In logic, own symbols are used in order to be able to represent the relations between propositions in a general and independent way to the proposition, in order to be able to find the relationship process that operates in the communicated message, the propositional logic.
For this purpose there are, among others, the following logical operators: conjunction (and) ∧, disjunction (or) ∨, denial (not) ¬, conditional (if - then) ⇒ and double conditional (if and only if, iff) ⇔.
So for this case we have:
Answer
a) Sam had pizza last night if and only if Chris finished her homework.
p⇔q
b) Pat watched the news this morning iff Sam did not have pizza last night.
r⇔¬p
c) Pat watched the news this morning if and only if Chris finished her homework and Sam did not have pizza last night.
r⇔(q∧¬p)
d) In order for Pat to watch the news this morning, it is necessary and sufficient that Sam had pizza last night and Chris finished her homework.
r⇔(p∧q)
e) q ⇔ r
Chris finished his homework if and only if Pat watched the news this morning
f) p ⇔ (q ∧ r)
Sam had pizza last night if and only if Chris finished his homework and Pat watched the news this morning
g) (¬p) ⇔ (q ∨ r)
Sam didn't have pizza last night if and only if Chris finished his homework or Pat watched the news this morning
h) r ⇔ (p ∨ q)
Pat watched the news this morning if Sam had pizza last night or Chris finished his homework
2 boats leave the same port at the same time.
1 traveled at a speed of 30 mph heading N 50 E
The other traveled at a speed of 26 mph heading S 70 E
How far apart are the two boats after 1 hour?
Answer: Hi!
First, if you think that a compass has degrees as units, then N50E would be
50 degrees from north in the direction of the east, so if you put our 0 in east and count counterclockwise this will be an angle of 40 degrees.
If you think north has te Y axis positive direction, and east as the X axis positive direction. then the first boat has an angle of 40° counterclockwise from the +x
so the velocity in y is Vy=30mph*sin(40°) and in x is Vx= 30mph*cos(40°)
then the total displacement will be 22.98m to east and 19.28 north
the second one goes to s 70 e, so using the same notation as before, you can write this has -20° degrees count counterclockwise.
so decomposing the velocity will give us
Vy = 26*sin(-20°) and the displacement in Y is -8.89m
Vx = 26*cos(-20°) and the displacement in X is 24.43m
so the distance between the boats in y will be 19.28m - (-8.99)m = 28.27m
and in x: 24.43m - 22.98m = 1.45m
and the total distance is [tex]D^{2} = 1.45^{2} + 28.27^{2}[/tex]
so D = 28.30 m
Find the point on the sphere (x+5)^2 + y^2 + (z−9)^2 = 99 nearest to
(a) the xy-plane.
(b) the point (−9,0,9).
Answer:
a) Since the sphere intersects the xy-plane then the set of points of the sphere nearest to the xy-plane is the set of points in the circumference [tex](x+5)^2+y^2=18[/tex].
b)(-14.9, 0, 9 )
Step-by-step explanation:
a) The centre of the sphere is (-5,0,-9) and the radio of the sphere is [tex]\sqrt{99} \sim 9.9[/tex]. Since |-9|=9 < 9.9, then the sphere intersect the xy-plane and the intersection is a circumference.
Let's find the equation of the circumference.
The equation of the xy-plane is z=0. Replacing this in the equation of the sphere we have:
[tex](x+5)^2+y^2+9^2=99[/tex], then [tex](x+5)^2+y^2=18[/tex].
b) Observe that the point (-9,0,9) has the same y and z coordinates as the centre and the x coordinate of the point is smaller than that of the x coordinate of the centre. Then the point of the sphere nearest to the given point will be at a distance of one radius from the centre, in the negative x direction.
(-5-[tex]\sqrt{99}[/tex], 0, 9)= (-14.9, 0, 9 )
An airplane flying at an altitude of 30,000 feet flies up to avoid a storm. Immediately after passing the storm, the airplane returns to its original altitude. What integer represents the airplane's change in altitude to avoid the storm? What integer represents the altitude after passing the storm?
Answer:
The integer representing the change of altitude to avoid the storm is 8,000
The integer representing the altitude after passing the storm is 30,000
Explanation:
The diagram of this question is shown in the attached image
We are given that the initial altitude of the plane was 30,000 ft
1- During the storm:
The plane flew at at altitude of 38,000 feet
To get the change in the altitude, we will subtract the final altitude from the initial one
change of altitude = final altitude - initial altitude
change of altitude = 38,000 - 30,000 = 8,000 ft
Therefore, the integer representing the change of altitude to avoid the storm is 8,000
2- After the storm:
We know that, after the storm, the plane returned to its initial altitude
Given that the initial altitude is 30,000 ft, this would mean that the integer representing the altitude after passing the storm is 30,000
Hope this helps :)
Final answer:
The integer representing the change in altitude when the airplane avoided the storm and then returned to its original altitude is zero. The altitude after passing the storm is 30,000 feet, the same as its original altitude before the ascent.
Explanation:
The integer representing the airplane's change in altitude to avoid the storm is zero because it returned to its original altitude after passing the storm. During the avoidance maneuver, the airplane would have increased in altitude (a positive change) and then decreased the same amount to return to its original altitude (a negative change). The sum of this positive and negative change is zero.
The integer representing the altitude after passing the storm is 30,000 feet, which is the same as the original altitude since the airplane returned to this altitude after avoiding the storm.
When considering aircraft performance, it's vital to take into account the rate of climb and descent, potential energy swaps from kinetic energy, and altitude effects on aircraft performance. However, in this instance, the specific figure for altitude change during the storm avoidance is not given, but the concept of returning to starting altitude implies no net change.
Are the points (-4,-1), (2,1) and (11,4) collinear? Justify your answer.
Answer: Yes , the points (-4,-1), (2,1) and (11,4) are collinear.
Step-by-step explanation:
We know that if three points [tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] are collinear, then their area must be zero.
The area of triangle passes through points[tex](x_1,y_1),(x_2,y_2)[/tex] and [tex](x_3,y_3)[/tex] is given by :-
[tex]\text{Area}=\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given points : (-4,-1), (2,1) and (11,4)
Then, the area of ΔABC will be :-
[tex]\text{Area}=\dfrac{1}{2}|-4(1-4)+(2)(4-(-1))+(11)(-1-1)|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|-4(-3)+(2)(5)+(11)(-2)||\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|12+10-22|\\\\\Rightarrow\text{Area}=\dfrac{1}{2}|0|=0 [/tex]
Hence, the points (-4,-1), (2,1) and (11,4) are collinear.
Determine the value (or values) of h such that the matrix: 2 - 3 h - 6 9 5 is the augmented matrix of a consistent linear system.
Answer:
In order to have a consistent linear system represented by the augmented matrix:
[tex]\left[\begin{array}{ccc}2&-3&h\\-6&9&5\end{array}\right][/tex]
the value of h must be:
[tex]h=-\frac{5}{3}[/tex]
Step-by-step explanation:
A system is consistent if it has a solution, this solution can be unique or a set of infinite solutions.
First, you take the augmented matrix and find the equivalent row echelon form using Gaussian-Jordan elimination:
To do this, you have to multiply the 1st row by 3 and add it to the 2nd row, the resulting matrix is:
[tex]\left[\begin{array}{ccc}2&-3&h\\0&0&5+3h\end{array}\right][/tex]
Now, write the system of equations:
[tex]2x_1-3x_2=h\\0x_1+0x_2=5+3h[/tex]
The only way this system has a solution is if 5+3h=0, then, to satisfy this, the value of h must be:
[tex]h=-\frac{5}{3}[/tex]
If we changed our speed limit signs to metric, what would probably replace 45 mi/h? (Please round your answer to the nearest 1 km/h.)
km/h
Consider the quadratic function f(x)=−x^2+4x+12
Determine the following:
The smallest xx-intercept is x=Incorrect
The largest xx-intercept is x=
The yy-intercept is y=
Answer:
a) -2 from (-2,0) b) 6 from (6,0) c) y-intercept: 12 from (0,12)
Step-by-step explanation:
The X intercepts in a quadratic function are the points of the x-axis crossed by the parabola. One quadratic equation may have up to two points on the X-axis. This or these points in the X-axis, the Zeros of this function, will be crossed by the parabola.
The Y-intercept is the point of the y-axis crossed by the parabola.
Solving the equation:
[tex]-x^{2} +4x+12=0\\ x'=\frac{-4+\sqrt{64}}{-2} \\ x"=\frac{-4-\sqrt{64}}{-2} \\ x'=-2\\ x"=6\\[/tex]
S={-2, 6} These values, or zeros of this quadratic function are the X, intercepts.
c) The indepent term, or c, in f(x)= ax²+bx+c in this case is 12, also is the Y coordinate for the Parabola Vertex. This point is our intercept for y.
As the owner of a small restaurant, you purchase 5 boxes of napkins for $75.00 every 3 months. Each box contains 525 napkins. To the nearest hundredth, what is the cost for each individual napkin?
As the owner of a small restaurant, you purchase 5 boxes of napkins for $75.00 every 3 months. Each box contains 525 napkins. To the nearest hundredth, what is the cost for each individual napkin?
A) 0.01
B) 0.02
C) 0.03
D) 0.05
Answer: 0.03
Step-by-step explanation:
Total number of napkins: 5 x 525 = 2,625
75/2626 = 0.02857, which rounds to 0.03
The cost per individual napkin, when rounded to the nearest hundredth, is $0.03.
Explanation:To begin finding the cost per napkin, we first need to find out how many napkins are purchased every 3 months. Since each box contains 525 napkins and you purchase 5 boxes every 3 months, that would be 525 * 5 = 2625 napkins. The cost of these napkins is $75.00.
So, to find the cost per individual napkin, you would divide the total cost by the total number of napkins. That would be 75 / 2625 = $0.028571... When rounded to the nearest hundredth, this becomes $0.03. So, each individual napkin costs $0.03. Therefore, the correct answer is (C) 0.03.
Learn more about Cost per Napkin here:https://brainly.com/question/34904419
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A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true proportion of families who own at least one DVD player. Place your limits, rounded to 3 decimal places, in the blanks. Place the lower limit in the first blank
The 99% confidence interval estimate for the genuine proportion of families who own at least one DVD player is:
Lower bound: 0.287.
Upper bound: 0.563.
To find the 99% confidence interval estimate of the true proportion of families who own at least one DVD player, follow these steps:
Step 1. Determine the sample proportion [tex](\( \hat{p} \))[/tex]:
Number of families surveyed ( n ) = 85
Number of families owning at least one DVD player ( x ) = 36
Sample proportion [tex](\( \hat{p} \)) = \( \frac{x}{n} = \frac{36}{85} = 0.4247 \)[/tex]
Step 2. Find the standard error (SE) of the sample proportion:
Standard error formula: [tex]\( SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \)[/tex]
Plug in the values: [tex]\( SE = \sqrt{\frac{0.4247 \times (1 - 0.4247)}{85}} = \sqrt{\frac{0.4247 \times 0.5753}{85}} = \sqrt{\frac{0.2443}{85}} = \sqrt{0.002875} = 0.0536 \)[/tex]
Step 3. Determine the z-value for a 99% confidence interval:
The z-value for a 99% confidence interval is approximately 2.576.
Step 4. Calculate the margin of error (ME):
Margin of error formula: [tex]\( ME = z \times SE \)[/tex]
Plug in the values: [tex]\( ME = 2.576 \times 0.0536 = 0.1381 \)[/tex]
Step 5. Determine the confidence interval
Lower limit: [tex]\( \hat{p} - ME = 0.4247 - 0.1381 = 0.2866 \)[/tex]
Upper limit: [tex]\( \hat{p} + ME = 0.4247 + 0.1381 = 0.5628 \)[/tex]
Therefore, the 99% confidence interval estimate of the true proportion of families who own at least one DVD player is:
Lower limit: 0.287
Upper limit: 0.563
Complete Question:
A survey of 85 families showed that 36 owned at least one DVD player. Find the 99 \% confidence interval estimate of the true proportion of families who own at least on DVD player. Place your limits, rounded to 3 decimal places, in the blanks. Do not use any labels or symbols other than the decimal point. Simply provide the numerical values. For example, 0.123 would be a legitimate entry.
Lower limit (first blank) [tex]$=$ $\qquad$[/tex] ______ , Upper limit (second blank) = _______
(2.5x10^-10) x (7x10^-6) express your answer in scientific notation
Answer:
Hello my friend! The answer is 1.75X10^-15
Step-by-step explanation:
If you multiply 2.5 x7 = 17.5
When we do the product of exponential terms with the same base, we can sum de exponents. In this case (-10) + (-6) = -16.
However, to scientific notation, we have to use 1.75
So, the final result wich were 17.5x10-16, will be "1.75x10^-15"
Total departmental sales in the Housewares Department were $513000.00. A salesperson made 14% of the total departmental sales of that month and earns 6.5% commission on his sales. Find the dollar amount of commission.
a.
$33345.00
b.
$4691.95
c.
$4668.30
d.
$71820.00
e.
$4683.19
f.
None of the above.
Answer: c. $4668.30
Explanation:
Given:
Sales = $513000
Sales made by an individual = 14% of $513000
Sales made by an individual = [tex]\frac{14}{100}\times 513000[/tex]
Sales made by an individual = $71280
Commission made on this sales = 6.5% of $71280
Commission made on this sales = [tex]\frac{6.5}{100}\times 71280[/tex]
Commission made on this sales = $4668.30
Find the length of the median of a trapezoid if the length
ofthe shorter base is 16cm and the length of the longer base
is24cm.
Answer:
20 cm
Step-by-step explanation:
We are given a trapezoid, where the length of shorter base or on of the parllel line is 16 cm and the length of other parallel side is 24 cm.
Let the two parallel sides be x and y that is x = 16 cm and y = 24 cm.
A median of a trapezoid is a line segment that divides the non parallel sides of a trapezoid equally or a line segment that passes through the mid points of non-parallel sides of a trapezoid.
The length of median of a trapezoid = [tex]\frac{\text{Sum of parallel sides}}{2}[/tex] = [tex]\frac{16+24}{2}[/tex] = 20 cm.
Thus, the length of median of trapezoid is 20 cm.
A small restaurant has a menu with 2 appetizers, 5 main courses, and 3 desserts. (a) How many meals are possible if each includes an main course and a dessert, but may or may not include an appetizer? (b) What if the dessert is also not required?
Answer: a) 45 b) 60
Step-by-step explanation:
Given : A small restaurant has a menu with 2 appetizers, 5 main courses, and 3 desserts.
a) Number of meals includes an main course , a dessert and a appetizer, :-
[tex]2\times5\times3=30[/tex]
Number of meals includes an main course and a dessert and but not appetizer , then total possible meals:-
[tex]5\times3=15[/tex]
Then, the number of meals are possible if each includes an main course and a dessert, but may or may not include an appetizer= 30+15=45
b) Number of meals includes an main course and appetizer but not dessert:
[tex]5\times2=10[/tex]
Number of meals includes only main course =5
Now, the number of meals if dessert is also not required= 45+5+10=60
Justify Reasoning Can you ever use a calculator to determine if a number is rational or irrational? Explain.
Answer:
Not always we can use a calculator to determine if a number is rational or irrational.
Step-by-step explanation:
Consider the provided information.
Can you ever use a calculator to determine if a number is rational or irrational.
Irrational number: A number is irrational if it cannot be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.
The calculators gives the approximate answer, whether the number is irrational or rational.
If it shows the terminating decimal then number is rational but otherwise, it is not possible to identify whether the number is rational or irrational as you can only see a few digits.Calculator shows the terminating decimal while the decimal expansion of an irrational number is not terminating.So, it would be difficult to identify whether a large number produced by the calculator is irrational or not. As we know that many rational numbers can be incredibly large.
So, we can say that not always we can use calculator to determine if a number is rational or irrational.
Thus, Not always we can use a calculator to determine if a number is rational or irrational.
Jorgensens, an Electronics
distributor, just received ashipment of 12 DVDPlayers. Shortly after arrival the
manufacturer called to saythat that he had accidentally shipped
five defective units with theshipment. Mr. Jorgensen immediately
pulled ten of the unitsand tested two of them. What is the
probability that neitherof them was defective?
Answer: 0.3399
Step-by-step explanation:
The binomial probability distribution formula to find the probability of getting success in x trial:-
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where n is the number of trials and p is the probability of getting success in each trial.
Given : Jorgensens received a shipment of 12 DVD Players. Shortly after arrival the manufacturer called to say that that he had accidentally shipped five defective units with the shipment.
i.e. The proportion of the defective units : [tex]p=\dfrac{5}{12}\approx0.417[/tex]
Also, Mr. Jorgensen pulled ten of the units and tested two of them.
For n=2, the probability that neither of them was defective:-
[tex]P(x=0)=^{2}C_0(0.417)^0(1-0.417)^{2}\\\\=(1)(1)(0.583)^{2}\ \ \ [\text{ Since}^nC_0=1]\\\\=0.339889\approx0.3399[/tex]
Hence, the probability that neither of them was defective = 0.3399
Rewrite the following system of linear equations in matrix equation form and in vector equation form. Solve the system.
a - b + 2x - 8y + z =3
2a - b - 4x + y - 2z = 1
-4a + b + 4x - 3x - z = -1
Answer:
The set of solutions is [tex]\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}[/tex]
Step-by-step explanation:
The matrix associated to the problem is [tex]A=\left[\begin{array}{ccccc}1&-1&2&-8&1\\2&-1&-4&1&-2\\-4&1&4&-3&-1\end{array}\right][/tex] and the vector of independent terms is (3,1,-1)^t. Then the matrix equation form of the system is Ax=b.
The vector equation form is [tex]a\left[\begin{array}{c}1\\2\\-4\end{array}\right]+b\left[\begin{array}{c}-1\\-1\\1\end{array}\right] + x\left[\begin{array}{c}2\\-4\\4\end{array}\right]+y\left[\begin{array}{c}-8\\1\\-3\end{array}\right] + z\left[\begin{array}{c}1\\-2\\-1\end{array}\right]=\left[\begin{array}{c}3\\1\\-1\end{array}\right][/tex].
Now we solve the system.
The aumented matrix of the system is [tex]\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\2&-1&-4&1&-2&1\\-4&1&4&-3&-1&-1\end{array}\right][/tex].
Applying rows operations we obtain a echelon form of the matrix, that is [tex]\left[\begin{array}{cccccc}1&-1&2&-8&1&3\\0&1&-8&-15&-4&-5\\0&0&1&-80&-9&-4\end{array}\right][/tex]
Now we solve for the unknown variables:
x-80y-90z=-4 then x=-4+80y+90zb-8x-15y-4z=-5, b-8(-4+80y+90z)-15y-4z=-5 then b=-37+655y+724z.a-b+2x-8y+z=3, a-(-37+655y+724z)+2(-4+80y+90z)-8y+z=3, then a=-26+503y+543zSince the system has two free variables then has infinite solutions.
The set of solutions is [tex]\{\left[\begin{array}{c}a\\b\\x\\y\\z\end{array}\right] = \left[\begin{array}{c}-26+503y+543z\\-37+655y+724z\\-4+80y+90z\\y\\z\end{array}\right] : \text{y, z are real numbers}\}[/tex]
A piecewise function is shown below
g(x) = { -3x^2 -2x+8 for -4 ≦ x < 1
-2x+7p for 1 ≦ x ≦ 5
(a) for what value of p will the function be continuous
(b) Because one piece stops and the next piece starts at the point identified in part a, the pieces can be set equal to each other to find p. Fine p. Show your work. If you did everything on a calculator, explain the steps you took and include screenshots of each step.
Answer:
p = 5/7
Step-by-step explanation:
The given function is:
[tex]g(x) = -3x^{2} - 2x + 8[/tex] for -4 ≦ x < 1
[tex]g(x) = -2x + 7p[/tex] for 1 ≦ x ≦ 5
Part a)
A continuous function has no breaks, jumps or holes in it. So, in order for g(x) to be continuous, the point where g(x) stops during the first interval -4 ≦ x < 1 must be equal to the point where g(x) starts in the second interval 1 ≦ x ≦ 5
The point where, g(x) stops during the first interval is at x = 1, which will be:
[tex]-3(1)^{2}-2(1)+8=3[/tex]
The point where g(x) starts during the second interval is:
[tex]-2(1)+7(p) = 7p - 2[/tex]
For the function to be continuous, these two points must be equal. Setting them equal, we get:
3 = 7p - 2
3 + 2 = 7p
p = [tex]\frac{5}{7}[/tex]
Thus the value of p for which g(x) will be continuous is [tex]\frac{5}{7}[/tex].
Part b)
We have to find p by setting the two pieces equal to each other. So, we get the equation as:
[tex]-3x^{2}-2x+8=-2x+7p\\\\ -3x^{2}+8=7p[/tex]
Substituting the point identified in part (a) i.e. x=1, we get:
[tex]-3(1)^{2}+8=7p\\\\ 5=7p\\\\ p=\frac{5}{7}[/tex]
This value agrees with the answer found in previous part.
A cubic function generally has the form f(x) = ax3 + bx2 + cx + d. If we know that for some x-value x = p we have f(p) = 0, then it must be true that x − p is a factor of f(x). Since we are told that f(3) = 0, we know that _____ is a factor.
Hi!
You know that if f(p) = 0, then (x-p) is a factor of the polynomial f(x)
Then, f(3)=0 is the case p=0, son the factor is (x-3)
Answer: Since we are told that f(3) = 0, we know that (x-3) is a factor.
Need help fast please!!!!
Answer:
∠DBC = 25°∠DCB = 65°∠ACD = 25°Step-by-step explanation:
All the right triangles are similar, so all will have the same angles.
The missing angle (B) in ΔABC is the complement of the given one:
∠DBC = 90° - 65° = 25°
The missing angles in the smaller triangles are the complements of the known acute angles in those triangles.
A diagram can help you see this.
Calculate:
3 pounds (lbs) =——grams (g)
Answer:
1360.78 g
Step-by-step explanation:
1 lb = 453.592 g
3 lbs = 3 * 453.592 g = 1360.78 g
What is an essential goal of a programmer and why?
Answer: A programmer is the person who is responsible for making computer programs.He/she makes sure that the program is created according to the requirement and accurate performing operations .The goals of the programmer are as follows:-
Keep progressing in the field of computer programmingLearning various new programming languages and technologiesEnhancing the skills to be in this field for long -run of timeGrabbing the opportunities as programmer for improvementProgrammer is indulged in these goals because there are always upcoming new technologies in the field of programming so, to keep theirselves updates and maintain their skill they improve theirselves time to time. Also it can affect the job of the programmer if they are not aware about programming skills quite well or might end up losing the job.
A penalty in Meteor - Mania is - 5 seconds. A penalty in Cosmic Calamity is - 7 seconds. Yolanda had penalties totaling -25 seconds in a game of meteor- Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties? Justify the answer.
Answer:
Yolanda had the same number of penalties in both games.
Step-by-step explanation:
Both of these penalties can be modeled by a first order equation.
Game of Meteor-Mania:
In a game of Meteor-Mania, each penalty is -5 seconds. So the expression for the total of penalties is:
Tp(n) = -5*n, where n is the number of penalties.
In the game of Meteor-Mania, Yolanda had penalties totaling -25 seconds. So
-25 = -5*n *(-1)
5n = 25
n = 25/5
n = 5
Yolanda had 5 penalties in the game of Meteor-Mania
Game of Cosmic Calamity
In a game of Meteor-Mania, each penalty is -7 seconds. So the expression for the total of penalties is:
Tp(n) = -7*n, where n is the number of penalties.
In the game of Cosmic Calamity, Yolanda had penalties totaling -35 seconds. So
-35 = -7n *(-1)
7n = 35
n = 35/7
n = 5
Yolanda had 5 penalties in the game of Cosmic Calamity
Yolanda had the same number of penalties in both games.
I need help quick please!!!
Solve the system of inequalities:
2x−1 < x+3
5x−1>6−2x
x−5<0
Final answer:
To solve the system of inequalities, first, solve each inequality separately. Then, combine the solutions to find the common range of values for x that satisfy all the inequalities.
Explanation:
To solve the system of inequalities:
2x - 1 < x + 3
5x - 1 > 6 - 2x
x - 5 < 0
First, let's solve the first inequality:So, the solution to the system of inequalities is: x < 4, x > 1, x < 5
oco serves a tennis ball at vs = 50 m/s and charges the net at vc = 10 m/s. The opponent, x = 25 m away on the other side of the court, returns the ball with a speed half that of the serve. How close does Coco get to the net (x/2 away) before she meets the return?
Answer:
3.055 m
Step-by-step explanation:
In this solution we will use next notation:
[tex]t_1[/tex]= time elapsed since oco serves the ball until it reaches its opponent.
[tex]t_2[/tex]= time elapsed since the opponent returns the ball until it reaches oco.
d= Total distance traveled by Oco since serving the ball until meeting the return.
We know that oco serves at vs = 50 m/s and her opponent is x=25 m away. Then, t_1 is given by
[tex]t_1=\frac{25m}{50m/s}=0.5s[/tex]
To compute t_2 observe that the return speed is 12.5 m/s and the distance that the ball will travel is [tex]25-(10t_1+10t_2)[/tex]. Then,
[tex]t_2=\frac{25-10t_1-10t_2}{12.5}=\frac{20-10t_2}{12.5}\implies t_2=\frac{20}{22.5}=\frac{8}{9}s[/tex].
Therefore,
[tex]d=10(t_1+t_2)=10(0.5+\frac{8}{9})=10(\frac{17}{18})=\frac{85}{9}m[/tex]
Finally, as Oco started 12.5m away from the net, when she meets the return she will be
[tex]12.5-\frac{85}{9}=\frac{55}{18}=3.055m[/tex]
away from the net.
S is the set of current U.S. Senators from states that begin with A
Write each set using the roster method. Pay attention to repeated elements and think about why you don't need to list the same element more than once.
The List of Senators is below:
John Boozman
Doug Jones
Martha McSally
Lisa Murkowski
Tom Cotton
Richard C. Shelby
Kyrsten Sinema
Dan Sullivan
Answer:
see below
Step-by-step explanation:
The "roster method" means you simply list them all:
{John Boozman, Doug Jones, Martha McSally, Lisa Murkowski, Tom Cotton, Richard C. Shelby, Kyrsten Sinema, Dan Sullivan}
_____
There are no senators from these states with the same name, so repeated elements is not an issue here.
The set S includes the Senators John Boozman, Tom Cotton from Arkansas, Richard C. Shelby, Doug Jones from Alabama, and Lisa Murkowski, Dan Sullivan from Alaska. Each state has two unique senators, thus there are no repeated elements in the set.
The set S of current U.S. Senators from states that begin with 'A' using the roster method can be written as follows:
John Boozman (Arkansas)
Tom Cotton (Arkansas)
Richard C. Shelby (Alabama)
Doug Jones (Alabama)
Lisa Murkowski (Alaska)
Dan Sullivan (Alaska)
Each state beginning with 'A' (Alabama, Alaska, and Arkansas) contributes two senators to the set. S, as defined, would not have repeated elements since senators are unique to each state they represent, and no senator represents more than one state.
Which ratio is NOT equivalent to the other choices? A) 6:15 B) 6 to 15 C) 6 15 D) 15 6
Answer:
D
Step-by-step explanation:
Because ordering in ratios is important, so it must stay constant like 6,15.
Answer:
The answer is: D) 15/6
Step-by-step explanation:
The ratio of two given numbers such as X and Y is expressed by the symbol ':' Therefore, the ratio of X and Y or X:Y can be referred to as X is to Y and can also be expressed as a fraction X/Y or X÷Y.
Therefore, the ratio can be expressed in a number of ways, 6:15 = 6 to 15 = 6/15
Whereas, 15/6 = 15:6 ≠ 6:15
determine the payment to amortized the debt quarterly payments on $16,500 at 3.6% for 6 years
Answer:
$767.49
Step-by-step explanation:
given,
Amount of money = $16,500
quarterly rate = 3.6/4 = 0.9 %
times = 6 × 4 = 24 quarters.
[tex]A =\dfrac{P(r(1+r)^n)}{(1+r)^n-1}\\\\A =\dfrac{16500\times(0.009(1+0.009)^{24})}{(1+0.009)^{24}-1}\\A = \$ 767.49[/tex]
hence, the payment to amortize the dept will be equal to $767.49 .
Suppose that f is a differentiable function of one variable. Show that all the tangent Planes to the the surface z = xf (y / x) intersect in a common point.
Answer:
If [tex]P_0 (x_0,y_0,z_0)[/tex] is a point on the surface, then the cartesian equation of the tangent plane at [tex]P_0 (x_0,y_0,z_0)[/tex] is
[tex](\ast)z = z_0 + \frac{\partial z}{ \partial x}(x_0,y_0)\cdot (x -x_0) + \frac{\partial z}{\partial y} (x_0, y_0) (y -y_0)[/tex],
where [tex]z_0 = x_0 f \left ( \frac{y_0}{x_0}\right )[/tex].
Given that
[tex]\frac{\partial z}{\partial x} (x_0 , y_0) = f \left( \frac{y_0}{x_0}\right ) - \frac{y_0}{x_0} \cdot \frac{\partial f}{\partial x}(x_0,y_0) \ , \ \frac{\partial z}{\partial y} (x_0 , y_0)=\frac{\partial f}{\partial y} (x_0,y_0)[/tex], then
[tex](\ast)[/tex] becomes
[tex](\ast \ast) z=x_0 f \left ( \frac{y_0}{x_0}\right ) + f \left( \frac{y_0}{x_0}\right ) - \frac{y_0}{x_0}\cdot \frac{\partial f}{\partial x} (x_0,y_0)\cdot (x -x_0)+\frac{\partial f}{\partial y} (x_0,y_0)\cdot (y -y_0)[/tex].
Finally, replacing [tex] (x,y,z)=(0,0,0)[/tex] in [tex](\ast \ast)[/tex] you have that the equality is true for all [tex]P_0[/tex]. This means that [tex]O(0,0,0)[/tex]
belongs to all tangent planes and therefore, the result follows.
At a bookstore, 960 books were placed on the discount shelf for 70% off the regular price. If 2/3 of the books sold, how many books remain on the discount shelf?
a.
320 books
b.
296 books
c.
293 books
d.
332 books
e.
356 books
f.
None of the above.
Answer: a. 320 books
Step-by-step explanation:
Given : The total number of books were placed on the discount shelf for 70% off the regular price = 960
The fraction of books sold = [tex]\dfrac{2}{3}[/tex]
Then, the number of books sold = [tex]\dfrac{2}{3}\times960=640[/tex]
Now, the number of books remain on the discount shelf = [tex]960-640=320[/tex]
Hence, the number of books remain on the discount shelf =320
The yield of strawberry plants depends on the amount of fertilizer fed to the plants. Agricultural research shows that an acre of strawberry plants will yield 770 pounds of strawberries when 70 cubic feet of fertilizer are applied. If 100 cubic of feet of fertilizer are applied, the yield will be 1100 pounds of strawberries. Use linear interpolation to estimate the yield if 75 cubic feet of fertilizer are applied. Select an answer
By using the principles of linear interpolation, the yield of strawberries with 75 cubic feet of fertilizer can be calculated as approximately 616.25 pounds.
Explanation:The yield of strawberries based on the amount of fertilizer fed to the plants can be estimated using linear interpolation. We can establish two points based on the given information: (70, 770) and (100, 1100), where the first number represents the amount of fertilizer and the second one, the yield. The interpolation line equation can be formulated as y = mx + c where m = (y2 - y1) / (x2 - x1); as such, m = (1100 - 770) / (100 - 70) = 8.25.
To find the value of c (y-intercept), we use the equation with one of the known points and solve c = y1 - m * x1 = 770 - 8.25 * 70 = -5.
The yield, y at 75 cubic feet of fertilizer can be calculated as y = 8.25 * 75 - 5 = 616.25. Therefore, the estimated yield of strawberries when 75 cubic feet of fertilizer is applied is approximately 616.25 pounds.
Learn more about Linear Interpolation here:https://brainly.com/question/30766137
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