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Mazyrski [523]
2 years ago
9

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After runni

ng for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k – 2 = 1/9(t – 18) k – 18 = 1/9(t – 2) k – 2 = 9(t – 18) k – 18 = 9(t – 2)
Mathematics
1 answer:
viktelen [127]2 years ago
4 0

Answer:

the answer is C

Step-by-step explanation:

using her first part 2 kilometers in 18 minutes

total kilometers - 2

and total time - 18

so you would get:

k – 2 = (t – 18)

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The quality control manager at a light bulb factory needs to estimate the mean life of a batch (population) of light bulbs. We a
Nadusha1986 [10]

Answer:

<em>a)95%  confidence intervals for the population mean of light bulbs in this batch</em>

(325.5 ,374.5)

b)

<em>The calculated value Z = 4 > 1.96 at 0.05 level of significance</em>

<em>Null hypothesis is rejected </em>

<em>The manufacturer has not right to take the average life of the light bulbs is 400 hours.</em>

Step-by-step explanation:

Given sample size n = 64

Given  mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

<em>95%  confidence intervals for the population mean of light bulbs in this batch</em>

<em></em>(x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )<em></em>

<em></em>(350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )<em></em>

(350 -24.5, 350 +24.5)

(325.5 ,374.5)

b)

<u><em>Explanation</em></u>:-

Given mean of the Population μ = 400

Given sample size n = 64

Given  mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

<u><em>Null hypothesis</em></u> : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

<u><em>Alternative Hypothesis: H₁:</em></u> μ ≠400

<u><em>The test statistic </em></u>

Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }

Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }

|Z| = |-4|

The tabulated value   Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

<u><em>Conclusion:</em></u>-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

5 0
2 years ago
Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t
Assoli18 [71]

Answer:

To determine the number of real number solutions of as system of equations in which one equation is linear and the other is quadratic

1) Given that there are two variables, x and y as an example, we make y the subject of the equation of the linear equation and substitute the the expression for y in x into the quadratic equation

We simplify and check the number of real roots with the quadratic formula, x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a} for quadratic equations  the form 0 = a·x² - b·x + c

Where b² > 4·a·c there are two possible solutions and when b² = 4·a·c equation there is only one solution.

Step-by-step explanation:

3 0
1 year ago
I need to solve this equation: x= r-h/ y<br> for h and then for r
ololo11 [35]
X= r-h/y
h= xy-r/-1
r= xy+h
7 0
2 years ago
Read 2 more answers
Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes
Ivan

Answer:

14.86 knots.

Step-by-step explanation:

<em>Given that:</em>

The boats leave the port at noon.

Speed of boat 1 = 12 knots due east

Speed of boat 2 = 8 knots due south

At 2 pm:

Distance traveled by boat 1 = 24 units due east

Distance traveled by boat 2 = 16 units due south

Now, speed of boat 1 changes to 9 knots:

At 3 pm:

Distance traveled by boat 1 = 24 + 9= 33 units due east

Distance traveled by boat 2 = 16+8 = 24 units due south

Now, speed of boat 1 changes to 8+7 = 15 knots

At 5 pm:

Distance traveled by boat 1 = 33 + 2\times 9= 51 units due east

Distance traveled by boat 2 = 24 + 2 \times 15 = 54 units due south

Now, the situation of distance traveled can be seen by the attached right angled \triangle AOB.

O is the port and A is the location of boat 1

B is the location of boat 2.

Using pythagorean theorem:

\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units

so, the total distance between the two boats is 74.28 units.

Change in distance per hour = \dfrac{Total\ distance}{Total\ time}

\Rightarrow \dfrac{74.28}{5} = 14.86\ knots

6 0
1 year ago
Points b,d, and f are midpoints of the sides of triangle ACE. EC=30 and DF= 17 find AC
Margaret [11]

Answer:

Your answer should be AC=2DF=34

Step-by-step explanation:


5 0
1 year ago
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