Answer:
let the larger and smaller number be x and y respectively
first condition
x + y = 49
second condition
3x = 2y+97
3x-2y =97
Multiplying first condition by two and adding both equations
2x + 2y = 98
<u>3x -2y = 97</u>
5x = 195
x = 195/5 = 39
putting the value of x in
x + y = 49
y = 49 -39 = 10
again
Step-by-step explanation:
A^2-5a = 6
a^2-5a-6 = 0
Discriminant = (-5)^2-4(1)(-6) = 49
Discriminant is positive so there are two solutions
Answer:
Part 1) The explanatory variable is the type of oven
It is a categorical variable
Part 2) The response variable is the baking time
It is a quantitative variable
part 3) two-sample z-test for proportions should be used for the test
Step-by-step explanation:
An explanatory variable is an independent variable that is not affected by all other variables. In this experiment, the type of oven is the input variable and it is not affected by any other variable
A categorical variable is one that has two or more categories without any intrinsic ordering of the categories. The type of oven is either gas or electric, so it is categorical.
A response variable is a dependent variable whose variation depends on other variables. The baking time in this experiment depends on the type of oven used
A quantitative variable is one that take on numerical values.
A two proportion z-test allows you to compare two proportions to see if they are the same. The null hypothesis (H0) for the test is that the proportions are the same. The alternate hypothesis (H1) is that the proportions are not the same.
Answer:
Area = pi X r^2 = pi x (1)^2 = 3.14 x 1 = 3.14
Step-by-step explanation:
For f(t) = 3 sin(t), the minimum is -3, the maximum is 3.
For additional information:
The period T of the function y=3sin(4t) is;
The period of y = 3 sin (4t) is (2pi) / 4 = pi / 2
The sine function with amplitude A = 0.75 and period T = 10, is
y = 0.75 sin( (2pi / 10) x )
= 0.75 sin( (pi/5) t)
y(4) = 0.75 sin( (pi/5) (4) )
= 0.75 sin ( (4/5) pi ) = .4408
Drawing the sine and cosine function on the same plot shows
that they are identical except for a horizontal shift.
The cosine
function leads the sine function by a shift of (2pi/4) = pi/2.
For the last part, y(4) = 0.75 cos( (2pi/10) (4) ) = - 0.6067
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