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2 years ago

12

The temperature at a mountain base camp was −4 degrees Celsius on Saturday. Sunday morning, the temperature was 2 degrees Celsiu

s lower than what it was on Saturday. By Sunday evening, the temperature was 1 degree Celsius lower than what it was that morning. What was the temperature at the base camp Sunday evening?

2 answers:

elixir [45]2 years ago

6 0

Well when you go lower with negatives the number gets bigger so
It was -4C then it was 2 lower which is -6C then it got lower again in the evening by 1 degree celcius which gives the answer -7 degrees celcius

Agata [3.3K]2 years ago

5 0

The equation you can use for this problem is -4 - 2 - 1

-4 - 2 - 1
-6 - 1
-7

The answer is -7

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A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

a

The 95% confidence interval is $0.0503 < p < 0.1297$

b

The sample proportion is $\r p = 0.09$

c

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

d

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

7 0

3 years ago

Question 9 (10 points)<br> Solve for x,<br> 2(x - 1) + 4 = 4(x + 1)

Nutka1998 [239]

1. Expand
2x − 2 + 4 = 4x + 4

2. Simply
2x + 2 = 4x + 4

3. Subtract
2 = 4x + 4 - 2x

4. Simplify
2 = 2x + 4

5.Subtract
2 - 4 = 2x

6. Simplify
-2 = 2x

7. Divide both sides by
-1 = x

8.Switch sides.
x = -1

6 0

3 years ago

Triangle MNP is dilated according to the rule DO,1.5 (x,y)Right arrow(1.5x, 1.5y) to create the image triangle M'N'P, which is n

Vikki [24]

Given:

The vertex of a triangle MNP are M(-4, 6), N(2, 6), and P(-1, 1).

The rule of dilation is:

$(x,y)\to (1.5x,1.5y)$

The image of triangle MNP after dilation is M'N'P'.

To find:

The coordinates of the endpoints of segment M'N'.

Solution:

The end points of MN are M(-4, 6) and N(2, 6).

The rule of dilation is:

$(x,y)\to (1.5x,1.5y)$

Using this rule, we get

$M(-4,6)\to M'(1.5(-4),1.5(6))$

$M(-4,6)\to M'(-6,9)$

And,

$N(2,6)\to N'(1.5(2),1.5(6))$

$N(2,6)\to N'(3,9)$

The endpoints of M'N' are M'(-6, 9) and N'(3, 9).

Therefore, the correct option is B.

8 0

3 years ago

Solve the following equation

Veronika [31]

The answer to the equation is x=4.5

7 0

2 years ago

Read 2 more answers

Find (a) the slope of the curve at the given point p, and (b) an equation of the tangent line at p. y=−2−9x2; p(2,−38)

Neporo4naja [7]

Answer:

a) -36

b) y = -36x +34

Step-by-step explanation:

a) The slope is found using the derivative of the function.

f'(x) = dy/dx = 0 -9(2x) = -18x

Then at x=2, the slope is ...

f'(2) = -18·2 = -36

___

b) The point-slope form of the equation can be written as ...

y = -36(x -2) -38

Simplifying to slope-intercept form, we get ...

y = -36x +34

6 0

2 years ago