Answer:
The age of Jenny=21 years
The age of Steve=9 years
Step-by-step explanation:
So... Let's make their age into unknown variables so it's easier to decipher:
Jenny's age: x
Steve's age: y
If 5 years ago Jenny was four times older than Steve the equation would look like:
y+12-4y=-15
First, you add like terms:
y+12-4y=-15
y-4y=-15-12
Now isolate the unknown variable:
3y=-27
y=9
But this was 5 years ago, and Jenny is 12 years older than Steve so add those two together:
9+12=21
Hope this helped!
Answer:
b.
Step-by-step explanation:
Answer:
Option E. None of the above.
Step-by-step explanation:
From the question given above, the following data were obtained:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
Recall:
When a function f(x) is multiplied by it's inverse f¯¹(x), the result is equal to 1 i.e
f(x) × f¯¹(x) = 1
With the above information, we can determine the inverse of function given above as follow:
f(x) = (x – 5)/(2x + 3)
Inverse of f(x) => f¯¹(x) =?
f(x) × f¯¹(x) = 1
(x – 5)/(2x + 3) × f¯¹(x) = 1
f¯¹(x)(x – 5) / (2x + 3) = 1
Cross multiply
f¯¹(x)(x – 5) = (2x + 3)
Divide both side by (x – 5)
f¯¹(x) = (2x + 3) / (x – 5)
Thus, the inverse of the function is (2x + 3) / (x – 5).
Option E gives the correct answer to the question.
B) (-30,30)
C) (-30,45)
D) (30,-30)
Hi There!
Answer: A) (45,-30)
Why: x = 45 and y = -30
-30 = -4/5(45) + 6
-30 = -36 + 6
-30 = -30
Hope This Helps :)
Answer:
A is the correct answer
Step-by-step explanation:
took the exam
O B. The students' ability in Health °
C.The score of Group 2 on the achievement test
O D. The score of Group 1 on the achievement test
Answer:
The correct answer is:
The score on the achievement test (A)
Step-by-step explanation:
Please note that the terms "response variable" can be used instead of "dependent variable", and the dependent variable is a variable whose outcome is as a result of the change in the independent variable. It is the variable that the experimenter sets out to study in an experiment.
In this example, the score of the achievement test is a measure that tells of how effective the teaching method was on the selected group, and this is the dependent variable because it completely depends on the teaching method employed.
Please note that the dependent variable is another kind of variable and it is one that is completely under the control of the experimenter. In this case, the teaching method is the dependent variable.
This question is incomplete, the complete question is;
find the critical points and classify them as local maxima, local minima, saddle points, or none of these.
f(x,y) = (x + y)(xy + 1)
Answer:
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
Step-by-step explanation:
Given that;
f(x,y) = (x + y)(xy + 1)
f(x,y) =x²y + xy² + x + y
for critical points fx =0 ,fy =0
fx = 2xy + y² + 1 = 0, fy = x² + 2xy + 1 = 0
2xy + y² + 1 = 0, x²+ 2xy + 1 = 0
2xy + y² + 1 - x² - 2xy - 1 = 0
x² = y²
=> x = y, x = -y
2xy + y² + 1 = 0, x = y
2yy + y² + 1 = 0
3y² = -1 , no solution
2xy + y² + 1 = 0, x = -y
-2yy + y² + 1 = 0
=> -y2 + 1 = 0
=> y = -1, y = 1
y = -1 => x = 1, y = 1 => x = -1
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
Answer:
P(X≥11) = 0.1648
Step-by-step explanation:
Given
Mean, μ = 7.3
Potholes, n = 11
The interpretation of the question is to calculate P(X ≥ 11)
It is known that
P(X) = P(1) + P(2) +.......+P(infinite)
We can say that
P(X) = P(X≤10) + P(X>10)
Make P(X>10) the subject of formula
P(X>10) = P(X) - P(X≤10)
P(X>10) is equivalent to P(X≥11) and P(X) = 1.
By substituton, we have
P(X≥11) = 1 - P(X≤10)
So, we'll solve P(X≤10) using the following steps using n as 10.
To solve the above question using Microsoft Office Excel, follow the highlighted steps below
1. First goto FORMULAS tan
2. Select INSERT FUNCTION.
3. Select the POISSON.DIST function.
4. Enter the values for the number of events and the mean of occurrences per interval. In this case, enter 10 and 7.8, in that order and 1 for Cumulative since this is a cumulative probability.
5. Press OK.
Excel would display the probability.
In this case, it is 0.83523
Remember that
P(X≥11) = 1 - P(X≤10)
By substituton
P(X≥11) = 1 - 0.83523
P(X≥11) = 0.16477
Approximately,
P(X≥11) = 0.1648
(See attachment)