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3 years ago

8

Adult tickets to a play cost $22.00 Tickets for children cost $15.00. Tickets for a group of 11 people cost a total of $228.00.

Write and solve a system of equations to find how many children and how many adults were in the group.

1 answer:

Mademuasel [1]3 years ago

6 0

There would be 2 children and 9 adults

Explanation: $22x 9 adults= 198
$15x 2 children= 30
Then you add them together and 198+30 = $228

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Round to the ne the nearest ten thousand in the number 120 400 607 thousand

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The answer would be 120,401,000.

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3 years ago

In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively

worty [1.4K]

Answer: ABCD is a quadrilateral

To prove : ∠AOB=

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1

(∠C+∠D)

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∠1=∠2∠3=∠4...(1)

∠A+∠B+∠C+∠D=360

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(∠A+∠B+∠C+∠D)=180...(2)

In △AOB

∠1+∠3+∠5=

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(∠A+∠B+∠C+∠D)

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{∠C+∠D}.

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3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.

For part b the $p_v>\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v>\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

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3 years ago

The coordinates of a point on a coordinate grid are (−2, 6). The point is reflected across the x-axis to obtain a new point. The

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The reflected coordinate will be (-2,-6)

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3 years ago

Read 2 more answers

Find the square. (1/4A + 1/4B)^2<br><br> a) 1/16A^2 + 1/8AB + 1/16B^2<br> b) 1/4A^2 + 1/8AB + 1/4B^2

alisha [4.7K]

$(a + b)^2 = a^2 + 2ab + b^2$

$(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =$

$= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B^2$

Answer: A.

Another way to solve by factoring 1/4.

$(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =$

$= [\dfrac{1}{4}(A + B)]^2$

$= (\dfrac{1}{4})^2(A + B)^2$

$= \dfrac{1}{16}(A^2 + 2AB + B^2)$

$= \dfrac{1}{16}A^2 + \dfrac{1}{16}2AB + \dfrac{1}{16}B)^2$

$= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B)^2$

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3 years ago

Read 2 more answers