which equations are true when k = - 50? Select two correct answers.
1.5 - k/5 = 11.5
-2k + 78 = -22
-4k + 80 = -120
6k - 150 = -150
K/10 -3 = -8
30 POINTS IF YOU ANSWER!!
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
Given,
The equations;
1.5 - k/5 = 11.5-2k + 78 = -22-4k + 80 = -1206k - 150 = -150K/10 -3 = -8The value of k = -50
We have to solve the given equations using k as -50 and find the true ones;
Lets check;
1.5 - k/5 = 11.51.5 - (-50/5) = 11.5
1.5 - (-10) = 11.5
1.5 + 10 = 11.5
11.5 = 11.5
This equation is true.
-2k + 78 = -22(-2 x -50) + 78 = -22
100 + 78 = -22
178 ≠ -22
This equation is false
-4k + 80 = -120(-4 x -50) + 80 = -120
200 + 80 = -120
280 ≠ -120
This equation is false
6k - 150 = -150(6 x -50) - 150 = -150
-300 - 150 = -150
-450 ≠ -150
This equation is false
k/10 -3 = -8(-50/10) - 3 = -8
-5 - 3 = -8
-8 = -8
This equation is true.
That is,
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
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Let k ? R and f(x, y-x2 + y2 + kxy. If you imagine the graph changing as k increases, at what values of k does the shape of the graph change qualitatively? Justify your answer.
The shape of the graph changes qualitatively at k = ± 2 and
\(k=\sqrt{(2)\).
The given function is f(x,y) = y-x²+y²+kxy.
The critical points of the function are found by taking the partial derivatives and equating them to zero:
∂f/∂x = -2x + ky = 0
y = 2x/k
∂f/∂y = 2y + kx = 0
y = -kx/2
Substituting y from the first equation into the second equation gives
x = k²x/4, so k² = 4 and k = ± 2.
Therefore, the critical points are (0,0), (2,4), and (-2,4)
We will now examine the critical points to see when the shape of the graph changes qualitatively.
There are two cases to consider:
Case 1: (0,0)At (0,0), the Hessian matrix is
H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]
=[ -2 0;0 2].
The determinant of the Hessian matrix is -4, which is negative.
Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.
Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is
H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]
=[ -2k 2k;2k 2].
The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).
Therefore, the critical points (2,4) and (-2,4) are local minima when
k > √(2).
Thus, the shape of the graph changes qualitatively at k = ± 2 and
k = √(2).
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Think of all the professors you have this term and consider them to be a sample of all FSU professors. You are going to use this sample of professors to construct a one-sample confidence interval estimate of the average height of all FSU professors.
(i) Would you do a Z-interval or a T-interval? Choose Z or T
(ii) Explain why you would do the type of interval (Z or T) that you selected above. Enter the letter of your answer choice:
A. Because I have a large number of professors.
B. Because I have a small number of professors.
C. Because I know the standard deviation of my professors' heights.
D. Because I know the standard deviation of all FSU professors' heights.
E. Because I have a large number of professors and I know the standard deviation of my professors' heights.
F. Because I don't have a large number of professors and I don't know the standard deviation of all FSU professors' heights.
(i) T-interval
(ii) F. Because I don't have a large number of professors and I don't know the standard deviation of all FSU professors' heights.
What is standard deviation?
Standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean value.
When constructing a confidence interval for the mean of a population using a sample, we use either a Z-interval or a T-interval based on the sample size and whether we know the population standard deviation.
If the sample size is large (usually taken to be greater than or equal to 30) and/or we know the population standard deviation, then we can use a Z-interval.
However, if the sample size is small (usually less than 30) and/or we don't know the population standard deviation, we should use a T-interval.
In this case, we don't have a large sample size (just the professors the student has this term), and we don't know the standard deviation of all FSU professors' heights, so we would use a T-interval.
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PLEASE HELPPP TEST TMR PROBLEM ISW IN PHOTO BELOW
Answer:
AB = A'B', AD = A'D', CD = C'D', CB = C'B'
Step-by-step explanation:
There is more then one way to give this problem a solution. The point of the question is to explain or provide an argument that will prove that the square ABCD is the same as A'B'C'D.
The way to prove it is by saying that the sides are equal, meaning the answer I provided above, by claiming that side AB is also equal to A'B', and so forth with all four sides.
Both Marker Farms and Jackson Farms sell apples at the farmer’s market. Maker offers 23 apples in 2 Baskets. Jackson farms offers 39 apples in 3 baskets. if price were the same for which farm provides a better value for a customer wanting apples
The farmer will make 14 baskets containing each of 5 apples and 7 peaches.
What is CGF?In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.
here, we have,
How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?
Given:
A farmer harvests 70 apples and 98 peaches.
They want to make baskets that have both apples and peaches to sell at the market.
Each basket should contain the same combinations of fruit.
They want to sell all the apples and peaches and as many baskets as possible.
Find:
How many baskets can the farm make having x apples and y peaches in the baskets?
Solution:
So, for solving this kind of question first we have to find the greatest common factor, we get;
70 = 2*5*7
98 = 2*7*7
the common factor are 2 and 7
the greatest common factor is 2*7=14
70 apples = 14*5
98 peaches = 14*7
So, the farmer will make 14 baskets each of 5 apples and 7 peaches.
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a rectangular room is times as long as it is wide, and its perimeter is meters. find the dimension of the room.
Answer: Use a variable
w
to represent the width of the room.
From the given information find that
10
w
=
80
, hence
w
=
8
.
So the room is
8
meters by
32
meters.
Explanation:
Let
w
represent the width of the room in meters.
Then the length of the room is
4
w
.
So the perimeter of the room is
w
+
4
w
+
w
+
4
w
=
10
w
.
Given that the perimeter is
80
meters, that translates as:
10
w
=
80
Divide both sides by
10
to get
w
=
8
.
Hence the width of the room is
8
meters and the length is
4
w
=
32
meters.
Step-by-step explanation:
The dimensions of the room are 5 meters long and 5 meters wide.
The perimeter of a rectangular room is equal to twice the sum of its length and width. In this case, the perimeter of the rectangular room is equal to 2 x (length + width) = 10 meters.
Therefore, we can write:
2 x (L + W) = 10
To find the dimensions of the room, we need to solve the equation for L and W.
L + W = 5
L = 5 - W
Substitute this equation for L in the original equation:
2 x (5 - W + W) = 10
2 x (5) = 10
10 = 10
Therefore, L = 5 and W = 5, so the dimensions of the room are 5 meters long and 5 meters wide.
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What is the answer for -3p(p+2) - (2p+3) using the distribution method?
Answer: -3p^2-8p-3
Step-by-step explanation: By distributing we get, -3p^2-6p-2p-3. Then simplify accordingly.
To figure out this problem, we need to break down the steps:
-3p(p + 2) - (2p + 3)
because -3p is next to the equation in parentheses, (p + 2), you should multiply -3p into both p and 2
-3p x p = -3p² (if you multiply a variable (p) by another of the same variable with no power, it becomes squared)
-3p x 2 = -6p
so the first part of the equation went from -3p(p + 2) to -3p² -6p
and the second part of the equation has no multiplying to do
so now we add like terms!
-3p² -6p - 2p + 3
-3p² -8p + 3
order from greatest power to least power (first goes the number/variable with the highest power, then the term with a variable, and lastly the number. Right now it is currently in the correct order).
-3p² -8p + 3 is your final answer
How is Jim characterized throughout the story by his relationship with his daughter, ’Lizabeth? How does he contrast with the most of the white male characters to which we’ve been introduced?
Jim is characterized as a caring and supportive father through his relationship with his daughter, 'Lizabeth. He contrasts with the majority of the white male characters introduced in the story by defying stereotypes and exhibiting empathy and understanding.
Throughout the story, Jim's relationship with his daughter, 'Lizabeth, portrays him as a caring and supportive father. He shows genuine concern for her well-being and takes the time to listen to her thoughts and feelings. Jim encourages 'Lizabeth to think critically and make her own decisions, empowering her to navigate the challenges they face as a family. His unconditional love and guidance demonstrate a strong bond between father and daughter.
In contrast to the majority of the white male characters introduced in the story, Jim stands out by defying stereotypes. While some of the white male characters exhibit prejudice, discrimination, or indifference, Jim showcases empathy and understanding. He treats 'Lizabeth with respect and dignity, embracing her individuality and supporting her aspirations. Jim's character challenges the notion that all white male characters in the story share the same mindset or exhibit negative qualities. Instead, he represents a positive portrayal of a white male character who breaks away from stereotypes and fosters a nurturing relationship with his daughter.
Overall, Jim's characterization through his relationship with 'Lizabeth highlights his caring nature as a father and his contrasting qualities to the other white male characters in the story, emphasizing his empathy and understanding.
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Using a calculator, find the value of each of the following ratios, giving your answer correct to 3 significant figures. (a) tan 16° (b) tan 89° (c) tan 18.7° (d) tan 45.4°
Answer: (a) tan 16°:
Using a calculator, we get:
tan 16° ≈ 0.291
Rounding to three significant figures, tan 16° ≈ 0.291.
(b) tan 89°:
Using a calculator, we get:
tan 89° ≈ 57.290
Note that this value is extremely large and not meaningful in most contexts.
(c) tan 18.7°:
Using a calculator, we get:
tan 18.7° ≈ 0.340
Rounding to three significant figures, tan 18.7° ≈ 0.340.
(d) tan 45.4°:
Using a calculator, we get:
tan 45.4° ≈ 1.058
Rounding to three significant figures, tan 45.4° ≈ 1.06.
Step-by-step explanation:
A car travels about 34 feet in one second. At this speed,
about how many feet will the car travel in 7 sebonds?
A
438 feet
B
2,800 feet
C. 238 feet
D. 2,140 feet
Answer:
C
Step-by-step explanation:
34 * 7= 238
34 feet per second, means that we have to mulitply 7 by 34.
Its really simple!
1 second: 34
7 seconds: ?
for example, if we needed 2 seconds we would muliplty by 2, 34 * 2 because we double it, the same way we would solve that, we would solve 34*7
\(Hey\) \(there!\)
\(The\) \(answer\) \(is\) \(238\)
\(We\) \(simply\) \(multiply\) \(34\) \(by\) \(7\):
\(34 * 7 = 238\)
\(Hope\) \(it\) \(helps!\) \(Have\) \(an\) \(amazing\) \(day!!!!!!\)
Determine the value of x in each figure.
Answer:
x=15is your answer
Step-by-step explanation:
8x=120 vertically opposite angle
x=120/8=15
8x = 120
x = 120/8 = 15.
so ans ia 15
adding fractions with unlike denominators worksheets
The simplification of the addition of two or more fraction with unlike denominator is:
Convert the denominator with like terms and then add the numerators.
Method of simplification of addition of fraction with unlike denominator is:
Calculate the least common multiple of all the denominator of unlike fraction.Convert the denominator of the fraction with like terms.Now add the numerator of the given fraction.Example : ( 1 / 2) + ( 3 / 5 )Least common multiple of 2 and 5 is 10.Multiply by ( 5 / 5) to ( 1/ 2) which is equal to ( 5 / 10 ).Multiply ( 2/ 2 ) to ( 3 /5 ) we get ( 6 /10).Add like fraction ( 5/10) + ( 6 /10) = ( 5+ 6 ) /10Result is 11 /10.Therefore, to simplify unlike fractions find least common multiple and add the like fractions.
The given question is incomplete, I answer the question in general according to my knowledge:
Simplification of adding fractions with unlike denominators with example?
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ASAP!!
The lengths of two sides of a triangle are given. The length of the third side must be between what two numbers?
Answer:
Step-by-step explanation:
If the lengths of two sides of a triangle are given the third side must be less than the sum of those two sides, but more than the value of the difference between the given two sides.
So for #9, the answer is 4 (which is 12-8) <x<16 (which is 12+8)
#10. 10<x<16
#11. 19<x<61
#12. 6<x<16
Below are what would happen if the 3rd side was too big (left) or too small (right)
suppose a 5 × 3 matrix has 3 pivot columns. is Col A = R^5 ? Is Nul A = R^2? Explain your results
A 5 × 3 matrix A has 3 pivot columns. Col A is a subspace of \(R^5\) with dimension 3, and Nul A is not equal to \(R^2\); it has a dimension of 0.
Suppose a 5 × 3 matrix A has 3 pivot columns. A pivot column is a column in a matrix that has a leading 1 (pivot position) after performing row reduction. Having 3 pivot columns in matrix A means there are 3 linearly independent columns.
Now, let's consider the two parts of your question:
1. Is Col A = R^5?
Col A represents the column space of matrix A, which is the span of its linearly independent columns. Since A is a 5 × 3 matrix with 3 linearly independent columns, the dimension of Col A (the column space) is 3. Therefore, Col A is a subspace of \(R^5\), but not equal to \(R^5\).
2. Is Nul A = \(R^2\)?
Nul A represents the null space of matrix A, which is the set of all solutions to the homogeneous system Ax = 0. The dimension of the null space called the nullity of A, is equal to the number of columns minus the number of pivot columns. In this case, nullity(A) = 3 (number of columns) - 3 (pivot columns) = 0. This means Nul A has a dimension of 0, not 2, and consists only of the zero vector. So, Nul A ≠ \(R^2\).
To summarize, Col A is a subspace of \(R^5\) with dimension 3, and Nul A is not equal to \(R^2\); it has a dimension of 0.
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Factor 24x−20 using the GCF.
need it asap!
Answer:
The factor is 4.
Step-by-step explanation:
You can divide both 24 and 20 by 4, leaving you with 6x-5.
Highest common factor should be 4.
Given that,
The equation is 24x - 20.Based on the above information, the calculation is as follows:
Here 24 and 20 should be divisible by 4
So,
= 4(6x - 5)
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How many grams of carbohydrates do 2.5 servings of rice have
Answer:
45 g
Step-by-step explanation:
what is the answer of 1/3pi x r^2 / 4 x 2h?
PLEASE ANSWER FAST ILL MARKYOU AS A BRAINLIST
Answer:
1/3pi x r^2 / 4 x 2h
Step-by-step explanation:
Ummm I'm just clueless. :/
In a computer store, 30% of the computers in stock are laptops, 60% are traditional desktops, and 10% are all-in-one touch screen machines. Ten percent of the laptops, thirteen percent of the desktops, and five percent of the all-in-one machines are on sale. A computer is randomly chosen from the inventory of the store. If the computer chosen is on sale, what is the probability that the computer is an all-in-one machine
The probability that the computer is an all-in-one machine is 10%
According to the statement
we have given that the 30% of the computers in stock are laptops, 60% are traditional desktops, and 10% are all-in-one touch screen machines.
And we have to find the probability that the computer is an all-in-one machine.
So, For this purpose, we know that the
The probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.
So, According to the statement
The computers in stock are laptops are 0.3
The computers in stock are traditional desktops are 0.6
The computers in stock are all-in-one touch screen machines are 0.1
Now the probability are
Probability that the computer is an all-in-one machine = Probability that the computers in stock are all-in-one touch screen machines / total computers in the stock.
Substitute the values in it then
Probability that the computer is an all-in-one machine = 0.1 / ( 0.3 + 0.6 + 0.1)
Probability that the computer is an all-in-one machine = 0.1 / 1
Probability that the computer is an all-in-one machine = 0.1.
So, The probability that the computer is an all-in-one machine is 10%.
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What is the equation for the line shown, in slope-intercept form?
Question 8 options:
A) y = 2x - 2
B) y = -2x + 4
C) y = -4x - 2
D) y = -2x - 4
Answer: Solution In Photo
Answer:
D) y = -2x - 4Step-by-step explanation:
Use the points:
(-2, 0) and (0, -4)The y- intercept is - 4 and the slope is:
m = (-4 - 0)/(0 - (-2)) = -2The line is:
y = -2x - 4Correct choice is D
Timothy has a savings account. His balance was $600 when he decided to start making weekly deposits. The table below shows the value of his account (y)
after each weekly deposit (%).
Deposit (x) Account Value (y)
1
$750
2
$900
3
$1,050
4
$1,200
If his account continues to increase at the same rate, what will be the value of his account after he makes his 8th deposit?
Answer:
2
Step-by-step explanation:
What is the slope of (-3,4) and (0.3)
Answer:
m=-1/3
Step-by-step explanation:
To find the slope you have to use the equation:y₂-y₁ divided by x₂-x₁
So you would have 3-4 divided by 0-(-3)
And then you would get -1/3
Answer:
-0.33333
//////Step-by-step explanation:///////
Solve the triangle
A=53° B=65° a=7
Answer:
16.71
Step-by-step explanation:
What is the sum?
X
3
2
+
X+3 x+3 x+3
O
+
colch
53
X+5
X+3
X+5
3x+27
6x
X+3
The outcome or result of adding two or more integers is known as the SUM.
What is a sum?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
the sum of two or more numbers, magnitudes, quantities, or specifics as determined by or as though decided by the addition process in mathematics.
The outcome of adding two or more numbers, objects, or things is referred to in mathematics as the sum.
The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined.
\(Simplify $\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}: \frac{x+5}{x+3}$Steps$$\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}$$Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$$=\frac{x+3+2}{x+3}$$Add the numbers: $3+2=5$$$=\frac{x+5}{x+3}$$\)
Therefore, the correct answer is option b) \($=\frac{x+5}{x+3}$\)
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YALL!! \0/
IM FAILING THIS CLASS I NEED THIS EXTRA CREDIT PLEASE HELP IM TRYING TO FIX MY LIFE AND I CANT GO TRICK OR TREATING IF IT ISN’T FIXEDDDD
Answer: x = 11
the length of the shortest side is 13
please work harder in your classes and bring your grade so this wont happen again.
ask if you want an explanation of the answer :D
Step-by-step explanation:
Customers arrive (randomly) to a ticket window at 5 per minute, and service takes 10 seconds (deterministic), therefore the model is model is M/D/1 . Predict the average number of waiting on the queue(Lq). (round your answer with two decimal points)
Therefore, the average number of customers waiting in the queue (Lq) is approximately 4.17.
To predict the average number of customers waiting in the queue (Lq) in an M/D/1 queuing model, we can use Little's Law, which states that Lq = λ * Wq, where λ is the arrival rate and Wq is the average time a customer spends waiting in the queue.
In this case:
Arrival rate (λ) = 5 customers per minute
Service time (D) = 10 seconds = 10/60 = 1/6 minutes
To calculate the average time a customer spends waiting in the queue (Wq), we need to use the formula Wq = Ls / λ, where Ls is the average number of customers in the system.
In an M/D/1 queuing model, Ls can be calculated using the formula Ls = (λ²) / (μ * (μ - λ)), where μ is the service rate.
Since the service time is deterministic and given by D = 1/6 minutes, the service rate (μ) is the reciprocal of the service time: μ = 1/D = 6 customers per minute.
Now we can calculate Ls:
Ls = (λ²) / (μ * (μ - λ))
= (5²) / (6 * (6 - 5))
= 25 / 6
≈ 4.17
Finally, we can calculate Lq:
Lq = λ * Wq
= λ * (Ls / λ)
= Ls
≈ 4.17
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find the total surface area of this cuboid.
6cm
5cm
4cm
Answer:
148cm^2
Step-by-step explanation:
The formula for surface area of a rectangular prism is 2(hl)+2(hw)+2(wl).
we just plug in the values.
2(6 x 5) + 2(6 x 4) + 2(4 x 5)
= 2(30) + 2(24) + 2(20) then simplify
= 60 + 48 + 40
= 148
If the table below represents a propornal relationship, what number will go
in the empty box?
Notes (pages)
8
Time (hours)
16
18
20
9
10
11. Helpp
Since the box represents a proportional relationship, the empty box would be = 22.
What is a proportional relationship between two variables?When proportional relationship exists between two variables, it means that a particular value would be times with one variable to give the next compared variable.
For example, using the figures given above;
8 pages of notes = 16hours
1 page = 16/8 = 2 hours
Therefore, each page should be times by two to give the number of hours.
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The graph of y = x(x + 2)(x – 4) is shown.
Which statement about the graph is accurate?
An x-intercept of the graph is (2, 0).
The graph has no y-intercepts.
A y-intercept of the graph is (4, 0).
The graph has three x-intercepts.
Answer:
D
Step-by-step explanation:
HELP ME PLEASE!!! I’ll give points
Answer:
85 degrees
Step-by-step explanation:
5 and 7 are equal and 7 and 11 are also equal so 5 and 11 are equal to each other
g jon's bathtub is rectangular and its base is 12 ft2. how fast is the water level rising if jon is filling the tub at a rate of 0.5 ft3/min? (use decimal notation. give your answer to three decimal places.) rate
Jon's rectangular bathtub's base is 18 feet two inches in width. If Jon is filling the tub at a rate of 0.2 ft3/min, the water level will rise at a rate of 0.011 ft/min.
The volume of a rectangular bathtub can be expressed as follows:
where;
the base = length × breadth = 18ft²
the rectangular bathtub's volume is equal to 18 hrs
When the rate of rise of the volume is 0.2 ft3/min, differentiation is used to implicitly differentiate 18h with respect to t, resulting in:
dV/dt = 18dh/dt
0.2 = 18 dh/dt
Dh/dt = 1/18 * 0.2
Dh/dt = 0.011 ft/min
Therefore, if Jon fills the tub at a rate of 0.2 ft3/min, the rate at which the water level rises is 0.011 ft/min.
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