Answer:
(A)
As per the given condition.
You have 2 equations for y.
i,e y =8x and y= 2x+2
then, they will intersect at some point where y is the same for both equations.
That is why in equation y=8x you exchange y with other equation you got which is y=2x+2 once you do this you will have
8x = 2x+2 and the solution of which will satisfy both equation.
(B)
8x = 2x + 2
to find the solutions take the integer values of x between -3 and 3.
x = -3 , then
8(-3) = 2(-3) +2
-24 = -6+2
-12 = -4 False.
similarly, for x = -2
8(-2) = 2(-2)+2
-16 = -2 False
x = -1
8(-1) = 2(-1)+2
-8= 0 False
x = 0
8(0) = 2(0)+2
0= 2 False
x = 1
8(1) = 2(1)+2
8= 4 False
x = 2
8(2) = 2(2)+2
16 = 6 False
x = 3
8(3) = 2(3)+2
24 = 8 False
there is no solution to 8x = 2x +2 for the integers values of x between -3 and 3.
(C)
The equations cab be solved graphically by plotting the two given functions on a coordinate plane and identifying the point of intersection of the two graphs.
The point of intersection are the values of the variables which satisfy both equations at a particular point.
you can see the graph as shown below , the point of intersection at x =0.333 and value of y = 2.667
Answer:
Step-by-step explanation:
<u>Given functions</u>:
Solve for p(x) = r(x):
As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:
<u>Quadratic Formula</u>
Therefore:
Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:
Therefore, the solutions are:
Learn more about quadratic equations here:
Answer:
(a) The median is 1478
(b) Null hypothesis H₀ : μ₁ = μ₂
Alternative hypothesis Hₐ : μ₁ > μ₂
(c) The test statistic is 6.678155
(d) The p value is 1.2×10⁻¹¹
(e) We reject our null hypothesis H₀. In terms of the test, there is sufficient evidence to suggest that there is a trend in the numbers of daily newspaper because the probability for a decrease in the numbers is very high
Step-by-step explanation:
(a) Here we have the data as follows;
1623 1586 1574 1554 1544 1531 1519 1513 1491 1484 1478 1471 1458 1456 1458 1453 1438 1428 1405 1395 1377
The median is = 1478
Therefore we have above the median
1623 1586 1574 1554 1544 1531 1519 1513 1491 1484
The mean, = 1541.9
Standard deviation, σ₁ = 41.38224257
n₁ = 10
Below the median
1471 1458 1456 1458 1453 1438 1428 1405 1395 1377
The mean, = 1433.9
Standard deviation, σ₂ = 30.04812806
n₂ = 10
(b) Null hypothesis H₀ : μ₁ = μ₂
Alternative hypothesis Hₐ : μ₁ > μ₂
(c) The formula for t test is given by;
df = 10 - 1 = 9, α = 0.05
Therefore, the test statistic = 6.678155
(d) The p value from statistical relations is Probability p = 1.2×10⁻¹¹
Critical z at 5% confidence level = 1.645
Since P << 0.05, e reject the
(e) Therefore, we reject our null hypothesis H₀. In terms of the test, there is sufficient evidence to suggest that there is a trend in the numbers of daily newspaper because the probability for a decrease in the numbers is very high.