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3 years ago

Estimate the measure of ∠DBC.Could someone please help me with this?

Mathematics

1 answer:

marshall27 [118]3 years ago

8 0

Answer:

Option (4). 135°

Step-by-step explanation:

From the figure attached,

Two pair of vertical angles have been given,

∠ABD and ∠CBE

∠ABE and ∠CBD

One pair of angles ∠ABD and ∠CBE are acute angles which are less than 90°.

Similarly, other pair ∠ABE and ∠DBC are obtuse angles which are more than 90°.

Therefore, out of the given options measure of one pair ∠DBC and ∠ABE should be 135°.

Option (4) will be the answer.

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Rectangleville's limits form a perfectly rectangular shape whose length is 202020 kilometers and width is 121212 kilometers. It

kotykmax [81]

Answer:

76,800

Step-by-step explanation:

Given the following :

Length = 20 kilometers

Width = 12 kilometers

Population density = 320 people per sq km

Population =?

Recall:

Area of rectangle = Length × width

Therefore,

Area of Rectangleville = 20 km × 12 km = 240km^2

Population is related to population density and Area by the formula ;

Population density = population ÷ Area

Therefore,

Population = population density × Area

Population = 320 × 240 = 76,800

Therefore, the population of Rectangleville is 76,800 people

7 0

3 years ago

a pizza costs $11 and $1.50 per topping write a equation for cost in dollars and the nunber of toppings

romanna [79]

Answer:

y= 11 + 1.50x. (y is the price, x is number of toppings)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Select all expressions that are equivalent to 5x + (x+6) + 3x.

liraira [26]

The correct answer is 9x+6.

5 0

3 years ago

Read 2 more answers

The National Transportation Safety Board publishes statistics on the number of automobile crashes that people in various age gro

ra1l [238]

Answer:

a) Null hypothesis: $p\leq 0.12$

Alternative hypothesis: $p > 0.12$

b) $z_{\alpha}=1.64$

c) $z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362$

d) $p_v =P(z>1.362)=0.0866$

e) For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

Step-by-step explanation:

Information given

n=1000 represent the random sample selected

X=134 represent the number of young drivers ages 18 – 24 that had an accident

$\hat p=\frac{134}{1000}=0.134$ estimated proportion of young drivers ages 18 – 24 that had an accident

$p_o=0.12$ is the value that we want to verify

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic

$p_v{/tex} represent the p valuePart aWe want to verify if the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%: Null hypothesis:[tex]p\leq 0.12$

Alternative hypothesis: $p > 0.12$

The statistic would be given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Part b

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the right and we got:

$z_{\alpha}=1.64$

Part c

For this case the statistic would be given by:

$z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362$

Part d

The p value can be calculated with the following probability:

$p_v =P(z>1.362)=0.0866$

Part e

For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12

8 0

3 years ago

Express the function graphed on the axes below as a piecewise function.

adoni [48]

Answer:

f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

f(x) = x-3 for x ≤ -1

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

y -(-1) = -3(x -5)

y = -3x +15 -1 = -3x +14

The second piece can be written ...

f(x) = -3x +14 for x > 5

<h3>Whole function</h3>

Putting these pieces together, we have ...

$\boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}$

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0

3 years ago