PART 1:

Jeremy gives the correct answer.

The value of 0.41 [with a bar over the digit 4 and 1] shows that the digit 4 and 1 are reoccurring = 0.414141414141414141....

Jenny's assumption of 41/100 will give a decimal equivalency of 0.41 [without a bar over digit 4 and 1]. This value is not a reoccurring decimal value.

PART 2:

The long division method is shown in the picture below

PART 3:

As mentioned in PART 1, the result of converting 41/100 into a decimal is 0.41 [non-reoccuring decimal] while converting 41/99 into a decimal is 0.41414141... [re-occuring decimal]. The conjecture in PART 1 is correct

8 0

2 years ago

Two lines intersect to form angles 1, 2, 3, and 4 as given. The measure of ∠3 is 38°. What is the measure of ∠2 ?

ss7ja [257]

Answer:

142° is the measure of angle 2.

Step-by-step explanation:

When two lines intersect, they make four angles. The angles facing each other are equal.

Let's say that two lines a and b intersected each other to make angles 1,2,3 and 4 respectively.

The measure of angle 3 = 38 degrees.

We know that the angle 1 is against angle 3 and is equal to 38.

Also Angle 2 and Angle 4 are also against each other and are equal let's say equal to x degrees.

Now, the sum of all four angles = 360 degrees

∠1 + ∠2+ ∠3 + ∠4 = 360°

38° + x + 38° + x = 360°

2x = 360° - 76°

2x = 284°

x = 142°

Hence, ∠2 = 142°

3 0

2 years ago

Read 2 more answers

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

Alexus [3.1K]

Answer:

Step-by-step explanation:

Hello!

So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:

X: "Lifetime of one shoe pair of the new model"

Applying CLT:

X[bar]≈N(μ;σ²/n)

Known values:

n= 30 shoe pairs

x[bar]: 17 months

S= 5.5 months

Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:

H₀:μ=15

H₁:μ≠15

The significance level for the test is given: α: 0.05

Your critical region will be two-tailed:

$Z_{\alpha /2} = Z_{0.025}= -1.96$

$Z_{1-\alpha /2} = Z_{0.975}= 1.96$

So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96

Now you calculate your observed Z-value

Z=<u>x[bar]-μ</u> ⇒ Z=<u> 17-15 </u> = 1.99

σ/√n 5.5/√30

Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.

I hope you have a SUPER day!

5 0

2 years ago

I need help plz !!!!!!!!!

katen-ka-za [31]

Answer:

it x=-2(y-7)

Step-by-step explanation:

4 0

2 years ago