Which expression is equal to “7 times the sum of a number and 4"?

Answers

Answer 1

Answer:

Answer: 7 (x+4)

Step-by-step explanation: Since the expression asks for 7 times the sum of a number and 4, you would put x + 4 in parentheses since multiplying 7 comes afterwards.

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A city received 2 inches of rain each day for 3 days. The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. How much snow would that city have received in the 3 days?

Answers

60 inches since there is 2 inches of snow for 3 days, so that equals 6 inches for 3 days and then you just have to multiply 6 by 10 and you get 60 inches of snow, or 5 feet

I think it would be 60 inches of snow

A computer processes jobs on a first-come, first served basis in a time-sharing environment. The jobs have Poisson arrival rates average 0.6 jobs per minute. The objective in processing these jobs is that they spend no more than 5 minutes, on average, in the system. Assuming exponential service times, how fast does the computer have to process jobs (in minutes), on average, to meet this objective

Answers

Answer:

0.8 minutes

Step-by-step explanation:

From the given information:

The arrival time for the jobs to the computer obeys a Poisson distribution;

Thus, the arrival rate is:

$\lambda = 0.6 \ jobs \ per \ minute$

Assuming the average time spent on the jobs in the system is denoted by:

$W_s= 5 \ minutes$

The average time a job process in the system can be expressed as follows:

$W_s = (1)/(\mu - \lambda)$

From above formula:

$\mu =$ service rate

$\lambda =$ arrival rate

replacing the values;

$5 = (1)/(\mu - 0.6)$

$5(\mu - 0.6) = 1$

Open brackets

$5 \mu - 3 = 1$

$5 \mu = 3+ 1 \n \n \mu = (4)/(5)$

$\mu =$ 0.8 minutes

The mass of a snowflake is approximately 0.000003 kilograms. Write this number in scientific notation.

Answers

Answer:

Step-by-step explanation:

3 x 10^-6 kg

I need some help real quick

Answers

V = 3.14 x (4)^2 x 13 = 653.12

In a sample of 49 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of a skin test reaction to an allergen. The sample mean and standard deviation were 21 and 11 mm erythema, respectively. a. Use a z- or t-distribution? Why?

b. One-sided or two-sided test? Why?

c. Can it be concluded from these data that the population mean is less than 24 mm erythema?

d. What is the range on the p-value?

Answers

Answer:

Step-by-step explanation:

a) We would use a t distribution because the population standard deviation is unknown.

b) it is a one sided test because we are trying to determine if the population mean is less than 24 mm erythema. The lesser than means that it is a left tailed test.

c) To determine the p value, we would apply the formula,

t = (x - µ)/(s/√n)

Where

x = sample mean = 21

µ = population mean = 24

s = samples standard deviation = 11

n = number of samples = 49

t = (21 - 24)/(11/√49) = - 1.91

Since n = 49

Degrees of freedom, df = n - 1 = 49 - 1 = 48

We would determine the p value using the t test calculator. It becomes

p = 0.031

Assuming alpha = 0.05, then

Since alpha, 0.05 > than the p value, 0.031, then we would reject the null hypothesis. Therefore, At a 5% level of significance, it can be concluded from these data that the population mean is less than 24 mm erythema.

d) p value = 0.031

For what side length(s) is the area of an equilateral triangle equal to 30 cm?? Only enter the number, in centimeters, rounded to two decimal places. A cm ►

Answers

Answer: The sides length are 8.32 cm

Step-by-step explanation:

An equilateral triangle has all his sides of the same lenght, so we assume that the triangle has an L lenght in his sides.

The area of a triangle is $Area = (base * height)/(2)$ where the base is L, the Area is 30 and an unknown height.

To determine the height, we cut the triangle in half and take one side. By simetry, one side has a base of $(L)/(2)$ , a hypotenuse of L and a the unknown height.

Then we apply the Pythagoras theorem, this states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, or, $hypotenuse = \sqrt{c^(2) + c^(2) }$ Where one c is $(L)/(2)$ and the other is the height.

Then we find one of the c of the equation wich will be the height.

$height = \sqrt{hypotenuse^(2)-base^(2) }$

$height = \sqrt{ L^(2) -(L)/(4) ^(2)}\nheight = \sqrt{( 3L^(2))/(4) } \n\nheight = (√(3)L )/(2)$

Finally, we use the triangle area mentioned before an find the value of L.

$30 = (L*(√(3)L )/(2) )/(2) \n\nL = \sqrt{(120)/(√(3) ) } \n\nL = 8.32 cm$

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