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3 years ago

The following information is obtained from two independent samples selected from two normally distributed populations.

Mathematics

1 answer:

AysviL [449]3 years ago

3 0

A. The point estimate of μ1 − μ2 is calculated using the value of x1 - x2, therefore:

μ1 − μ2 = x1 – x2 = 7.82 – 5.99

μ1 − μ2 = 1.83

B. The formula for confidence interval is given as:

Confidence interval = (x1 –x2) ± z σ

where z is a value taken from the standard distribution tables at 99% confidence interval, z = 2.58

and σ is calculated using the formula:

σ = sqrt [(σ1^2 / n1) + (σ2^2 / n2)]

σ = sqrt [(2.35^2 / 18) + (3.17^2 / 15)]

σ = 0.988297

Going back to the confidence interval:

Confidence interval = 1.83 ± (2.58) (0.988297)

Confidence interval = 1.83 ± 2.55

Confidence interval = -0.72, 4.38

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Mark save $258 more than Neil. In fact Mark saved $7 for every $4 Neil saved. How much money did Mark say?

olasank [31]

Let

x---------> amount of money saved by Mark

x---------> amount of money saved by Neil

we know that

x=y+258-------> equation 1

x/y=(7/4)-------> equation 2

substitute equation 1 in equation 2

(y+258) /y=7/4--------> 4*(y+258)=7*y------> 4y+1032=7y

7y-4y=1032--------> 3y=1032------> y=$344

x=344+258------>x=$602

the answer is

$602

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3 years ago

Use the net below.<br><br> 288cm<br> 312cm<br> 336cm<br> 368cm

vichka [17]

Add all shapes area together to know the figures complete area
triangles area 1 & 2 : 6×8 /2 -> 48/2 = 24
rectangle 1 : 6×12 -> 72
rectangle 2 : 8×12 -> 96
rectangle 3 : 10×12 -> 120
24+72+96+120
96+96+120
192+120
312cm

8 0

3 years ago

Finding area ? <br><br>How did they get a=90 in sq

Burka [1]

Step-by-step explanation:

The total area in the figure can be divided into two areas.

The $area_{rectangle}$ is the area of the $8\times 10$ rectangle.

The $area_{triangle}$ is the area of the adjacent triangle to the rectangle.

$area_{rectangle}=length\times breath=10\times 8=80$

$area_{triangle}=\frac{1}{2}\times base \times height=\frac{1}{2}\times 4\times 5=10$

Total area= $area_{rectangle}+area_{triangle}=$ 90

6 0

3 years ago

One week, Gabriel bought 2 bags of beans and 3 bags of rice. The next week, he bought 4 bags of beans and 1 bag of rice. Let b r

Leni [432]

Answer:

Step-by-step explanation:

6b+4r

8 0

3 years ago

Read 2 more answers

two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no tr

Verdich [7]

Answer:

A. single triangle. C = 8.74°, A = 1.26°, a = 1.01

Step-by-step explanation:

When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.

<h3>Law of Sines</h3>

The law of sines tells us the sides and angles have the relation ...

sin(A)/a = sin(B)/b = sin(C)/c

We can use this first to find angle C:

sin(C) = c/b·sin(B)

C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°

∠C ≈ 8.74°

<h3>Remaining measures</h3>

Now that we know two angles, we can find the third:

A = 180° -B -C = 180° -170° -8.74° = 1.26°

∠A = 1.26°

Using the law of sines again, we can find the measure of side 'a'.

a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346

The measure of segment 'a' is about 1.01 units.

<em>Additional comment</em>

If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.

8 0

2 years ago