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3 years ago

Tell whether the given value is a solution of the inequality.

Mathematics

1 answer:

Sloan [31]3 years ago

4 0

We have:

$w \geqslant 18$

So: w = 15 is not a solution of the inequality.

Ok done. Thank to me :>

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$456 is divided between the telephone and electricity bills in a ratio of 2 : 1. What amount goes to the telephone bill?

kipiarov [429]

$304 is the answer because 456/3 and then multiply by 2

5 0

2 years ago

Find the slope of the line that passes through the points (0, 6) and (20, 14).

mihalych1998 [28]

Answer:

2/5

Step-by-step explanation:

4 0

3 years ago

What line is parallel to 2x+5y=6 that goes through (5,3)

Anna11 [10]

Answer:

4y = x - 17

Step-by-step explanation:

First off, in the equation given : 2x + 5y = 6 , make y the subject of the formula which will give y = $\frac{-2x}{5}$ + $\frac{6}{5}$ which make the gradient, m, the coefficient of x = $\frac{-2}{5}$ . Since the line we're looking for is parallel to the one we were given, their respective gradients would be the same. (If they were perpendicular, the gradient of the new line would be a negative inverse of the given line)

Then you proceed to use the one-point formula : y - y₀ = m(x - x₀), where y₀ = 3 and x₀ = 5 from the point it goes through (5, 3)

y - 3 = $\frac{1}{4}$ (x - 5); y - 3 = $\frac{x}{4}$ - $\frac{5}{4}$ ; y = $\frac{x}{4}$ - $\frac{5}{4}$ +3

y = $\frac{x}{4}$ - $\frac{17}{4}$ ; y = $\frac{x-17}{4}$ ; 4y = x - 17

7 0

2 years ago

Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Consider the

Dafna1 [17]

Answer:

a) $\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

b) The 90% confidence interval would be given by (63.330;81.070)

$63.330 < \mu_{left}- \mu_{right}$

Step-by-step explanation:

1) Previous concepts and notation

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Let put some notation

x=left arm , y = right arm

x: 175 169 182 146 144

y: 102 101 94 79 79

The first step is define the difference $d_i=x_i-y_i$ , that is given so we have:

d: 73, 68, 88, 67, 65

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=72.2$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =9.311$

2) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s_d}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=5-1=4$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,4)".And we see that $t_{\alpha/2}=2.13$