25 divided by 405 as a decimal

A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1 F and a standard deviation of 0.56 F. Co

Ira Lisetskai [31]

Answer:

The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

Step-by-step explanation:

The first step is finding the confidence interval

The sample size is 103.

The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So

$df = 103-1 = 102$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.99}{2} = \frac{0.01}{2} = 0.005$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 102 and 0.005 in the t-distribution table, we have $T = 2.63$ .

Now, we need to find the standard deviation of the sample. That is:

$s = \frac{0.56}{\sqrt{103}} = 0.055$

Now, we multiply T and s

$M = T*s = 2.63*0.055 = 0.145$

For the lower end of the interval, we subtract the mean by M. So 98.1 - 0.145 = 97.955F.

For the upper end of the interval, we add the mean to M. So 98.1 + 0.145 = 98.245F.

The 99% confidence interval estimate of the mean body temperature of all healthy humans is (97.955F, 98.245F).

98.6F is above the upper end of the interval, which means that the sample suggests that the mean body temperature could be lower than 98.6F.

5 0

3 years ago

A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

Lisa purchased almonds for $3.00 per pound and she spent $24.90. How many pounds of almonds did she purchase? The price went up

aleksandr82 [10.1K]

Answer:

1. Lisa purchased almonds for $3.00 and spent $24.90.

The quantity of almonds bought is therefore:

= Total amount spent / Cost per pound

= 24.90 / 3

= 8.3 pounds

2. If the price goes up to $3.50 per pound and the maximum Lisa can spend is $25, the number of pounds she can get is:

= Maximum amount for almonds / Price per almonds

= 25 / 3.5

= 7.14 pounds

5 0

3 years ago

Find the mean of this data set: {– 78, -12, 3, – 44}

blagie [28]

Answer:

Answer: A. -32.75

$\dashrightarrow{ \tt{mean = \frac{ \sum f(n)}{n} }} \\$

• f(n) are the values of the set

• n is the number of items

$\dashrightarrow \: { \tt{mean = \frac{ - 78 + ( - 12) + 3 + ( - 44)}{4} }} \\ \\ \dashrightarrow \: { \tt{ \frac{ - 131}{4} }} \\ \\ \dashrightarrow \: { \boxed{ \tt{mean = - 32.75}}}$

5 0

3 years ago

Akira and a business associate agree to invest in a project estimated to cost $1.8 million (1,800,000). They decide to split the

MariettaO [177]

If it's relationship Akira : Business A. = 7:5

The part of Akira is 7k

and the part of the Business A. is 5k

Then

7k+5k=12k => 12k=1,800,000 => k= 1,800,00/12=150,000$

Akira part is 7k= 7 * 150,000 = 1,050,000$

Good luck!!!!

8 0

3 years ago