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4 years ago

If two triangles are congruent, which of the following statements must be true? Check all that apply.

Mathematics

2 answers:

REY [17]4 years ago

8 0

Answer:

All that type are true.

Step-by-step explanation:

Given : Statements .

To find : which of the following statements must be true.

Solution : We have given statements of congruent.

Two triangle are congruent if they have same size and if their corresponding angles are equal.

Two triangle are congruent if their corresponding sides are equal .

Therefore, all that type are true.

zimovet [89]4 years ago

7 0

Congruent means the two figures have the same size, shape, and angles. All of the answers are correct.

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Alex needs to buy compressed air to fill empty cylindrical tanks for his tire store. Each tank is 12 feet deep and has a radius

agasfer [191]

---------------------------------------
Formula
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Volume = πr²h

---------------------------------------
Find Volume of one tank
---------------------------------------
Volume of 1 tank = πr²h
Volume of 1 tank = 3.14 x 6² x 12
Volume of 1 tank = 678.24 ft³

---------------------------------------
Find Volume of 5 tanks
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Volume of 1 tank = 678.24
Volume of 5 tanks = 678.24 x 5
Volume of 5 tanks = 3391.2 ft³

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Answer: 3391.2 ft³
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4 0

3 years ago

A car has a windshield wiper on the driver's side that has total arm length of 10 inches. It rotates

son4ous [18]

Answer:

75.44 Square Inches

Step-by-step explanation:

The diagram of the problem is produced and attached.

To determine the area of the cleaned sector:

Let the radius of the larger sector be R

Let the radius of the smaller sector be r

Area of the larger sector $=\frac{\theta}{360}X\pi R^2$

Area of the smaller sector $=\frac{\theta}{360}X\pi r^2$

Area of shaded part =Area of the larger sector-Area of the smaller sector

$=\frac{\theta}{360}X\pi R^2-\frac{\theta}{360}X\pi r^2\\=\frac{\theta \pi}{360}X (R^2- r^2)$

From the diagram, R=10 Inch, r=10-7=3 Inch, $\theta=95^\circ$

Therefore, Area of the sector cleaned

$=\frac{95 \pi}{360}X (10^2- 3^2)\\=75.44$ Square Inches$

7 0

3 years ago

Tanner collected 360 cans and bottles while fundraising for his baseball team. This was 40% of what Reggie collected. How many c

Vanyuwa [196]

The amount Reggie collected is equal to x
$\frac{360}{.4}= \frac{x}{1}$

$x = \frac{360}{.4} = \frac{360}{ \frac{4}{10} } = \frac{360*10}{4} = 900$

4 0

3 years ago

Read 2 more answers

Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body b

sesenic [268]

Answer:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095$

-The sample is too small to make judgments about skewness or symmetry.

H0: $\mu_{1}=\mu_{2}$

H1: $\mu_{1} \neq \mu_{2}$

$t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013$

$p_v =2*P(t_{(14)}$

So the p value is a very high value and using any significance level for example $\alpha=0.05, 0,1,0.15$ always $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

Step-by-step explanation:

First we need to find the difference defined as:

(Operator 1 minus Operator 2)

d1=1.326-1.323=0.003 d2=1.337-1.322=0.015

d3=1.079-1.073=0.006 d4=1.229-1.233=-0.004

d5=0.936-0.934=0.002 d6=1.009-1.019=-0.01

d7=1.179-1.184=-0.005 d8=1.289-1.304=-0.015

Now we can calculate the mean of differences given by:

$\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001$

And for the sample deviation we can use the following formula:

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095$

Describe the distribution of these differences using words. (which one is correct)

We can plot the distribution of the differences with the folowing code in R

differences<-c(0.003,0.015,0.006,-0.004,0.002,-0.01,-0.005,-0.015)

hist(differences)

And we got the image attached. And we can see that the distribution is right skewed but we don't have anough info to provide a conclusion with just 8 differnences.

-The sample is too small to make judgments about skewness or symmetry.

Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)

$\bar X_{1}=1.173$ represent the mean for the operator 1

$\bar X_{2}=1.174$ represent the mean for the operator 2

$s_{1}=0.1506$ represent the sample standard deviation for the operator 1

$s_{2}=0.1495$ represent the sample standard deviation for the operator 2

$n_{1}=8$ sample size for the operator 1

$n_{2}=8$ sample size for the operator 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0: $\mu_{1}=\mu_{2}$

H1: $\mu_{1} \neq \mu_{2}$

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:

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

$t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013$

Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case: