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2 years ago

Are the triangles shown congruent? If so, how do you know? Please help

Mathematics

1 answer:

lesya [120]2 years ago

7 0

Answer:

6. yes they are congruent, they are exactly the same shape and size

7. no they are not congruent, they are different sizes

8. they are congruent, they have the same shape and size

Step-by-step explanation:

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The average weight of a male labrador retriever is believed to be well-approximated by a normal distribution with mean 71.5 lbs

Oliga [24]

Answer: We will reject the null hypothesis.

Step-by-step explanation:

Since we have given that

Mean μ = 71.5 lbs

Standard deviation σ = 7.5 lbs

So, the hypothesis are given below:

$H_0:\mu =71.5\\\\H_1:\mu \neq 71.5$

Since α = 5% level of significance = 0.05

So, there is two tail test.

Critical values of z are 1.96 and -1.96.

So, we will reject H₀ if z<-1.96 or z>1.96

So, first we will find the value of z.

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\\x=\dfrac{80-71.5}{\dfrac{7.5}{\sqrt{15}}}\\\\\\z=4.39$

According to test statistic approach:

Since z >1.96

as 4.39>1.96

So, we will reject the null hypothesis.

4 0

3 years ago

Solve the following equation for y. Y= 2y+4y-3=27

sammy [17]

Answer:

$2y + 4y - 3 = 27 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6y = 27 + 3 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 6y = 30 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = \frac{30}{6} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 5$

4 0

3 years ago

Dear Math Helper,

valentina_108 [34]

Answer:

n = 98, that is, she scored at the 98th percentile.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

She scored 38, so $X = 38$

Test scores are normally distributed with a mean of 25 and a standard deviation of 6.4.

This means that $\mu = 25, \sigma = 6.4$

Find the percentile:

We have to find the pvalue of Z. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{38 - 25}{6.4}$

$Z = 2.03$

$Z = 2.03$ has a pvalue of 0.98(rounding to two decimal places).

So n = 98, that is, she scored at the 98th percentile.

5 0

3 years ago

Four resistors are connected in series such that their total resistance is 50ohm . If the resistance of resistors is 5 ohm , 10o

Katyanochek1 [597]

<h2>Answer:</h2>

$\boxed{R_{4}=20\Omega}$

<h2>Step-by-step explanation:</h2>

If resistors are in series, so the current $I$ is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance of series combination and the four resistors as follows: