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3 years ago

Sam is 5 years old. His older brother, Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?

1 answer:

katrin2010 [14]3 years ago

3 0

Sam is 5
Tom is 3 times older so 3*5=15
The difference between them is 15-5=10 years
When Sam is 20 we add the difference 20+10=30, and we have Tom's age :)

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Kira had some money sitting in a savings account that earns 2.75% simple interest each year. She left it there for 8 years and e

Aleksandr [31]

Answer:

$2250

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 2.75%/100 = 0.0275 per year,

then, solving our equation

I = 2250 × 0.0275 × 8 = 495

I = $ 495.00

The simple interest accumulated

on a principal of $ 2,250.00

at a rate of 2.75% per year

for 8 years is $ 495.00.

7 0

2 years ago

Suppose that a random sample of size 10 from the N(µ, 9) distribution resulted in a sample mean of x = 2.7. Give an 85% condiden

stellarik [79]

Answer:

a) $CI: 1.3$

b) $CI: 2.5$

c) $CI: 2.0$

Step-by-step explanation:

a) We have a sample of size n=10 and a sample mean of x=2.7.

The σ² of the population is known and is σ²=9 or σ=3.

For a CI of 85%, the z-value is 1.44.

Then the lower and upper limits of the CI are:

$LL=M-z*\frac{\sigma}{\sqrt{n} } =2.7-1.44*\frac{3}{\sqrt{10} }=2.7-1.44*\frac{3}{3.162} =2.7-1.4=1.3\\\\UL=M+z*\frac{\sigma}{\sqrt{n} } =2.7+1.4=4.1$

The 85% confidence interval for the mean is defined by the values LL=1.3 and UL=4.1.

$CI: 1.3$

b) In this case, the variance of the population is unknown.

We have to estimate the variance of the population from the variance of the sample.

Sample data:

n = 100

x(mean) = 2.7

s² = 1.1

The CI is defined as

$x-t*\frac{s}{\sqrt{n} }$

The value of t depends of the degrees of freedom and the percentage of confidence.

In this case, the degrees of freedom are n-1=100-1=99 and the CI is of 90%.

We look up in a t-table and the t-value for this conditions is 1.6604.

We can now calculate the CI

$LL: x-t*\frac{s}{\sqrt{n} }=2.7-1.6604*\frac{\sqrt{1.1} }{\sqrt{100} } =2.7-0.2=2.5\\\\UL: x+t*\frac{s}{\sqrt{n} }=2.7+0.2=2.9$

The 90% confidence interval for the mean is defined by the values LL=2.5 and UL=2.9.

$CI: 2.5$

c) In this case, the variance of the population is unknown.

We have to estimate the variance of the population from the variance of the sample.

Sample data:

n = 10

x(mean) = 2.7

s² = 1.1

The CI is defined as

$x-t*\frac{s}{\sqrt{n} }$

The value of t depends of the degrees of freedom and the percentage of confidence.

In this case, the degrees of freedom are n-1=10-1=9 and the CI is of 95%.

We look up in a t-table and the t-value for this conditions is 2.2622.

We can now calculate the CI

$LL: x-t*\frac{s}{\sqrt{n} }=2.7-2.2622*\frac{\sqrt{1.1} }{\sqrt{10} } =2.7-0.7=2.0\\\\UL: x+t*\frac{s}{\sqrt{n} }=2.7+0.7=3.4$

The 95% confidence interval for the mean is defined by the values LL=2.0 and UL=3.4.

$CI: 2.0$

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2 years ago

Which postulate or theorem would you use to prove the triangles congruent?; Which pair of triangles Cannot be proved congruent?;

Lunna [17]

Proving triangles are congruent triangles uses theorems (postulates), the Angle Side Angle (ASA), Side Angle Side (SAS), Side Side Side (SSS), and AAS (Angle-Angle-Side). Two triangles with equal corresponding angles may not be congruent to each other because one triangle might be an enlarged copy of the other.

Triangles that have exactly the same size and shape are called congruent triangles. The congruent triangles can be used using the Angle Side Angle (ASA), Side Angle Side (SAS), Side Side Side (SSS), and AAS (Angle-Angle-Side) theorems.

Angle Side Angle (ASA) theorem states that if any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent.

Side-angle-side (SAS) theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

Side Side Side (SSS) theorem states that if all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent.

AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

Learn more about Congruent triangles:

brainly.com/question/1675117

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1 year ago

How many solutions does the equation have<br> y=2x^2+3x-10=0

Natali [406]

Answer:it has two

Step-by-step explanation: x =(3-√89)/4=-1.608

x =(3+√89)/4= 3.108

8 0

2 years ago

Hi, please help!

Vlad1618 [11]

Answer: 5-/5-10/-3

Explaination: just fill in the letter it corresponds to

8 0

2 years ago