Wilbur ran 27.6 miles more than Totsakan

Which rules would result in a triangle A being congruent to or not congruent to B?

Ipatiy [6.2K]

Well the only thing that would make these triangles not congruent is dilation, Thus, translation, reflection, and rotations all make the triangles congruent.

The bottom one and third one are not congruent while everything else is.
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3 0

3 years ago

A square of side x is cut out of a larger square of side y. What is the area of the remaining

KonstantinChe [14]

Answer:

The area of the remaining figure is $y^2-x^2$

Step-by-step explanation:

<u>Area of the Square Shape</u>

Given a square of side length x, the area is calculated by the formula:

$A_x=x^2$

It's given a square of side x is cut out of a larger square of side y. Please refer to the image below.

The area of the square of side length y is:

$A_y=y^2$

The shaded area of the remaining figure is the difference between both areas:

$A=A_y-A_x$

$A=y^2-x^2$

The area of the remaining figure is $\mathbf{y^2-x^2}$

3 0

3 years ago

A principal of $4,570 is placed in an account that earns 4. 5% interest. If the interest is compounded annually, how much money

iVinArrow [24]

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4570\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4570\left(1+\frac{0.045}{1}\right)^{1\cdot 5}\implies A=4570(1.045)^5\implies A\approx 5695.05$

8 0

3 years ago

Is (-3.4) a rational number? And why is (-3.4) a rational number?

KIM [24]

Answer:

Yes

Step-by-step explanation:

a rational number is a number that can be written as a fraction. Rational numbers are all real numbers, and can be positive or negative. A number that is not rational is called irrational. Most of the numbers that people use in everyday life are rational. These include fractions and integers.

- 3.4 is a integer and also a rational number.

4 0

3 years ago

Consider the following hypothesis test:H0: 20Ha: < 20A sample of 60 provided a sample mean of 19.6. The population standard d

elixir [45]

Answer:

a: z = -1.936

b: 0.0265

d: z < -1.645

Reject H0 if z < -1.645

Step-by-step explanation:

We are given:

H0: µ = 20

HA: µ < 20

n = 60, sample mean: 19.6, σ = 1.6

Since the alternate hypothesis has a < sign in it, it is a left tailed test. The < or > sign in the alternate hypothesis points towards the rejection region.

For a: We need to calculate the test statistic for our situation. This is done with a z-score formula for samples.

For b: we need to use the z-score table to look up the p-value for the score we calculate in part a. The p-value is 0.0265. This means that there is only about a 2.65% chance that the sample values were a result of random chance.

For d: Since the significance level is 0.05, and this is a one tailed test, we have a critical value of z < - 1.645. This means that if the z-score we calculate in part a is less than -1.645, we will reject the null hypothesis

See attached photo for all the calculations!

4 0

3 years ago