (2,6), (3,1)(3,2)(3,3)(3,4),(3,5)(3,6)(4,1) (4,2),(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
so the total sample space =36
From de possible outcome, probability of getting a die that five does not appear on either side is given by total outcome of not getting five from either side/sample space
=30/36 = 5/6
And also probability of getting the difference of numbers to be 2 are (3,1)(4,2) (5,3) (6,4) =4outcomes
the probability of getting a difference of 2 is given by outcome/sample space 4/36 = 1/9
probability of getting the summation of two numbers to be equal to or greater than ten are; Outcome/sample space.
the outcome are (4,6) (5,5) (5,6)(6,4)(6,5)and (6,6)= 6outcomes
=6/36 =1/12.
The probabilities for the three events are approximately 0.6944, 0.2222, and 0.1667 respectively. These figures were achieved by comparing the number of favorable outcomes to the total number of outcomes when rolling two dice.
Explanation:The subject of this question is probability which involves using numbers for calculation. When you roll two dice, there are 36 possible outcomes.
Event A: The probability that a 5 does not appear on either die can be calculated by subtracting the outcomes where one or both dice show five (11 outcomes) from total outcomes. So the probability is (36-11)/36, or around 0.6944 as a decimal approximation.Event B: The difference of the numbers is 2 happens in 8 cases (3 and 1, 4 and 2, 5 and 3, 6 and 4, 1 and 3, 2 and 4, 3 and 5, 4 and 6). So the probability is 8/36, which simplifies to 2/9 or around 0.2222 in decimal approximation.Event C: The sum of the numbers is 10 or more happens in 6 cases (5 and 5, 6 and 4, 4 and 6, 6 and 5, 5 and 6, 6 and 6). So the probability is 6/36, which simplifies to 1/6 or around 0.1667 in decimal approximation.
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please answer 1 and 2 and if you can explain!!! i need help asap i’ll mark brainliest!!!
Answer:
1) A.
2) No
Step-by-step explanation:
1 is A because the shaded line extends over numbers greater than -8 but less than -1. The reason it is greater than or EQUAL to -1 is because the dot above -1 is shaded in.
2 is No because in order to solve this equation, you plug in the numbers from the coordinates into the inequality. An ordered pair is always structured as (x,y), so in this case x = -1 and y = 4. To solve, the first step is to plug the numbers in, and you end up with 4< 2(-1) +5.
Then, simplify by adding and multiplying as needed. Now you will end up with 4<-2 +5. Simplify again. Finally you end up with 4<3. The reason the answer is NO, not a solution is because the statement '4<3' (four is less than three) is false. if the equation had ended up being 4>3, then it would have been true.
An amount of $15,000 is invested in a fund that has a return of
6%. How much money is invested in a fund with a 4% return if the
total return on both investments is $1380?
Answer:
$12000 should be invested in a fund with a 4% return.
Step-by-step explanation:
Consider the provided information.
An amount of $15,000 is invested in a fund that has a return of 6%.
We need to calculate how much money is invested in a fund with a 4% return if the total return on both investments is $1380.
Let $x should be invested in a fund with a 4% return.
The above information can be written as:
[tex]1380=15000\times 6\%+x\times 4\%[/tex]
[tex]1380=15000\times \frac{6}{100}+x\times \frac{4}{100}[/tex]
[tex]1380=150\times6+x\times 0.04[/tex]
[tex]1380-900=0.04x\\480=0.04x\\x=12000[/tex]
Hence, $12000 should be invested in a fund with a 4% return.
After calculating the sample size needed to estimate a population proportion to within 0.05, you have been told that the maximum allowable error (E) must be reduced to just 0.025. If the original calculation led to a sample size of 1000, the sample size will now have to be
Answer: 40000
Step-by-step explanation:
The formula to find the sample size is given by :-
[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex], where p is the prior estimate of the population proportion.
Here we can see that the sample size is inversely proportion withe square of margin of error.
i.e. [tex]n\ \alpha\ \dfrac{1}{E^2}[/tex]
By the equation inverse variation, we have
[tex]n_1E_1^2=n_2E_2^2[/tex]
Given : [tex]E_1=0.05[/tex] [tex]n_1=1000[/tex]
[tex]E_2=0.025[/tex]
Then, we have
[tex](1000)(0.05)^2=n_2(0.025)^2\\\\\Rightarrow\ 2.5=0.000625n_2\\\\\Rightarrow\ n_2=\dfrac{2.5}{0.000625}=4000[/tex]
Hence, the sample size will now have to be 4000.
The new sample size will have to be approximately 4000.
The formula to calculate the sample size (n) needed to estimate a population proportion with a given maximum allowable error (E) and confidence level (usually 95% or 1.96 standard deviations for a two-tailed test) is given by:
[tex]\[ n = \left(\frac{z \times \sigma}{E}\right)^2 \][/tex]
Given that the original maximum allowable error was 0.05 and the sample size calculated was 1000, we can set up the equation:
[tex]\[ 1000 = \left(\frac{1.96 \times 0.5}{0.05}\right)^2 \][/tex]
Now, we want to find the new sample size when the maximum allowable error is reduced to 0.025. The new sample size can be calculated by:
[tex]\[ n_{new} = \left(\frac{z \times \sigma}{E_{new}}\right)^2 \][/tex]
Since \( z \) and[tex]\( \sigma \)[/tex] remain constant, and only \( E \) changes, the relationship between the original sample size and the new sample size is inversely proportional to the square of the ratio of the original error to the new error:
[tex]\[ n_{new} = n_{old} \times \left(\frac{E_{old}}{E_{new}}\right)^2 \] \[ n_{new} = 1000 \times \left(\frac{0.05}{0.025}\right)^2 \] \[ n_{new} = 1000 \times \left(\frac{0.05}{0.025}\right)^2 \] \[ n_{new} = 1000 \times \left(2\right)^2 \] \[ n_{new} = 1000 \times 4 \] \[ n_{new} = 4000 \][/tex]
Therefore, the new sample size will have to be approximately 4000 to reduce the maximum allowable error to 0.025."
Use a truth table to verify the first De Morgan law (p ∧ q)’ ≡ p’ ∨ q’.
Answer:
(p ∧ q)’ ≡ p’ ∨ q’
Step-by-step explanation:
First, p and q have just four (4) possibilities, p∧q is true (t) when p and q are both t.
p ∧ q
t t t
t f f
f f t
f f f
next step is getting the opposite
(p∧q)'
f
t
t
t
Then we get p' V q', V is true (t) when the first or the second is true.
p' V q'
f f f
f t t
t t f
t t t
Let's compare them, ≡ is true if the first is equal to the second one.
(p∧q)' ≡ (p' V q')
f f
t t
t t
t t
Both are true, so
(p ∧ q)’ ≡ p’ ∨ q’
The owner of the Rancho Los Feliz has 7000 yd of fencing with which to enclose a rectangular piece of grazing land along the straight portion of a river. Fencing is not required along the river, and the length of the fencing parallel to the river is to exceed the length of the fencing perpendicular to it by 2500 yd. Find the area of the enclosed land (in sq yd).
Answer:
6000000 sq yd
Step-by-step explanation:
Data provided in the question:
Length of the fencing = 7000 yd
let the perpendicular sides be 'P'
and the length parallel to the river be 'L'
according to the given question
L = P + 2500 ............(1)
also,
Length to be fenced = 2P + L
thus,
2P + L = 7000 ...........(2)
substituting L from (1), we get
2P + P + 2500 = 7000
or
3P = 7000 - 2500
or
3P = 4500
or
P = 1500 yd
Thus,
L = 1500 + 2500 = 4000 yd
Therefore,
the area of the rectangular land = L × P = 4000 × 1500 = 6000000 sq yd
Answer:
Area of land = 6000000 sq yd
Step-by-step explanation:
Given,
length of fencing= 7000 yd
Let's assume that the length of the land parallel to the river is l and the breadth of the land perpendicular to the river is b.
Then, it is given that
l = b +2500
Since, there is no need of fencing along the river so, we can write
l +2b = 7000
=>b+2500 = 7000
=> b = 7000-2500
= 4000
As the area of rectangular land can be given as
A = length x breadth
= 4000 x 2500 sq yd
= 6000000 sq yd
So, the area of the enclosed land will be 6000000 sq yd.
If a population of dolphins increases at a constant rate of 1.5% every year for 20 years what will be the total percentage increase over the 20 years.
Answer:
The population increased by 34.69% over 20 years.
Step-by-step explanation:
It is given that the population of dolphins increases at a constant rate of 1.5% every year for 20 years.
Formula for population increase:
[tex]P=a(1+r)^t[/tex]
where, a is initial population, r is growth rate and t is time in years.
If the population of dolphins increases at a constant rate of 1.5% every year for 20 years, then the population after 20 years is
[tex]P=a(1+0.015)^{20}[/tex]
[tex]P=a(1.015)^{20}[/tex]
[tex]P=1.346855a[/tex]
Where, a is the initial population.
The total percentage increase over the 20 years is
[tex]\% change=\frac{P-a}{a}\times 100[/tex]
where, P is population after 20 years and a is initial amount.
[tex]\% change=\frac{1.346855a-a}{a}\times 100[/tex]
[tex]\% change=\frac{0.346855a}{a}\times 100[/tex]
[tex]\% change=0.346855\times 100[/tex]
[tex]\% change=34.6855[/tex]
[tex]\% change\approx 34.69[/tex]
Therefore the population increased by 34.69% over 20 years.