In the diagram given, AB is parallel to DC. If M is the midpoint of AC, must it also be the midpoint of BD? Why?

The cost of having photos taken includes a sitting fee and $12 for each portrait. The cost of 3,6, and 9 photos respectively is

Eddi Din [679]

Answer:The sitting fee is 15 dollars

Step-by-step explanation:If you were to use the formula y=mx+b then the starting equation would be y=12x+b. It already gave you the cost for the amount of photos respectively so 51=12(3)+b. 12 times 3 equals 36 and 51 minus 36 equals 15. The same way would be used for 87 dollars and 123 dollars while using the amount of photos respectively. 87=12(6)+b. 12 times 6 equals 72. 72 plus 15 equals 87. 123=12(9)+b. 12 times 9 equals 108. 108 plus 15 equals 123. Therefore the sitting fee is 15. (51=12(3)+15, 87=12(6)+15, 123=12(9)+15)

4 0

3 years ago

Bella saw that 7:11 people brought an umbella to the beach. There were 99 peopel there. How many of them did not have a beach um

Rina8888 [55]

Answer:

36 people of them did not have a beach umbrella.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Let x represents the number of people did not have a beach umbrella.

As per the statement:

Bella saw that 7 : 11 people brought an umbrella to the beach.

Out of 11 people, only 7 people brought an Umbrella to the beach.

Remaining people did not brought an Umbrella to the beach = 11 -7 = 4 people

It is also given that there were 99 people there.

then by definition of proportion:

$\frac{4}{11} = \frac{x}{99}$

By cross multiply we have;

$99 \times 4 = 11x$

Divide both sides by 11 we get;

$x = 9 \times 4$

Simplify:

x = 36 people.

Therefore, 36 people of them did not have a beach umbrella.

7 0

3 years ago

A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven

AnnyKZ [126]

Answer:

$t=\frac{17.71-28.71}{\sqrt{\frac{4.461^2}{7}+\frac{7.387^2}{7}}}}=-3.372$

$df=n_{S}+n_{N}-2=7+7-2=12$

Since is a one sided test the p value would be:

$p_v =P(t_{(12)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean time for the new treatment is significantly lower than the time for the standard treatment at 5% of significance.

Step-by-step explanation:

New: 12, 13,15,19,20,21

Standard: 18,23,24,30,32,35

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Data given and notation

$\bar X_{N}=17.71$ represent the mean for the new case

$\bar X_{S}=28.71$ represent the mean for the standard case

$s_{N}=4.461$ represent the sample standard deviation for the new case

$s_{S}=7.387$ represent the sample standard deviation for the standard case

$n_{S}=7$ sample size selected for the standard case

$n_{N}=7$ sample size selected for the new case

$\alpha=0.05$ 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)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if recovery time for patients who receive the new treatment is less than the mean for patients who receive the standard treatment, the system of hypothesis would be:

Null hypothesis: $\mu_{N} \geq \mu_{S}$

Alternative hypothesis: $\mu_{N} < \mu_{S}$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{N}-\bar X_{S}}{\sqrt{\frac{s^2_{N}}{n_{N}}+\frac{s^2_{S}}{n_{S}}}}$ (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:

$t=\frac{17.71-28.71}{\sqrt{\frac{4.461^2}{7}+\frac{7.387^2}{7}}}}=-3.372$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{S}+n_{N}-2=7+7-2=12$

Since is a one sided test the p value would be:

$p_v =P(t_{(12)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean time for the new treatment is significantly lower than the time for the standard treatment at 5% of significance.

6 0

4 years ago

Tell if the measures 6, 14, and 13 make a triangle that is acute, right, or obtuse.

ycow [4]

Right angle - c²=a²+b²

Obtuse angle - c²>a²+b²

Acute angle - c²<a²+b²

To see which ones go into a, b, and c, know that the largest number is the hypotenuse (variable c). The other two letters can be either a or b, so it doesn't matter which place they are put it because you will get the same answer.

right angle 14²=6²+13²

196=36+169

196≠205

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obtuse angle 14²>6²+13²

196>36+169

196>205 is false

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So since it is not a right angle or an obtuse angle, that means that it's a right angle because it's the only option left. Though we now know that's the answer, I will still put down the steps.

acute angle 14²<6²+13²

196<36+169

196<205 is true so it's an acute triangle.

Hope this helps, now you know the answer and how to do it. Stay safe and healthy and HAVE A BLESSED AND WONDERFUL DAY! :-)

- Cutiepatutie ☺❀❤

5 0

3 years ago

The table below shows all of the possible outcomes for rolling two six-sided number cubes.

Paha777 [63]

There are a total of 36 possibilities, and out of those 5 would give you a sum of 8. Therefore the probability is 5/36

8 0

4 years ago

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