Maggie's brother is 4 years younger than three times her age. The sum of their ages is 20. How old is Maggie?

I need to figure out if I'm doing this correctly

kogti [31]

To prove that triangles TRS and SUT are congruent we can follow these statements:

1.- SR is perpendicular to RT: Given

2.-TU is perpendicular to US: Given

3.-Angle STR is congruent with angle TSU: Given.

4.-Reflexive property over ST: ST is congruent with itself (ST = ST)

From here, we can see that both triangles TRS and SUT have one angle of 90 degrees, another angle that they both have, and also they share one side (ST) ,then:

5.- By the ASA postulate (angle side angle), triangles TRS and SUT are congruent

5 0

1 year ago

Anyone know how to do this

svlad2 [7]

Answer:

The area of the rectangle on the left side is

$9cm \: \times 4cm = 36 {cm}^{2}$

The area of the bottom rectangle is

$6cm \times 2cm = 12 {cm}^{2}$

The total area of the composite figure will be

$36 {cm}^{2} + 12 {cm}^{2} = 48 {cm}^{2}$

Step-by-step explanation:

The area of any given rectangle can be found by multiplying the length of that rectangle by its width. The rectangle on the left side has a length of 9cm but the width is unknown. To find the width, we subtract 6cm from the width of the bottom rectangle: 10cm. And that gives us 4cm.

Therefore, we can now calculate the area to be: length × width = 9cm × 4cm = 36cm²//

The area of the bottom rectangle can be found similarly by multiplying the length: 2cm by the width: 6cm of that rectangle. And the result gives us: 2cm × 6cm = 12cm²//

The total area of the composite figure is calculated by adding the results from the left and bottom rectangles together. And that gives us: 36cm² + 12cm² = 48cm²//

8 0

3 years ago

Indigo Depot is having a clearance sale of their fall items. A jacket that originally cost $110 before any discount is on sale f

Korvikt [17]

Answer:

$88.00

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 110 × 20/100

Discount = 110 x 0.2

You save = $22.00

3 0

3 years ago

What is the value of n? Enter your answer in the box. n = cm Circle with two intersecting chords forming an x shape in the circl

Contact [7]

Answer: The length of the bottom left side is 14.

To find the length of this side, we need to know the relationship between the different sections when chords cross each other.

The relationship is that if you multiply the 2 parts of each chord together, it will equal the product of the two sides in the other chord.

Our equation can be written as:

7(8) = 4(x)
56 = 4x
14 = x

3 0

3 years ago

Read 2 more answers

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating

Natali [406]

Answer:

a) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

b) Test statistic t=-1.565

P-value = 0.0612

NOTE: the sample size is n=65.

c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

d) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

Test statistic t=-1.565

Critical value tc=-1.669

t>tc --> Do not reject H0

Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Then, the null and alternative hypothesis are:

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

The significance level is 0.05.

The sample has a size n=65.

The sample mean is M=30.15.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565$

The degrees of freedom for this sample size are:

$df=n-1=65-1=64$

This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

<u>Critical value approach</u>

<u></u>

At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.

As the test statistic is greater than the critical value, it falls in the acceptance region.

The null hypothesis failed to be rejected.

6 0

3 years ago