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3 years ago

What is the area of the trapezoid?

Mathematics

2 answers:

Setler [38]3 years ago

8 0

Your answer is b: 24

Artemon [7]3 years ago

8 0

Answer: The correct option is (B) 24 square units.

Step-by-step explanation: We are given to find the area of the trapezium in the figure.

The AREA of a TRAPEZIUM with lengths of parallel sides as 'a' and 'b' units and height 'h' units is given by the formula:

$A=\dfrac{1}{2}(a+b)h.$

In the given trapezium, we have

lengths of the parallel sides are

a = 4 units and b = 8 units,

and height, h = 4 units.

Therefore, the area of the given trapezium is

$A\\\\\\=\dfrac{1}{2}(a+b)h\\\\\\=\dfrac{1}{2}\times(4+8)\times 4\\\\\\=12\times 2\\\\=24~\textup{sq. units.}$

Thus, the area of the trapezium is 24 square units.

Option (B) is correct.

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The following data comparing wait times at two rides at Disney are listed below: Position Pirates Splash Mountain Sample Size 32

myrzilka [38]

Answer:

a) $(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

b) $t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

Step-by-step explanation:

Data given and notation

$\bar X_{A}=14.68$ represent the mean for Pirates

$\bar X_{B}=18.77$ represent the mean for Splash Mountain

$s_{A}=11.87$ represent the sample standard deviation for the sample Pirates

$s_{B}=16.79$ represent the sample standard deviation for the sample Slpash Mountain

$n_{A}=32$ sample size selected for Pirates

$n_{B}=30$ sample size selected for Splash Mountain

$\alpha=0.02$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

Part a

The confidence interval would be given by:

$(\bar X_A -\bar X_B) \pm t_{\alpha/2} \sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}$

The degrees of freedom are given by:

$df = n_A +n_B -2 = 32+30-2 = 60$

Since we want 98% of confidence the significance level is $\alpha =1-0.98 =0.02$ and $\alpha/2 =0.01$ , we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:

$t_{\alpha/2}= 2.39$

And replacing we got for the confidence interval:

$(14.68 -18.77) - 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =-12.968$

$(14.68 -18.77) + 2.39 \sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}} =4.788$

Part b

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:

Null hypothesis: $\mu_{A} = \mu_{B}$

Alternative hypothesis: $\mu_{A} \neq \mu_{B}$

the statistic is given by:

$t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{14.68-18.77}{\sqrt{\frac{11.87^2}{32}+\frac{16.79^2}{30}}}}=-1.10$

6 0

3 years ago

PLZZZZZZZ HELLPPPP MEEEE I HAVE A HEADACHE WITH THIS<br><br> Find the measure of angle b.

Salsk061 [2.6K]

31) 27
32) 75
33) 74
34) 90 (because it’s a right angle and adds up to 180)

4 0

3 years ago

Given the equation: = 4, which property should be applied first?

Ghella [55]

This is = 4 therefore no property is applied

3 0

4 years ago

1) Lisa is planning on baking a birthday cake for a party. The recipe calls for

Allushta [10]

Answer:

eggs milk baking soda sugar butter

4 0

3 years ago

Read 2 more answers

Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

weeeeeb [17]

Answer:

\[y = (-1/2) * x + 6\]

Step-by-step explanation:

Equation of the given line: y=2x+2

Hence the slope of the line is given by 2

Any line which is perpendicular to the given line will have a slope m such that m*2 = -1

Or, \[m = \frac{-1}{2}\]

Only options 2 and 3 satisfy this condition.

The line is also supposed to pass through the point (6,3).

Substituting these values in the option 2:

\[3 = (-1/2) * 6 + 3\]

Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.

Now substituting (6,3) in option 3:

\[3 = (-1/2) * 6 + 6\]

Or, \[ 3 =3 \] which is true . Hence option 3 is the required equation of the line.

5 0

3 years ago