Answer:
21 and 22
Step-by-step explanation:
Let's work backward from that 81%: x/25 = 0.81 yields x = 20.25. Nominally, 20.25 / 25 = 0.81, but x must be an integer. Let's round 20.25 off to 20.
Thus, if Kalsom got 81%, it was a result of his having done 20 questions correctly.
81% corresponds to 20 questions correct;
82% to 20.5 questions correct, or, rounding up, to 21 questions correct;
83% to 20.75, or 21;
84% to 21 questions correct; this is the only result that makes sense (whole number of questions answered correctly)
85% to 21.25;
86% to 21.5;
87% to 21.75;
88% to 22 questions correct (this makes sense, unlike the last three)
89% to 22.25;
90% to 22.5;
91% to 22.75;
Assuming that the number of questions correct MUST be integer, then the possible number correct are 21 and 22, corresponding to 84% and 88% respectively.
<h3>
Answer: -19, -15, -9, -1, 9 (choice A)</h3>
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Explanation:
If we plug in x = -2, then we get,
y = x^2 + 7x - 9
y = (-2)^2 + 7(-2) - 9
y = 4 - 14 - 9
y = -10 - 9
y = -19
So x = -2 leads to y = -19. The answer is between A and D.
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If you repeat those steps for x = -1, then you should get y = -15
Then x = 0 leads to y = -9
x = 1 leads to y = -1
Finally, x = 2 leads to y = 9
The outputs we get are: -19, -15, -9, -1, 9 which is choice A
Choice D is fairly close, but we won't have a second copy of -15, and we don't have an output of -19.
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
<h3>How to estimate a definite integral by numerical methods</h3>
In this problem we must make use of Euler's method to estimate the upper bound of a <em>definite</em> integral. Euler's method is a <em>multi-step</em> method, related to Runge-Kutta methods, used to estimate <em>integral</em> values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
- Define the function seen in the statement by the label f(x₀, y₀).
- Determine the different variables by the following formulas:
xₙ₊₁ = xₙ + (n + 1) · Δx (2)
yₙ₊₁ = yₙ + Δx · f(xₙ, yₙ) (3) - Find the integral.
The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the <em>numerical</em> approximation of the <em>definite</em> integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the <em>numerical approximate</em> solution of the <em>definite</em> integral is 4.189 648.
To learn more on Euler's method: brainly.com/question/16807646
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Answer:
If you are reffering to GCF then the GCF would be explained like this
Find the prime factorization of 18
18 = 2 × 3 × 3
Find the prime factorization of 60
60 = 2 × 2 × 3 × 5
To find the gcf, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 3
GCF = 6
Answer:
B.
Step-by-step explanation:
f(x - c) shift the function <em>c</em> units to the right.
In this case, if (x - 1) was substituted in place of the x, the graph would shift 1 unit to the right.
If you want to graph the new function and know the graph of the previous one, this relationship avoids you the substitution of (x - 1) into the function and expansion of the expression to obtain a new quadratic formula.
