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Sunny_sXe [5.5K]
3 years ago
12

Write an equation of the line that passes through the given point and has the given slope.

Mathematics
1 answer:
ycow [4]3 years ago
5 0

Answer:

y = 1/2x + 1

Step-by-step explanation:

m = 1/2

Slope-intercept:

y - y1 = m(x - x1)

y - 3 = 1/2(x - 4)

y - 3 = 1/2x - 2

y = 1/2x + 1

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Each year, all final year students take a mathematics exam. It is hypothesized that the population mean score for this test is 8
drek231 [11]

Answer:

95% Confidence interval:  (96.06,103.94)

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 85

Sample mean, \bar{x} = 100

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 11

95% Confidence interval:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

100 \pm 1.96(\frac{11}{\sqrt{30}} ) = 100 \pm 3.94= (96.06,103.94)

(96.06,103.94) is the 95% confidence interval for  the population mean test score.

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3 years ago
Mackenzie practices the piano 609 minutes in 3 weeks. At what rate did she practice, in minutes per day?​
Step2247 [10]

Answer:

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Step-by-step explanation:

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3 years ago
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Choose the correct description of the graph of the compound inequality: x − 2 &gt; −3 and 3x less than or equal to 12
STALIN [3.7K]
<span>X - 2 > -3 x > -3 + 2 x > -1 A number line with an open circle -1, closed circle on 4 and shading in between.,when dividing/multiplying by a negative, the inequality sign changes. An open circle is used when there is no equal sign involved. A closed circle is used when there is an equal sign involved. If it is greater then, shading goes to the right. If it is less then, shading goes to the left</span>
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros for
timama [110]
The general form of a polynomial is: x² + bx + c = 0. Substituting the roots,

3² + b(3) + c = 0
3b + c = -9 --> eqn 1

(5 + √5)² + (5 +√5)(b) + c = 0
(5+√5)b + c = -30-10√5 --> eqn 2

Solving both equations simultaneously by subtracting eqn 2 from eqn 1,
(-2 - √5)b = 21 + 10√5
b = -8 - √5

Using eqn 1,
3(-8 - √5) + c = -9
-24 - 3√5 + c = -9
c = -9 + 24 + 3√5
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Hence, the polynomial is: <em>f(x) = x² + (-8 - √5)x + (15 + 3√5)</em>.
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