F(x, y, z) = xe^(5yz) find the gradient of f
Solve for x.
5x - 1 = 26
x = 27/5
x = 5
x = -5
A company makes 3 types of cable. cable a requires 3 black, 3 white, and 2 red wires. b requires 1 black, 2 white, and 1 red wire. c requires 2 black, 1 white, and 2 red wire. they used 120 black, 110 white and 100 red wires. how many of each cable were made? setup the system of equations to solve this problem by selecting the coefficients and constants for each colored wires.
To determine the number of each cable produced, a system of equations is set up with variables representing the cable types and coefficients corresponding to the number of wires used per cable. The system consists of three equations based on the colors of wires and the totals used.
To solve this problem, we can set up a system of equations where the unknowns are the number of each type of cable produced. Let's represent the number of type A cables as x, type B cables as y, and type C cables as z. Considering the number of wires used for each type of cable and the total used, we form the following equations:
3x + y + 2z = 120 (black wires)3x + 2y + z = 110 (white wires)2x + y + 2z = 100 (red wires)To find the number of each cable made, we need to solve this system of equations simultaneously. The coefficients represent the number of each color wire needed for each cable type, and the constants (120, 110, 100) represent the total number of wires used.
Find the indicated partial derivatives. w = x y + 7z
GEOMETRY!! Provide the missing reasons for the proof.
Given: AB ≅ CD
BA ⊥ AC
DC ⊥ AC
Prove: BC ≅ DA
The triangle ΔABC is congruent to the triangle ΔCDA. Then the side BC is equal to the side DA.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The triangles are said to be identical if the two sides and that included aspect of one triangle match the two sides and that includes the degree of the other triangle.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Statements Reason
AB = CD (Given)
AC = AC (Reflexive Property)
BA ⊥ AC and DA ⊥ AC (Given)
∠BAC = ∠DCA (Perpendicular makes right angle)
ΔABC ≅ ΔCDA (Congruent triangle)
BC = DA (Corresponding sides are equal to a congruent triangle)
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Suppose that work hours in new zombie are 200 in year 1 and productivity is $18 per hour worked. instructions: in part a, enter your answer as a whole number. in part b, round your answer to 2 decimal places.
a. what is new zombie's real gdp
The ratio 30 in. To 9ft in simplest form
what is the equation of the horizontal line passing through the point (2,-8)
Each newborn baby has a probability of approximately 0.49 of being female and 0.51 of being male. for a family with four children, let x = the number of children who are girls.
I believe this problem has 3 questions:
a. Explain why the three conditions are satisfied for X to have the binomial distribution.
b. Identify n and p for the binomial distribution.
c. Find the probability that the family has two girls and two boys.
Answers:
a. First because there are only 2 possible outcomes for
each birth: male or female. Hence a binomial distribution.
Second, because the probability of giving out a girl is
constant: 0.49 for each birth.
Third, the probability of a giving out a girl does not depend
on whether or not there is already a boy or a girl in the family.
b. The n is the total number of children, so n = 4
While the p is the success of being a girls, so P = 0.49
c. We use the binomial probability equation:
P (X) = nCx * p^x * q^(n-x)
P(X=2) = 4!/(2!2!) * 0.49^2 * 0.51^2 = 0.3747
Final answer:
Inheritance of sex chromosomes in babies is determined by the father, leading to a 50:50 chance of a male or female child. The likelihood of a newborn being female is around 0.49.
Explanation:
Sex Inheritance: The sex of a baby is determined by the father, who has a 50 percent chance of passing on a Y chromosome resulting in a male child. If the baby inherits two X chromosomes, it will be female. This 50:50 chance applies to each baby. For a family with four children, let x = the number of girls, the probability of a child being female is approximately 0.49.
In one month Miranda earned $800 at her part-time job, and $70 was withheld for federal income tax. Suppose she earns $1200 next month. How much will be withheld for federal income tax?
In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a row so that those of the same nationality sit together?
The total number of ways in which the members of the different nationalities can be seated such that those of the same nationality sit together is 331776 ways. This is calculated using the concept of permutations.
Explanation:This question can be solved using the concept of permutations and combinations. We assume that groups of people of the same nationality are distinct. Thus, we can treat them as individual entities. We have four entities in total: a group of 3 Americans, a group of 4 Frenchmen, a group of 4 Danes, and a group of 2 Italians.
Firstly, these 4 entities can be arranged in 4! ways, which is 4*3*2*1 = 24 ways.
Within each nationality group, the people can be arranged amongst themselves in the following ways: Americans - 3!, Frenchmen - 4!, Danes - 4! and Italians - 2!. This is equal to 3*2*1 = 6, 4*3*2*1 = 24, 4*3*2*1 = 24 and 2*1 = 2 respectively.
Therefore, the total number of ways in which the nationalities can be seated such that those of the same nationality sit together is:
4! * (3! * 4! * 4! * 2!) = 24 * (6 * 24 * 24 * 2) = 331776 ways.
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The number of ways the Americans, Frenchmen, Danes, and Italians can be seated together is 20,736.
Explanation:To count the number of ways the Americans, Frenchmen, Danes, and Italians can be seated together, we can treat each nationality as a single group and consider the groups as individuals. Therefore, we have 4 groups to arrange in a row. Within each group, the individuals can be arranged among themselves. The number of ways to arrange the individuals within a group is given by the factorial of the number of individuals in that group. So, the total number of arrangements is:
Number of arrangements = 4! × 3! × 4! × 2!
Substituting the factorials with their corresponding values:
Number of arrangements = 24 × 6 × 24 × 2 = 20,736
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There are four large groups of people, each with 1000 members. any two of these groups have 100 members in common. any three of these groups have 10 members in common. and there is 1 person in all four groups. all together, how many people are in these groups? (scheinerman 116) scheinerman, edward
a. mathematics: a discrete introduction, 3rd edition. cengage learning, 20120305. vitalbook file.
Final answer:
Using the principle of Inclusion-Exclusion, and taking the common members in two, three, and four groups into account, we find that there are 3439 unique members across the four groups.
Explanation:
To solve this problem, we need to use the principle of Inclusion-Exclusion. Let's denote the four groups as A, B, C, and D. According to the question, each group has 1000 members (n(A) = n(B) = n(C) = n(D) = 1000).
Any two groups have 100 members in common. That means, for instance, n(A ∩ B) = n(A ∩ C) = n(A ∩ D) = n(B ∩ C) = n(B ∩ D) = n(C ∩ D) = 100.
Any three groups have 10 members in common, which gives us n(A ∩ B ∩ C) = n(A ∩ B ∩ D) = n(A ∩ C ∩ D) = n(B ∩ C ∩ D) = 10.
There is 1 person in all four groups, so n(A ∩ B ∩ C ∩ D) = 1.
The total number of unique members in all groups, denoted as n(A ∩ B ∩ C ∩ D), is given by:
n(A ∩ B ∩ C ∩ D) = n(A) + n(B) + n(C) + n(D) - [sum of the number of common members between every two groups] + [sum of the number of common members between every three groups] - [number of members common to all four groups].
Substituting the values:
n(A ∩ B ∩ C ∩ D) = 4(1000) - [6(100)] + [4(10)] - 1 = 4000 - 600 + 40 - 1 = 3439.
Therefore, there are 3439 unique members across all groups.
Does x=5 in this equation? ... 2+3(x+1)=6x
Paul has decided to set up his own recording studio. He needs to purchase four speakers at $435 apiece and two mixers at $772 apiece. He also needs to soundproof a room, which will cost him $838. If Paul has $4,500 in his savings account, how close can he come to setting up his studio? a. Paul can set up his studio and have $378 left over. b. Paul can set up his studio and have $410 left over. c. Paul needs an additional $1,166 to set up his studio. d. Paul needs an additional $296 to set up his studio.
Answer:
Paul can set up his studio and have $378 left over.
Step-by-step explanation:
Consider the provided information,
He needs to purchase four speakers at $435 a piece.
The total cost of four speakers is $435×4=$1740
He needs to purchase two mixers at $772 a piece.
The total cost of two mixers is $772×2=$1544
He also needs to soundproof a room, which will cost him $838.
Thus, the total money he needs to spend is:
$1740+$1544+$838=$4122
Paul has $4,500 in his savings account.
It is clear that $4500 is more than $4122.
$4500-$4122=$378
Hence, Paul can set up his studio and have $378 left over.
Geraldo wants to start a group bike ride on Sunday mornings for students at his school. He asked 30 students in the lunchroom how many miles they ride their bikes each month. He obtained the following results. 8, 3, 0, 1, 2, 3, 6, 3, 0, 4, 13, 1, 3, 12, 15, 2, 1, 3, 2, 2, 0, 3, 4, 2, 6, 7, 12, 8, 4, 0 The fraction x/30 shows the ratio of the number of students who ride their bikes more than 10 miles each month to the number of students surveyed. What is the value of x?
Answer:
x = 4 is the answer.
Step-by-step explanation:
List of rides in a month of 30 students have been given in the question.
We have to find the value of x if fraction x/30 shows the ratio of the number of students who ride their bikes more than 10 miles each month to the number of students surveyed.
Therefore x/30 = 4/30
x = 4×30/30 = 4
So x = 4 is the answer.
A=4[tex] \pi r2[/tex]. solve for R
There are currently 3 students signed up for a trip. The van can transport only 7 students.
Which graph shows all the possible values for the extra number of students that need to sign up so that more than one van is needed to transport them?
Number line with closed circle on 4 and shading to the right.
Number line with closed circle on 4 and shading to the left.
Number line with open circle on 4 and shading to the right.
Number line with open circle on 4 and shading to the left.
Answer:
what he said up so he can get brainliest
Step-by-step explanation:
Solve the system
4x+2y=7 y=5x
A. (1,5)
B. (3,15)
C. (2,10)
D. (0.5,2.5)
Consider the function below.
x -1 0 1 2
f(x) -2 3 8 13
Which of the following functions could be the inverse of function f?
x -2 3 8 13
q(x) -1 0 1 2
x -2 -3 -8 -13
r(x) 1 0 -1 -2
x -1 0 1 2
p(x) 2 -3 -8 -13
x 1 0 -1 -2
s(x) -2 3 8 13
7,243 ÷ 4.
What is the remainder?
If the temperature at which a certain compound melts is a random variable with mean value 120 ???? ???? and standard deviation 2 ???? ???? , what are the mean temperature and standard deviation measured in �
The standard error of the sample mean is approximately 0.0671 degrees Fahrenheit when rounded to two decimal places. The distribution of the sample mean is a t-distribution due to the use of the sample standard deviation as an estimate.
Explanation:The question involves calculating the standard error of the sample mean for a set of body temperature measurements. To find the standard error, we use the formula: standard error = sample standard deviation / sqrt(sample size). With a sample standard deviation of 0.3 degrees Fahrenheit and a sample size of 20, the standard error is calculated as:
standard error = 0.3 / sqrt(20)
standard error = 0.3 / 4.472
standard error ≈ 0.0671 (rounded to two decimal places)
The distribution of the sample mean is a t-distribution because we are using the sample standard deviation as an estimate of the population standard deviation, which is unknown.
Determine whether the graph represents a proportional relationship.
A graph is shown. The x-axis is labeled from 0 to 9. The y-axis is labeled from 0 to 15. Four points are shown on the graph on ordered pairs 0, 2 and 1, 6 and 2, 10 and 3, 12. These points are joined by a line. The label on the x-axis is Number of cars. The title on the y-axis is Number of wheels.
Yes, it is a proportional relationship because the graph goes through the origin
Yes, it is a proportional relationship because the graph is a straight line
No, it is not a proportional relationship because the graph is not a straight line
No, it is not a proportional relationship because the graph does not go through the origin
Answer:
No, it is not a proportional relationship because the graph does not go through the origin
Step-by-step explanation:
that is the awnser hope i helped
The equation for line g is given by 5y=2x-20. Suppose line g is parallel to like r and line e is perpendicular to line g. Point (10,-8) lies on both line r and line
Randall record 8 songs on his most recent cd. The total length of the cd is 49 minutes find a unit rate to represent the average
Which of the following is the correct factored form of the given equation? 4x 2 - 11x + 6 = 0
[tex]4x^2-11x+6=0\\\\4x^2-8x-3x+6=0\\\\4x(x-2)-3(x-2)=0\\\\(x-2)(4x-3)=0[/tex]
Answer:
(4x - 3)(x - 2) = 0
Paula runs around the local park. What is the perimeter of the park. Give your and in kilometres
you put 500$ in a savings account. The account earns 15.75$ simple interest in 6 months.what is the annual interest rate
There is a probability of 0.93 that a visitor to a website will bounce (leave the website without clicking on any links). what is the probability that at least 10 of the next 12 visitors to the website will bounce?
Final answer:
To find the probability that at least 10 of the next 12 website visitors will bounce, you calculate the sum of the binomial probabilities for 10, 11, and 12 successes (bounces) out of 12 trials.
Explanation:
To find the probability that at least 10 of the next 12 visitors to a website will bounce, we can use the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
C(n, k) is the combination of n items taken k at a time.
p is the probability of a single success (in this case, a bounce).
k is the number of successes.
n is the total number of trials.
In this question:
p = 0.93 (probability of bounce)
n = 12 (total visitors)
We want to calculate the probability of at least 10 bounces, so we need to calculate P(X = 10) + P(X = 11) + P(X = 12).
P(X = 10) = C(12, 10) * 0.93^10 * (1 - 0.93)^(12 - 10)
P(X = 11) = C(12, 11) * 0.93^11 * (1 - 0.93)^(12 - 11)
P(X = 12) = C(12, 12) * 0.93^12 * (1 - 0.93)^(12 - 12)
The final probability is the sum of these three probabilities.
Roy is saving to buy a new bike, which costs $258. He has $16 towards this purchase. Express how much more Roy needs in the form of an equation?
If an item is 1/3 off, to calculate the final price simply divide the original price by 3.
true or false